Statistical Methods and Applications

Educational objectives

General goals
Knowledge at an intermediate and advanced level of the main issues in Bayesian statistics.
Ability to apply Bayesian statistical techniques to applicative context.

Knowledge and understanding
Knowledge and understanding of the Bayesian approach to statistical inference, of its models and of its methodologies

Applying knowledge and understanding
Ability to apply Bayesian statistical methods for inferential problems in real-data problems

Making judgements
Ability of choosing appropriate Bayesian methods and models in different inferential problems

Communication skills
Ability of communicating results of the analyses in written and oral form

Learning skills
Students acquire skills useful to approach more advanced topics in Bayesian inference, Advanced data analysis, Statistical computing and Mathematical statistics

Educational objectives

Educational objectives
The educational goal of the course is students' learning of the fundamentals of probability calculus and statistical inference.

Knowledge and understanding
At the end of the course, students know and understand how to formalize the uncertainty and how to make inference about unknown parameters.

Ability to apply knowledge and understanding
Students learn how to formalize a problem in the field of probability calculus or statistical inference.

Judgment independence
The discussion of the various methods, even with team works, provides students with the skills necessary to analyze real situations critically and independently.

Communicative skills
Students acquire the basic elements for reasoning in quantitative terms about uncertainty and inference problems.

Learning skills
Students who pass the exam are able to apply the methods learned in different application contexts.

Educational objectives

Learning goals
Knowing how to reorganize multidimensional data with a complex structure for their statistical analysis. Starting from the multivariate statistical methodologies, knowing how to realize complex strategies of analysis that have an easy interpretation. To be able to make decisions based on empirical evidence giving appropriate answers to corporate information requests. Knowing how to extract relevant information from large data (big data).

Knowledge and understanding
Knowledge of advanced multivariate statistical methodologies and advanced formal data analysis strategies with a model-based statistical approach.

Applying knowledge and understanding
Understanding the most appropriate complex techniques to be able to make decisions based on empirical evidence, respond to corporate information requests and be able to extract relevant information from the observed data.

Making judgements
Students develop critical skills through the application of complex multivariate statistical methodologies. They learn to critically interpret the results obtained by applying the procedures to real data sets.

Communication skills
Students, through the study and performance of practical exercises, acquire the technical-scientific language of the discipline, which must be used in the world of work. Communication skills are also developed through group activities.

Learning skills
Students who pass the exam have learned a method of analysis that allows them to face, the world of work having acquired advanced statistical analysis tools for complex and large data.

Educational objectives

The overall goal of these activities is to enable students to blend their academic knowledge with professional skills. By tackling practical, real-world problems, students develop judgment and communication skills.
Students can agree on internship-type activities with the study course coordinator or his delegate for a total of no less than 72 hours. Hackathons or similar types of challenges that require statistical expertise may also be offered. Occasionally, students can otherwise agree on some activities with the study program coordinator, such as in-depth studies on specific topics, sometimes linked to in-depth studies or extensions of teachings within the study program. Sometimes the study course coordinator proposes specifically organized thematic teaching modules.

Educational objectives

The overall goal of these activities is to enable students to blend their academic knowledge with professional skills. Students can agree on internship-type activities with the study course coordinator or his delegate for a total of no less than 144 hours.
Sometimes the study course coordinator proposes specifically organized thematic teaching modules.
By tackling practical, real-world problems, students develop judgment and communication skills.

Educational objectives

General Objectives.
The objective of this course is to present the basics necessary for the use of a general-purpose imperative programming language. In particular, the use of the Python 3 programming language will be demonstrated.

Specific objectives
(a) Knowledge and understanding skills.
Students will know the basic constructs of the Python 3 language, will be able to understand a simple program written in Python 3 and to write programs in the same language. They will also be able to use an integrated development environment (IDE).

(b) Ability to apply knowledge and understanding.
At the end of the course, students will be able to solve simple algorithmic problems using the Python 3 programming language, correct syntactic and semantic errors using an IDE, and evaluate the correctness and complexity of the identified solutions.

(c) Autonomy of judgment.
Students will develop the ability to formalize algorithms using a programming language, choosing the constructs best suited to solve the individual problem. They will be able to evaluate the correctness, readability and generality of the solutions identified.

(d) Communication skills.
Students will acquire the ability to formally express a mental procedure for solving a problem, and to understand the crucial points of an algorithm.

(e) Learning skills
Students will be able to easily learn the use of imperative programming languages, appreciating similarities and differences from the Python 3 language.

Educational objectives

Learning goals.
General learning targets:
The course is organised as a series of classes where the students will have the possibility to solve and discuss the solutions of a series of advanced exercises on the theory of stochastic processes.

Knowledge and understanding.
At the end of the course the students will acquire the ability to solve autonomously simple and more advanced exercises on the theory of stochastic processes.

Applying knowledge and understanding.
During the course the students will exercise the ability to grasp and formalize, in the language of stochastic processes, phenomena that evolve in time and space and to solve simple applied problems in new environments and broader contexts.

Making judgements At the end of the course the students will have the tools to evaluate critically and choose between different stochastic models to model phenomena that evolve in time and space.

Communication skills.
The students will exercise the intuition and the communication skills necessary to describe phenomena in the mathematical language of stochastic processes.
In particular the student will acquire familiarity with the main ideas that are behind the stochastic model, e.g., the ideas of Markovianity, transience, recurrence, equilibrium, stationarity, long and short-time behaviour. Learning skills.
The students will acquire autonomy in studying more advanced theoretical aspects of stochastic processes and in applying the main ideas of stochastic processes to the subsequent studies in the area of statistics and finance.

Educational objectives

General goals
The course aims to introduce HPC (High Performance Computing) systems, their architecture, and their principles of operation. Additionally, the course aims to introduce parallel and distributed programming, with the goal of reducing resolution times for particularly complex problems through the
coordinated use of a large number of computing units.

Knowledge and comprehension
Students will understand the principles underlying HPC systems and how to organize a resolution strategy for an algorithm that can benefit from the
presence of multiple computing units.

Applying knowledge and comprehension
Upon completion of the course, students will be able to create simple parallel and distributed applications that leverage the increased computing capacity of an HPC system. Students will also be able to execute the developed algorithms using an existing computing infrastructure.

Judgement skills
Students will develop the ability to identify particular types of problems for which the use of a parallel or distributed approach is significantly helpful.

Communication skills
The students will acquire the technical-scientific language commonly used in this discipline, also thanks to the study and to the practice.

Learning skills
Students who pass the exam will have learned the paradigms to apply parallel and distributed computing techniques to solve complex problems, utilizing the computing capabilities of an HPC system.

Educational objectives

Learning goals.
The lab consists of the application of machine learning techniques to the analysis of images and/or textual documents.
The language used is Python 3.x with the Tensorflow package for the application of Convolutional and Recurrent Neural Networks (deep learning).

Knowledge and understanding.
Acquire the basics of machine learning techniques.
Understanding how and why to choose between alternative methods, or possibly how to combine different methods.
Ability to handle large amounts of images or text with the help of appropriate open source software.

Applying knowledge and understanding.
Students develop critical skills through the application of a wide range of statistical and machine learning models.
They also develop the critical sense through the comparison between alternative solutions to the same problem obtained using different learning logics.
They learn to critically interpret the results obtained by applying the procedures to real data sets.

Making judgements.
Students develop critical skills through the application of a wide range of machine learning and statistical models.
They also develop the critical sense through the comparison between alternative solutions to the same problem obtained using different learning logics.
They learn to critically interpret the results obtained by applying the procedures to real data sets.

Communication skills.
Students, through the study and execution of practical exercises, acquire the technical-scientific language of the discipline, which must be used appropriately in both the intermediate and final written tests and in the oral tests.
Communication skills are also developed through group activities.

Learning skills.
Students who pass the exam have learned a method of analysis that allows them to tackle the analysis of the images or text documents by machine learning techniques.

Educational objectives

Learning goals

Students will be introduced to the following topics

1. The Monetary, banking and financial statistics.
Why Bank of Italy collects statistics and what collects. Application: recent developments of the banks.
2. The financial accountsThe financial accounts structure.Household wealth after Piketty: an international comparison.The financial structure of the companies.
3. The balance of payments and international investment positionThe Italian balance of payments: the structure and recent developments.The procedure on excessive macroeconomic imbalances in Europe.Funds held abroad by the families.
4. The sample surveys of the Bank of ItalyThe survey on Household Income: recent results and a long-term look.The survey on inflation and growth expectations.

Educational objectives

Learning goals
Prepare students to proposing solutions to real statistical problems in many research areas.

Knowledge and understanding
At the end of the course the students have the ability to understand and solve real practical statistical problems and to propose adequate solutions.

Applying knowledge and understanding
Students are required to apply theoretical and computational skills to real problems and case-studies in a wide range of domains.

Making judgements
One of the main goals of practical activities is to develop the ability to understand problems and to propose and compare alternative statistical approaches to solve them.

Communication skills
Students acquire the ability of discussing problems and of presenting oral and written reports of their practical analyses.

Learning skills
The students acquire a series of skills useful for future academic and professional activities.

Educational objectives

The primary educational objective of the laboratory is students' learning and practice of the main
tools for Data Driven Decision Making, that is the use of computer tools to analyze data and
formalize optimization or decision models and produce decisions that create value.

Knowledge and ability to understand
After attending the laboratory, students will be able to use decision support methods (like,
the Analytical Hierchical Process), optimization solvers (like CPLEX or Gurobi) and computer
algorithms for modelling multicriteria decision and optimization problems.

Ability to apply knowledge and understanding
The models are formalized in the realm of problems. The most appropriate quantitative
method, experimenting with the effectiveness of the problem.

Autonomy of judgment
Students develop critical skills through the application of modeling, analysis and
optimization to a broad set of decision problems. They also develop the critical sense
through the comparison between alternative solutions to the same problem using
methods of analysis and realistic scenarios different from each other. They learn to
critically interpret the results obtained by applying the procedures to real data sets.

Communication skills
Students, through the study and the carrying out of the practical exercises, acquire the
technical-scientific language of the course, which should be used in the tests.
Communication skills are also developed through group activities.

Learning ability
Students who pass the exam have acquired the main methods of analysis and optimization
of decision problems that allow them to face decision-making and quantitative
management in competitive nowadays enterprises.

Educational objectives

Learning goals
Devising new machine learning methods and statistical models is a fun and extremely fruitful “art”. But these powerful tools are not useful unless we understand when they work, and when they fail. The main goal of statistical learning theory is thus to study, in a
statistical framework, the properties of learning algorithms mainly in the form of so-called error bounds.
This course introduces the techniques that are used to obtain such results, combining methodology with theoretical foundations and computational aspects. It treats both the basic principles to design successful learning algorithms and the “science” of analyzing an algorithm’s statistical properties and performance guarantees.
Theorems are presented together with practical aspects of methodology and intuition to help students develop tools for selecting appropriate methods and approaches to problems in their own data analyses.
Methods for a wide variety of applied problems will be explored and implemented on open-source software like R (www.r-project.org), Keras (https://keras.io/) and TensorFlow (https://www.tensorflow.org/).

Knowledge and understanding
On successful completion of this course, students will:
know the main learning methodologies and paradigms with their strengths and weakness;
be able to identify a proper learning model for a given problem;
assess the empirical and theoretical performance of different learning models;
know the main platforms, programming languages and solutions to develop effective implementations.

Applying knowledge and understanding
Besides the understanding of theoretical aspects, thanks to applied homeworks and a final project possibly linked to hackathons or other data analysis competitions, the students will constantly be challenged to use and evaluate modern learning techniques and algorithms.

Making judgements
On successful completion of this course, students will develop a positive critical attitude towards the empirical and theoretical evaluation of statistical learning paradigms and techniques.

Communication skills
In preparing the report and oral presentation for the final project, students will learn how to effectively communicate original ideas, experimental results and the principles behind advanced data analytic techniques in written and oral form. They will also understand how to offer constructive critiques on the presentations of their peers.

Learning skills
In this course the students will develop the skills necessary for a successful understanding as well as development of new learning methodologies together with their effective implementation. The goal is of course to grow a active attitude towards continued learning throughout a professional career.

Educational objectives

General objectives

The primary objective is to study algorithms and data structures that efficiently solve problems whose solution, using trivial approaches, would require very high resources. The algorithms studied will be implemented in Java language.

Specific objectives

Knowledge and ability to understand
Basic data structures and their use in solving sorting, searching, and graph problems will be shown. It will be shown how the data structures described are made available in Java language. The student will be able to determine the computational complexity of algorithms, and associate them with the appropriate complexity class.

Ability to apply knowledge and understanding
At the end of the course the students will be able to determine algorithms to efficiently solve complex problems, in particular problems on graphs, and choose the most suitable data structures to obtain an efficient implementation of the algorithm. They will also be able to use the Java classes that implement the data structures studied.

Autonomy of judgment
Students will be able to distinguish the computational complexity of problems and algorithms, and to identify the computationally more costly steps in solving a problem.

Communication skills
Students will be able to describe, in appropriate terms, the characteristics of the main data structures, and identify the primitives needed to efficiently implement an algorithm.

Learning ability
Students who pass the exam will be able to take advanced courses, of an applicative nature, that require the use of sophisticated algorithms. They will also be able to appreciate software engineering and computational complexity theory teachings.

Educational objectives

Finally, some statistical learning models, supervised and unsupervised, for the analysis of Big Data, will be presented.
Real-world problems will be addressed during the course using suitable software.

Knowledge and understanding.
The student will learn as to apply some statistical learning techniques for dimensionality reduction, based on feature extraction and feature selection.
Moreover, he will know and understand some powerful statistical learning models, supervised and unsupervised, to analyse Big Data.

Applying knowledge and understanding.
The student will be able to manage Big Data collected from various sources.
He will learn as to apply dimensionality reduction techniques, based on feature extraction and feature selection.
Moreover, he will be able to choose and apply some powerful statistical learning models to analyse Big Data.

Making judgements.
Students will develop critical skills through the application of a wide range of machine learning and statistical models.
They also will develop the critical sense through the comparison between alternative solutions to the same problem obtained using different learning logics.
They will learn to critically interpret the results obtained by applying the procedures to real data sets.

Communication skills.
Students, through the study and execution of practical exercises, acquire the technical-scientific language of the discipline, which must be used appropriately in both the intermediate and final written tests and in the oral tests.
Communication skills are also developed through group activities.

Learning skills.
Students who pass the exam will have learned an analytical approach that allows them to tackle Big Data analysis with statistical models and machine learning methods.

Educational objectives

Finally, some statistical learning models, supervised and unsupervised, for the analysis of Big Data, will be presented.
Real-world problems will be addressed during the course using suitable software.

Knowledge and understanding.
The student will learn as to apply some statistical learning techniques for dimensionality reduction, based on feature extraction and feature selection.
Moreover, he will know and understand some powerful statistical learning models, supervised and unsupervised, to analyse Big Data.

Applying knowledge and understanding.
The student will be able to manage Big Data collected from various sources.
He will learn as to apply dimensionality reduction techniques, based on feature extraction and feature selection.
Moreover, he will be able to choose and apply some powerful statistical learning models to analyse Big Data.

Making judgements.
Students will develop critical skills through the application of a wide range of machine learning and statistical models.
They also will develop the critical sense through the comparison between alternative solutions to the same problem obtained using different learning logics.
They will learn to critically interpret the results obtained by applying the procedures to real data sets.

Communication skills.
Students, through the study and execution of practical exercises, acquire the technical-scientific language of the discipline, which must be used appropriately in both the intermediate and final written tests and in the oral tests.
Communication skills are also developed through group activities.

Learning skills.
Students who pass the exam will have learned an analytical approach that allows them to tackle Big Data analysis with statistical models and machine learning methods.

Educational objectives

Finally, some statistical learning models, supervised and unsupervised, for the analysis of Big Data, will be presented.
Real-world problems will be addressed during the course using suitable software.

Knowledge and understanding.
The student will learn as to apply some statistical learning techniques for dimensionality reduction, based on feature extraction and feature selection.
Moreover, he will know and understand some powerful statistical learning models, supervised and unsupervised, to analyse Big Data.

Applying knowledge and understanding.
The student will be able to manage Big Data collected from various sources.
He will learn as to apply dimensionality reduction techniques, based on feature extraction and feature selection.
Moreover, he will be able to choose and apply some powerful statistical learning models to analyse Big Data.

Making judgements.
Students will develop critical skills through the application of a wide range of machine learning and statistical models.
They also will develop the critical sense through the comparison between alternative solutions to the same problem obtained using different learning logics.
They will learn to critically interpret the results obtained by applying the procedures to real data sets.

Communication skills.
Students, through the study and execution of practical exercises, acquire the technical-scientific language of the discipline, which must be used appropriately in both the intermediate and final written tests and in the oral tests.
Communication skills are also developed through group activities.

Learning skills.
Students who pass the exam will have learned an analytical approach that allows them to tackle Big Data analysis with statistical models and machine learning methods.

Educational objectives

General
Managers worldwide, beyond their personal experience, rely more and more on the use of
quantitative decision models which allow to take advantage of today’s data availability. Morover,
new computational tools, including algorithms, cloud computing and distributed processing, make
it possible to both develop and compute analytical models in a very short time, meeting the
requirement of practical applications and often using real time data. Data Driven Decision Making
is the new paradigm for managers to make better, evidence based, more rational, transparent and
reliable decisions.
In this context, the primary educational objective of the course is students' learning of the main
decision problems that arise in real world and the quantitative methods to model them and to
feed them with adequate data. Students must also be able to correctly use, for decision-making
and management purposes, computer tools to analyze data generated by real problems in
different contexts (e.g. service management, marketing, transportation, operations management
and production, and finance) through the analysis of several case studies.

Specific objectives

a) Knowledge and ability to understand
After attending the course the students know and classify the main decision problems arising in
real world organization and the main analytical methods (decision and optimization models and
algorithms) to be used to support a Manager during his/her decision process.

b) Ability to apply knowledge and understanding
At the end of the course the students are able to formalize real problems in terms of decision
problems and to apply the specific methods taught in the course to solve them. They are also able
to classify the type of problem to it the most appropriate quantitative method, experimenting the
effectiveness for decisional purposes also on real problems.

c) Autonomy of judgment
Students develop critical skills through the application of modeling, decision analysis and multi
objective optimization methodologies to a broad set of practical problems. They also develop the
critical sense through the comparison between alternative solutions to the same problem
obtained using methods of analysis and realistic scenarios different from each other. They learn to
critically interpret the results obtained by applying the procedures to real data sets.

d) Communication skills
Students, through the study and the carrying out of practical exercises, acquire the technical-
scientific language of the course, which must be properly used both in the intermediate and final
written tests and in the oral tests. Communication skills are also developed through group
activities.

e) Learning ability
Students who pass the exam have learned methods of decision analysis and multiobjective
optimization that allow them to face, decision-making problems and optimization on complex
organizations.

Educational objectives

Learning goals
The main goal of the course is to learn about common general computational tools and methodologies to perform reliable statistical analyses. Students will be able
- to understand the theoretical foundations of the most important methods;
- to appropriately implement and apply computational statistical procedures;
- to interpret the results deriving from their applications to real data.

Knowledge and understanding
After attending the course, students will know and understand the most important computational techniques in statistical analysis. In addition, students will be able to appropriately implement the learned tools with the statistical software R and to develop original ideas often in a research context.

Applying knowledge and understanding
At the end of the course, students will be able to formalize statistical problems from a computational point of view, to apply the learned methods to solve them, also in contexts not covered in the lessons, and to interpret the results deriving from their applications to real data.

Making judgements
Students will develop critical skills through the application of computational methodologies to a wide range of statistical problems and through the comparison of alternative solutions to the same problem by using different tools. Furthermore, they will learn to interpret critically the results obtained by applying procedures to real datasets.

Communication skills
By studying and carrying out practical exercises, students will acquire the technical-scientific language of the discipline, which must be suitably used in the final written test.
Communication skills will be also developed through group activities.

Learning skills
Students who pass the exam have learned computational techniques useful in the statistical analysis and to work self-sufficiently to face with the complexity of the statistical problems.

Educational objectives

Learning goals
The main goal is acquiring advanced modelling techniques for mutivariate economic data. Students are expected to understand the theoretical foundations of the methods studied and to apply them to real datasets.

Knowledge and understanding
The focus of the course will on the Vector Autoregressive (VAR) model in stationary and non stationary settings, using both asymptotic and simulation (bootstrap) inference

Applying knowledge and understanding
After the course students will be able to specify a VAR model, evaluate if is adequate to the dataset of interest , use for estimating causal relationship and formatulate forecasts

Making judgements
Learning how to judging the adequacy of the models and assessing the uncertainty of the estimated relationships and forecasts will be an essential part of the course

Communication skills
Learning to communicate the results of the estimation process both in oral and written form will be an essential part of the course

Learning skills
The models object of the course are essential parts of the most advanced and complex models used in quantitative economic analysis, which the students will then be able to tackle.

Educational objectives

General Targets:
Prior educational teaching concern is the students’ understanding of the main (Economic Statistics Modeling) problems and methods for Panel Data making use of parametric estimation. Here the empirical focus is on individuals represented by Decisional Making Units (DMU). More specifically, these are banks typically involved in the European (and also international) banking system. The course will focus on managerial problems of these firms by studying equations such as cost (mostly) and profit functions which are relevant to asses on the Efficiency of banks. Furthermore, students should know both how to solve analytical problems, in order to apply the appropriate methodology, and to interpret results obtained from empirical applications to actual data.
Specific Targets:
a) Knowledge and capability in understanding.
After attending the course, students know and understand main problems of Panel Data. In particular, the course will account for the logic for building empirical models, related to the underlying economic theory (and the consequent subdivisions in endogenous and exogenous variables), with one or more equations in order to evaluate the degree of efficiency of a typical Decisional Making Unit (here the bank and possibly the insurance company). We will study the main estimation methods of Panel Data for solving efficiency problems pertaining a firm traditionally operating in the private sector.
b) Capability of applying knowledge and comprehension
At the end of the course students are able to formalize and solve problems by means of specific methods as well as treating fundamental models of Panel Data to answer questions on the Efficiency and Productivity Analysis for the banking system. Finally, students will be able to apply the methods studied to real data and interpret results correctly also from a theoretical point of view.
c) Autonomy in assessment.
Students develop analytical skills and capacity of facing different alternative approaches for solving actual empirical problems.
d) Communication ability.
Students learn technical language which is appropriate for the subject studied and that will be used at the oral and written exam, by means of practical exercises.
e) Learning capacity.
Students passing the exam are capable to extend the methodology studied also to other fields and derive conclusions.

Educational objectives

Learning goals
Knowing how to reorganize multidimensional data with a complex structure for their statistical analysis. Starting from the multivariate statistical methodologies, knowing how to realize complex strategies of analysis that have an easy interpretation. To be able to make decisions based on empirical evidence giving appropriate answers to corporate information requests. Knowing how to extract relevant information from large data (big data).

Knowledge and understanding
Knowledge of advanced multivariate statistical methodologies and advanced formal data analysis strategies with a model-based statistical approach.

Applying knowledge and understanding
Understanding the most appropriate complex techniques to be able to make decisions based on empirical evidence, respond to corporate information requests and be able to extract relevant information from the observed data.

Making judgements
Students develop critical skills through the application of complex multivariate statistical methodologies. They learn to critically interpret the results obtained by applying the procedures to real data sets.

Communication skills
Students, through the study and performance of practical exercises, acquire the technical-scientific language of the discipline, which must be used in the world of work. Communication skills are also developed through group activities.

Learning skills
Students who pass the exam have learned a method of analysis that allows them to face, the world of work having acquired advanced statistical analysis tools for complex and large data.

Educational objectives

Educational objectives
The educational goal of the course is students' learning of the fundamentals of probability calculus and statistical inference.

Knowledge and understanding
At the end of the course, students know and understand how to formalize the uncertainty and how to make inference about unknown parameters.

Ability to apply knowledge and understanding
Students learn how to formalize a problem in the field of probability calculus or statistical inference.

Judgment independence
The discussion of the various methods, even with team works, provides students with the skills necessary to analyze real situations critically and independently.

Communicative skills
Students acquire the basic elements for reasoning in quantitative terms about uncertainty and inference problems.

Learning skills
Students who pass the exam are able to apply the methods learned in different application contexts.

Educational objectives

General goals
Knowledge at an intermediate and advanced level of the main issues in Bayesian statistics.
Ability to apply Bayesian statistical techniques to applicative context.

Knowledge and understanding
Knowledge and understanding of the Bayesian approach to statistical inference, of its models and of its methodologies

Applying knowledge and understanding
Ability to apply Bayesian statistical methods for inferential problems in real-data problems

Making judgements
Ability of choosing appropriate Bayesian methods and models in different inferential problems

Communication skills
Ability of communicating results of the analyses in written and oral form

Learning skills
Students acquire skills useful to approach more advanced topics in Bayesian inference, Advanced data analysis, Statistical computing and Mathematical statistics

Educational objectives

Learning goals
The main goal of the course is to learn about common general computational tools and methodologies to perform reliable statistical analyses. Students will be able
- to understand the theoretical foundations of the most important methods;
- to appropriately implement and apply computational statistical procedures;
- to interpret the results deriving from their applications to real data.

Knowledge and understanding
After attending the course, students will know and understand the most important computational techniques in statistical analysis. In addition, students will be able to appropriately implement the learned tools with the statistical software R and to develop original ideas often in a research context.

Applying knowledge and understanding
At the end of the course, students will be able to formalize statistical problems from a computational point of view, to apply the learned methods to solve them, also in contexts not covered in the lessons, and to interpret the results deriving from their applications to real data.

Making judgements
Students will develop critical skills through the application of computational methodologies to a wide range of statistical problems and through the comparison of alternative solutions to the same problem by using different tools. Furthermore, they will learn to interpret critically the results obtained by applying procedures to real datasets.

Communication skills
By studying and carrying out practical exercises, students will acquire the technical-scientific language of the discipline, which must be suitably used in the final written test. Communication skills will be also developed through group activities.

Learning skills
Students who pass the exam have learned computational techniques useful in the statistical analysis and to work self-sufficiently to face with the complexity of the statistical problems.

Educational objectives

Finally, some statistical learning models, supervised and unsupervised, for the analysis of Big Data, will be presented.
Real-world problems will be addressed during the course using suitable software.

Knowledge and understanding.
The student will learn as to apply some statistical learning techniques for dimensionality reduction, based on feature extraction and feature selection.
Moreover, he will know and understand some powerful statistical learning models, supervised and unsupervised, to analyse Big Data.

Applying knowledge and understanding.
The student will be able to manage Big Data collected from various sources.
He will learn as to apply dimensionality reduction techniques, based on feature extraction and feature selection.
Moreover, he will be able to choose and apply some powerful statistical learning models to analyse Big Data.

Making judgements.
Students will develop critical skills through the application of a wide range of machine learning and statistical models.
They also will develop the critical sense through the comparison between alternative solutions to the same problem obtained using different learning logics.
They will learn to critically interpret the results obtained by applying the procedures to real data sets.

Communication skills.
Students, through the study and execution of practical exercises, acquire the technical-scientific language of the discipline, which must be used appropriately in both the intermediate and final written tests and in the oral tests.
Communication skills are also developed through group activities.

Learning skills.
Students who pass the exam will have learned an analytical approach that allows them to tackle Big Data analysis with statistical models and machine learning methods.

Educational objectives

Learning goals
Devising new machine learning methods and statistical models is a fun and extremely fruitful “art”. But these powerful tools are not useful unless we understand when they work, and when they fail. The main goal of statistical learning theory is thus to study, in a
statistical framework, the properties of learning algorithms mainly in the form of so-called error bounds.
This course introduces the techniques that are used to obtain such results, combining methodology with theoretical foundations and computational aspects. It treats both the basic principles to design successful learning algorithms and the “science” of analyzing an algorithm’s statistical properties and performance guarantees.
Theorems are presented together with practical aspects of methodology and intuition to help students develop tools for selecting appropriate methods and approaches to problems in their own data analyses.
Methods for a wide variety of applied problems will be explored and implemented on open-source software like R (www.r-project.org), Keras (https://keras.io/) and TensorFlow (https://www.tensorflow.org/).

Knowledge and understanding
On successful completion of this course, students will:
know the main learning methodologies and paradigms with their strengths and weakness;
be able to identify a proper learning model for a given problem;
assess the empirical and theoretical performance of different learning models;
know the main platforms, programming languages and solutions to develop effective implementations.

Applying knowledge and understanding
Besides the understanding of theoretical aspects, thanks to applied homeworks and a final project possibly linked to hackathons or other data analysis competitions, the students will constantly be challenged to use and evaluate modern learning techniques and algorithms.

Making judgements
On successful completion of this course, students will develop a positive critical attitude towards the empirical and theoretical evaluation of statistical learning paradigms and techniques.

Communication skills
In preparing the report and oral presentation for the final project, students will learn how to effectively communicate original ideas, experimental results and the principles behind advanced data analytic techniques in written and oral form. They will also understand how to offer constructive critiques on the presentations of their peers.

Learning skills
In this course the students will develop the skills necessary for a successful understanding as well as development of new learning methodologies together with their effective implementation. The goal is of course to grow a active attitude towards continued learning throughout a professional career.

Educational objectives

General objectives

The primary objective is to study algorithms and data structures that efficiently solve problems whose solution, using trivial approaches, would require very high resources. The algorithms studied will be implemented in Java language.

Specific objectives

Knowledge and ability to understand
Basic data structures and their use in solving sorting, searching, and graph problems will be shown. It will be shown how the data structures described are made available in Java language. The student will be able to determine the computational complexity of algorithms, and associate them with the appropriate complexity class.

Ability to apply knowledge and understanding
At the end of the course the students will be able to determine algorithms to efficiently solve complex problems, in particular problems on graphs, and choose the most suitable data structures to obtain an efficient implementation of the algorithm. They will also be able to use the Java classes that implement the data structures studied.

Autonomy of judgment
Students will be able to distinguish the computational complexity of problems and algorithms, and to identify the computationally more costly steps in solving a problem.

Communication skills
Students will be able to describe, in appropriate terms, the characteristics of the main data structures, and identify the primitives needed to efficiently implement an algorithm.

Learning ability
Students who pass the exam will be able to take advanced courses, of an applicative nature, that require the use of sophisticated algorithms. They will also be able to appreciate software engineering and computational complexity theory teachings.

Educational objectives

Learning goals
Aim of the course is to explore the role of financial systems in the economic development process. Lectures will deal with topics related to the deepening, outreach, efficiency and stability of financial systems. The focus will be on applied and policy-oriented research, which can serve as basis for public policy discussions on the financial system issues, especially in developing and emerging markets.

Knowledge and understanding
Knowledge of the basic concepts and of the main theories elaborated in the field. Historical perspective and awareness of the existence of different interpretative positions.

Applying knowledge and understanding
At the end of the course students are able to formalize problems and to apply the specific methods of the discipline to solve them. They are also able to link methods to short-term data.

Making judgements
Students develop critical skills through the application of the same methodology to a wide range of economic models, which are affected by different theoretical approaches.

Communication skills
Students, through the study, acquire the technical-scientific language of the discipline, which must be appropriately used both in written and oral exams.

Learning skills
Students who pass the exam have learned a method of analysis that allows them to tackle the study of more complex models in economics.

Educational objectives

Learning goals.
Aim of the course is to allow students to broaden their knowledge of economics, sociology, and other social sciences in an interdisciplinary way.

Knowledge and understanding.
Historical perspective and awareness of the existence of different interpretative positions in the context of social sciences.

Applying knowledge and understanding.
At the end of the course students will be able to deal with different models in a critical way.

Making judgements.
Students will develop critical skills through different theoretical approaches.

Communication skills.
Students, through the study, acquire the language of different disciplines, which must be appropriately used both in written and oral exams.

Learning skills.
Students who pass the exam have learned a method of analysis that allows them to tackle the study of more complex models.

Educational objectives

Learning goals.
General learning targets:
The course is organised as a series of classes where the students will have the possibility to solve and discuss the solutions of a series of advanced exercises on the theory of stochastic processes.

Knowledge and understanding.
At the end of the course the students will acquire the ability to solve autonomously simple and more advanced exercises on the theory of stochastic processes.

Applying knowledge and understanding.
During the course the students will exercise the ability to grasp and formalize, in the language of stochastic processes, phenomena that evolve in time and space and to solve simple applied problems in new environments and broader contexts.

Making judgements At the end of the course the students will have the tools to evaluate critically and choose between different stochastic models to model phenomena that evolve in time and space.

Communication skills.
The students will exercise the intuition and the communication skills necessary to describe phenomena in the mathematical language of stochastic processes.
In particular the student will acquire familiarity with the main ideas that are behind the stochastic model, e.g., the ideas of Markovianity, transience, recurrence, equilibrium, stationarity, long and short-time behaviour. Learning skills.
The students will acquire autonomy in studying more advanced theoretical aspects of stochastic processes and in applying the main ideas of stochastic processes to the subsequent studies in the area of statistics and finance.

Educational objectives

The overall goal of these activities is to enable students to blend their academic knowledge with professional skills. By tackling practical, real-world problems, students develop judgment and communication skills.
Students can agree on internship-type activities with the study course coordinator or his delegate for a total of no less than 72 hours. Hackathons or similar types of challenges that require statistical expertise may also be offered. Occasionally, students can otherwise agree on some activities with the study program coordinator, such as in-depth studies on specific topics, sometimes linked to in-depth studies or extensions of teachings within the study program. Sometimes the study course coordinator proposes specifically organized thematic teaching modules.

Educational objectives

Learning goals

Students will be introduced to the following topics

1. The Monetary, banking and financial statistics.
Why Bank of Italy collects statistics and what collects. Application: recent developments of the banks.
2. The financial accountsThe financial accounts structure.Household wealth after Piketty: an international comparison.The financial structure of the companies.
3. The balance of payments and international investment positionThe Italian balance of payments: the structure and recent developments.The procedure on excessive macroeconomic imbalances in Europe.Funds held abroad by the families.
4. The sample surveys of the Bank of ItalyThe survey on Household Income: recent results and a long-term look.The survey on inflation and growth expectations.

Educational objectives

Learning goals.
The lab consists of the application of machine learning techniques to the analysis of images and/or textual documents.
The language used is Python 3.x with the Tensorflow package for the application of Convolutional and Recurrent Neural Networks (deep learning).

Knowledge and understanding.
Acquire the basics of machine learning techniques.
Understanding how and why to choose between alternative methods, or possibly how to combine different methods.
Ability to handle large amounts of images or text with the help of appropriate open source software.

Applying knowledge and understanding.
Students develop critical skills through the application of a wide range of statistical and machine learning models.
They also develop the critical sense through the comparison between alternative solutions to the same problem obtained using different learning logics.
They learn to critically interpret the results obtained by applying the procedures to real data sets.

Making judgements.
Students develop critical skills through the application of a wide range of machine learning and statistical models.
They also develop the critical sense through the comparison between alternative solutions to the same problem obtained using different learning logics.
They learn to critically interpret the results obtained by applying the procedures to real data sets.

Communication skills.
Students, through the study and execution of practical exercises, acquire the technical-scientific language of the discipline, which must be used appropriately in both the intermediate and final written tests and in the oral tests.
Communication skills are also developed through group activities.

Learning skills.
Students who pass the exam have learned a method of analysis that allows them to tackle the analysis of the images or text documents by machine learning techniques.

Educational objectives

Learning goals
Prepare students to proposing solutions to real statistical problems in many research areas.

Knowledge and understanding
At the end of the course the students have the ability to understand and solve real practical statistical problems and to propose adequate solutions.

Applying knowledge and understanding
Students are required to apply theoretical and computational skills to real problems and case-studies in a wide range of domains.

Making judgements
One of the main goals of practical activities is to develop the ability to understand problems and to propose and compare alternative statistical approaches to solve them.

Communication skills
Students acquire the ability of discussing problems and of presenting oral and written reports of their practical analyses.

Learning skills
The students acquire a series of skills useful for future academic and professional activities.

Educational objectives

The overall goal of these activities is to enable students to blend their academic knowledge with professional skills. Students can agree on internship-type activities with the study course coordinator or his delegate for a total of no less than 144 hours.
Sometimes the study course coordinator proposes specifically organized thematic teaching modules.
By tackling practical, real-world problems, students develop judgment and communication skills.

Educational objectives

Learning goals
Aim of the course is to explore the role of financial systems in the economic development process. Lectures will deal with topics related to the deepening, outreach, efficiency and stability of financial systems. The focus will be on applied and policy-oriented research, which can serve as basis for public policy discussions on the financial system issues, especially in developing and emerging markets.

Knowledge and understanding
Knowledge of the basic concepts and of the main theories elaborated in the field. Historical perspective and awareness of the existence of different interpretative positions.

Applying knowledge and understanding
At the end of the course students are able to formalize problems and to apply the specific methods of the discipline to solve them. They are also able to link methods to short-term data.

Making judgements
Students develop critical skills through the application of the same methodology to a wide range of economic models, which are affected by different theoretical approaches.

Communication skills
Students, through the study, acquire the technical-scientific language of the discipline, which must be appropriately used both in written and oral exams.

Learning skills
Students who pass the exam have learned a method of analysis that allows them to tackle the study of more complex models in economics.

Educational objectives

Learning goals
Aim of the course is to explore the role of financial systems in the economic development process. Lectures will deal with topics related to the deepening, outreach, efficiency and stability of financial systems. The focus will be on applied and policy-oriented research, which can serve as basis for public policy discussions on the financial system issues, especially in developing and emerging markets.

Knowledge and understanding
Knowledge of the basic concepts and of the main theories elaborated in the field. Historical perspective and awareness of the existence of different interpretative positions.

Applying knowledge and understanding
At the end of the course students are able to formalize problems and to apply the specific methods of the discipline to solve them. They are also able to link methods to short-term data.

Making judgements
Students develop critical skills through the application of the same methodology to a wide range of economic models, which are affected by different theoretical approaches.

Communication skills
Students, through the study, acquire the technical-scientific language of the discipline, which must be appropriately used both in written and oral exams.

Learning skills
Students who pass the exam have learned a method of analysis that allows them to tackle the study of more complex models in economics.

Educational objectives

Mod. I

Learning goals
Aim of the course is to explore the role of financial systems in the economic development process. Lectures will deal with topics related to the deepening, outreach, efficiency and stability of financial systems. The focus will be on applied and policy-oriented research, which can serve as basis for public policy discussions on the financial system issues, especially in developing and emerging markets.

Knowledge and understanding
Knowledge of the basic concepts and of the main theories elaborated in the field. Historical perspective and awareness of the existence of different interpretative positions.

Applying knowledge and understanding
At the end of the course students are able to formalize problems and to apply the specific methods of the discipline to solve them. They are also able to link methods to short-term data.

Making judgements
Students develop critical skills through the application of the same methodology to a wide range of economic models, which are affected by different theoretical approaches.

Communication skills
Students, through the study, acquire the technical-scientific language of the discipline, which must be appropriately used both in written and oral exams.

Learning skills
Students who pass the exam have learned a method of analysis that allows them to tackle the study of more complex models in economics.

Mod.II
Versione Inglese
General goals
This module complements the course on “development finance”, for an overall training on issues pertaining to the economics and financial aspects of human development. The course is based on a general overview of development economics and on a series of case studies.

Knowledge and understanding
Knowledge of the basic concepts and of the main theories elaborated in the field. Historical perspective and awareness of the existence of different interpretative positions.

Applying knowledge and understanding
At the end of the course the students will be able to formalize development problems and to recur to theoretical and empirical methods to try to solve them.

Making judgements
The students will develop critical skills through the analysis of several case studies over a wide range of economic models, which are affected by different theoretical approaches.

Communication skills
The students will acquire the technical-scientific language of the discipline, which must be appropriately used both in written and oral exams.

Learning skills

The students who pass the exam will have learned a method of analysis that allows them to tackle the study of more complex issues in development from the perspective of an economist.

Educational objectives

Learning goals
Working knowledge of the main models of international economics and international finance.

Knowledge and understanding.
Upon successful completion of the course, students will be able to analyse actual economic problems in terms of competing theories and models.

Applying knowledge and understanding.
Upon successful completion of the course, students will be able to understand the explicit and implicit hypotheses informing the main economic policy proposals in the current debate.

Making judgements.
The course is explicitly based on the principle of methodological and theoretical pluralism.
Students will be introduced to at least two competing models for each economic problem considered, and will understand the criteria with which to personally choose their favorite interpretation.

Communication skills.
Through study and hands-on sessions, students will become proficient in the jargon and technical language of the discipline, which they must use in both written and oral examinations.

Learning skills.
Students that successfully complete the course will have learnt a method of analysis that will allow them to tackle and understand the main economic issues of today, both in subsequent economic courses and in the fruition and participation to the public debate.

Educational objectives

Learning goals
The primary learning goal of this course is that of exposing students to the body of econometric techniques that are customised to economics applications. The aim of the course is to review this body of techniques, to demonstrate their use in hands-on style, drawing on as wide a range of example as possible, and to interpret each set of results in ways that are most useful to read and represent economic phenomena.

Knowledge and understanding.
The course is supposed to broaden students' knowledge of the various econometric techniques that appear in the economics literature, their properties and the way these are applied to data in order to verify economic theory.

Applying knowledge and understanding.
Upon successful completion of the course, students will be able to carry out a wide range of tasks in empirical economics, such as recognising the most suitable approaches to analyse the data at hand in order to capture and model its regularities, and intelligibly convey its messages to both economists and broader audiences.

Making judgements.
The course develops in a way to spurs students on researching empirical evidence of competing economic theories by respecting the nature of convenient data.

Communication skills.
Through study and hands-on sessions, students will acquire the terminology characterising the discipline, which they are required to use in both written and oral dissemination.

Learning skills.
Students who complete the course successfully will be acquainted with a method of analysis enabling them to endeavour the main economic issues from an empirical point of view.

Educational objectives

General goals
Knowledge at an intermediate and advanced level of the main issues in Bayesian statistics.
Ability to apply Bayesian statistical techniques to applicative context.

Knowledge and understanding
Knowledge and understanding of the Bayesian approach to statistical inference, of its models and of its methodologies

Applying knowledge and understanding
Ability to apply Bayesian statistical methods for inferential problems in real-data problems

Making judgements
Ability of choosing appropriate Bayesian methods and models in different inferential problems

Communication skills
Ability of communicating results of the analyses in written and oral form

Learning skills
Students acquire skills useful to approach more advanced topics in Bayesian inference, Advanced data analysis, Statistical computing and Mathematical statistics

Educational objectives

General goals
Knowledge at an intermediate and advanced level of the main issues in Bayesian statistics.
Ability to apply Bayesian statistical techniques to applicative context.

Knowledge and understanding
Knowledge and understanding of the Bayesian approach to statistical inference, of its models and of its methodologies

Applying knowledge and understanding
Ability to apply Bayesian statistical methods for inferential problems in real-data problems

Making judgements
Ability of choosing appropriate Bayesian methods and models in different inferential problems

Communication skills
Ability of communicating results of the analyses in written and oral form

Learning skills
Students acquire skills useful to approach more advanced topics in Bayesian inference, Advanced data analysis, Statistical computing and Mathematical statistics

Educational objectives

General goals
Knowledge at an intermediate and advanced level of the main issues in Bayesian statistics.
Ability to apply Bayesian statistical techniques to applicative context.

Knowledge and understanding
Knowledge and understanding of the Bayesian approach to statistical inference, of its models and of its methodologies

Applying knowledge and understanding
Ability to apply Bayesian statistical methods for inferential problems in real-data problems

Making judgements
Ability of choosing appropriate Bayesian methods and models in different inferential problems

Communication skills
Ability of communicating results of the analyses in written and oral form

Learning skills
Students acquire skills useful to approach more advanced topics in Bayesian inference, Advanced data analysis, Statistical computing and Mathematical statistics

Educational objectives

The Role of International Organizations in Producing Official Statistics

Tentative syllabus

Learning goals
The main objective of this course is to introduce students to the statistical work of International Organizations and their contribution to the production of International Official Statistics. The differences between the statistical work of International Organizations and those of National Statistical Organizations, as well as the specific contribution of International Organizations to the global statistical system will be explained in detail.

Knowledge and understanding
The course is organized in two distinct parts: the first part of the course (12 lessons) will provide students with an introduction to the Global Statistical System, its key institutions and coordination mechanism, and the statistical work of International Organizations; the second part of the course (12 lessons) will familiarize students with the main statistical techniques used in international organizations for the production of official statistics, through hands-on practical training.
In particular, the first part of the course will describe:
1) How the international statistical system is organized: what are the main actors/Institutions involved, what are the key governance bodies, what are the key international statistical frameworks (SNA, BoP, IMTS, SEEA) and standards (including standards on international classifications; code-lists, flag systems) that guide the statistical work at national, regional and global levels; how international statistical standards are developed and implemented. Special focus on the System of National Accounts.
2) The statistical work of International Statistical Organizations: what are the key data sources and how the data flows from national to international organizations is structured; the main quality frameworks used at international level and how the quality of input data is assessed; the techniques used for data validation, editing and imputation; data discrepancies between national and international databases: how they can be explained and addressed; the data dissemination practices of international organizations, including the dissemination of microdata and the challenges it poses in terms of protection of data confidentiality.
3) The demand for new statistics resulting from the 2030 Agenda for Sustainable Development. The evolution of the concept of sustainable development and the ambition of the 2030 Agenda; The Global SDG Indicator Framework and its governance mechanisms; the role of the international Organizations as Custodian Agencies, the data flows between countries and International Organizations
 
The second part of the course will focus on the following six statistical techniques:
1. Theory and practice of index numbers
2. Composite indices for summarizing multidimensional phenomena
3. Time series and seasonal adjustment
4. Measuring latent variables
5. Measuring SDG progress
6. Using remote sensing data for estimating SDG indicators

Applying knowledge and understanding
At the end of the course, students will have the necessary instruments be start working in an international organization, having acquired an in-depth knowledge of the institutional, methodological, and technical aspect of its statistical work. Moreover, students will become familiar with the main statistics published in international databases; the compilation methodology and time series of selected SDG indicators; the main techniques used for the compilation of index numbers, latent variables, composite indices, trend indices and seasonally adjusted data.

Making judgements
At the end of the course, students will be able to apply their skills in analyzing and interpreting official statistics published by international organizations.

Communication skills
At the end of the course, students will acquire the ability of discussing statistical problems in an international environment and presenting oral and written reports of their practical analyses.

Learning skills
At the end of the course, students will be able to further improve their skills and knowledge of international official statistics by self-study and consultation of international organization databases, which will be helpful for future academic and professional activities.
 
The Role of international Organizations in Producing Official Statistics
Outline of the course

Theory and Practice of the International Statistical System (12 lessons)
1st lesson
1. Introduction: what is official statistics?
a. Official statistics at national level: the Statistics Law
b. The National Statistical Office and its coordinating role of the National Statistical System
c. Other data producers at national level
d. International organizations as producers of official statistics

2. The International Statistical System: an overview
e. The UN Statistical System
f. Non-UN Statistical Organizations
g. Statistical and Policy Organizations (independence of statistics from political influence)
h. Coordination across international/regional organizations: allocation of responsibilities

3. Data Governance for the global statistical system
a. The UN Statistical Commission and its subsidiary bodies
b. The Regional Statistical Commissions
c. Statistics governance of UN Organizations
d. The Committee of the Chief Statisticians of the UN System
e. The Committee for the Coordination of the Statistical System (CCSA)
2nd lesson
4. International Statistical Standards: Main International Classifications, Code lists and Flags
a. International Family of Classifications
b. Main economic classifications: ISIC; CPC; HS; COICOP; COFOG.
c. Classifications by statistical domain: e.g., Land Cover & Land Use Classification.
d. Country/Area Codes for Statistical Use; Regional groupings.
e. SDMX Observation status codes and flags
3rd lesson
5. International Statistical Frameworks
a. Main International Statistical Frameworks
System of National Accounts
International Merchandise Trade Statistics
Balance of Payments
System of Environmental Economic Accounting
b. How International Statistical Frameworks have been developed and how they continue to evolve.
 
4th lesson
6. Introduction to the System of National Accounts
a. Overview of national accounts
b. Economic actors and transactions
c. GDP: Production approach
d. GDP: Expenditure approach
e. GDP: Income approach
f. National accounts criticism and challenges
5th lesson
7. Data sources of International Organizations
a. National Statistics System (NSO, line ministries) and other national data providers (NGOs, Research Institutions, private sector, citizens, etc.)
i. Questionnaire design for secondary data collections from National Institutions
b. Direct data collection
ii. Internationally led surveys (LSMS-WB; MICS-UNICEF; DHS-USAID; LFS-ILO).
iii. Questionnaire design for primary data collections (from households; farms, businesses)
c. Geospatial data
d. Big data
6th lesson
8. Statistics Principles and Quality Frameworks
a. UN Fundamental Principles of Official Statistics
b. UN National Quality Assurance Framework
c. IMF Data Quality Assurance Frameworks
d. Principles Governing (International) Statistical Activities (CCSA)
e. Statistical Quality Assurance Framework of International Organizations (UN Statistical Quality Assurance Framework; European Statistics Code of Practice - CoP).
7th lesson
9. Quality Assessments
a. EUROSTAT Survey Manager Checklist and Quality Indicators
b. UN Self-assessment checklist
c. IMF General Data Diss. System (e-GDDS), Special Data Diss. Standard (SDDS)
d. OECD Global Assessment
e. UNECE Global Assessments and Sector Reviews
f. EUROSTAT Peer Review
8th lesson
10. Data editing and Imputation of macro data
a. Data availability at international level: the Statistical Capacity Index
b. Methods and sources for the validation of country data
c. System of editing rules
d. Editing procedures: macro-editing and selective editing
e. Overview of main imputation methods
9th lesson
11. Discrepancies between national and international data
a. Type of data discrepancies
b. Consequences of data discrepancies
c. Possible solutions to resolve data discrepancies.

12. Data validation and country ownership
a. Validation of data disseminated and/or methods of data production.
b. Principles of data validation: IAEG-SDG guidelines of global data flows
c. Different modalities of data validation
10th lesson
13. Data dissemination and key data users
a. Defining user requirements for planning purposes: users-producers’ consultations
b. Relevant information for different type of data users:
a. Central Government/ Ministries
b. Regional/local government
c. Public and media
d. Businesses
e. Academia and Research Institutions
f. Other International Organizations
c. Dissemination of data and metadata
d. Main international statistical databases (WB WDI; OECD.Stat; FAOSTAT)
e. User consultations
f. What should IOs disseminate? Only data and statistics (historical time series) or also statistical analysis (and forecasts)?
11th lesson
14. Protection of data confidentiality and Microdata dissemination
a. Principle of data confidentiality
b. Informed consent of respondent
c. Dissemination of microdata set
d. Anonymisation & Statistical disclosure control
e. Terms of use for microdata dissemination
12th lesson
15. The 2030 Agenda for Sustainable Development and Its Monitoring Framework
a. The evolution of the concept of sustainable development
b. The key differences between the MDGs and the SDGs.
c. Separation between the Political (definition of Goals and Targets) and the Statistical process (definition of the SDG indicator framework)
d. Governance of Global SDG monitoring
e. Role of the international Organizations as Custodian Agencies
f. Data flows between countries and International Organizations
 
Statistical Techniques (12 lessons)
(1 lesson methodological introduction; 1 lesson laboratory)
13th -14th lessons
1. Theory and Practice of Index numbers
a. Methodology (Problems in constructing index numbers; Methods of constructing index numbers; Laspeyer’s, Paasche’s, Marshall-Edge worth’s and Fisher’s ideal index numbers; Test of Consistency; Chain Base Index Numbers; Shifting of Base year)
b. Calculation of the Consumer Price index

15th – 16th lessons
2. Composite indices for summarizing multidimensional phenomena
a. Methodology (Pros and cons in the use of composite indices; Pre-requisites for the compilation of composite indices; Steps in the production of composite indices; Criteria for choosing the ‘best’ method)
b. Calculation of the Human Development Index
17th-– 18th lessons
3. Time series and seasonal adjustment
a. Methodology (The components of a time series; The causes of seasonality; Why to adjust for seasonality; Decomposition models; Official software procedures for seasonal adjustment)
b. The use of RJDemetra+: Illustrative example
19th-– 20th lessons
4. Measuring latent variables
a. The Rasch model
b. The calculation of the Food insecurity Experience Scale (SDG indicator 2.1.2)
21st – 22nd lessons
5. Measuring SDG progress
a. Methodology
b. Calculating the distance from the SDG target
c. Calculating the likelihood of achieving the SDG target by 2030
23rd – 24th lessons
6. Using remote sensing data for estimating SDG indicators
a. Combining remote sensing and survey data for producing global estimates of land cover
b. The Mountain Green Cover Indicator (SDG indicator 15.4.1)

Educational objectives

Educational objectives
The educational goal of the course is students' learning of the fundamentals of probability calculus and statistical inference.

Knowledge and understanding
At the end of the course, students know and understand how to formalize the uncertainty and how to make inference about unknown parameters.

Ability to apply knowledge and understanding
Students learn how to formalize a problem in the field of probability calculus or statistical inference.

Judgment independence
The discussion of the various methods, even with team works, provides students with the skills necessary to analyze real situations critically and independently.

Communicative skills
Students acquire the basic elements for reasoning in quantitative terms about uncertainty and inference problems.

Learning skills
Students who pass the exam are able to apply the methods learned in different application contexts.

Educational objectives

Learning goals
Knowing how to reorganize multidimensional data with a complex structure for their statistical analysis. Starting from the multivariate statistical methodologies, knowing how to realize complex strategies of analysis that have an easy interpretation. To be able to make decisions based on empirical evidence giving appropriate answers to corporate information requests. Knowing how to extract relevant information from large data (big data).

Knowledge and understanding
Knowledge of advanced multivariate statistical methodologies and advanced formal data analysis strategies with a model-based statistical approach.

Applying knowledge and understanding
Understanding the most appropriate complex techniques to be able to make decisions based on empirical evidence, respond to corporate information requests and be able to extract relevant information from the observed data.

Making judgements
Students develop critical skills through the application of complex multivariate statistical methodologies. They learn to critically interpret the results obtained by applying the procedures to real data sets.

Communication skills
Students, through the study and performance of practical exercises, acquire the technical-scientific language of the discipline, which must be used in the world of work. Communication skills are also developed through group activities.

Learning skills
Students who pass the exam have learned a method of analysis that allows them to face, the world of work having acquired advanced statistical analysis tools for complex and large data.

Educational objectives

Learning goals
The main goal of the course is to learn about common general computational tools and methodologies to perform reliable statistical analyses. Students will be able
- to understand the theoretical foundations of the most important methods;
- to appropriately implement and apply computational statistical procedures;
- to interpret the results deriving from their applications to real data.

Knowledge and understanding
After attending the course, students will know and understand the most important computational techniques in statistical analysis. In addition, students will be able to appropriately implement the learned tools with the statistical software R and to develop original ideas often in a research context.

Applying knowledge and understanding
At the end of the course, students will be able to formalize statistical problems from a computational point of view, to apply the learned methods to solve them, also in contexts not covered in the lessons, and to interpret the results deriving from their applications to real data.

Making judgements
Students will develop critical skills through the application of computational methodologies to a wide range of statistical problems and through the comparison of alternative solutions to the same problem by using different tools. Furthermore, they will learn to interpret critically the results obtained by applying procedures to real datasets.

Communication skills
By studying and carrying out practical exercises, students will acquire the technical-scientific language of the discipline, which must be suitably used in the final written test. Communication skills will be also developed through group activities.

Learning skills
Students who pass the exam have learned computational techniques useful in the statistical analysis and to work self-sufficiently to face with the complexity of the statistical problems.

Educational objectives

General Targets:
Prior educational teaching concern is the students’ understanding of the main (Economic Statistics Modeling) problems and methods for Panel Data making use of parametric estimation. Here the empirical focus is on individuals represented by Decisional Making Units (DMU). More specifically, these are banks typically involved in the European (and also international) banking system. The course will focus on managerial problems of these firms by studying equations such as cost (mostly) and profit functions which are relevant to asses on the Efficiency of banks. Furthermore, students should know both how to solve analytical problems, in order to apply the appropriate methodology, and to interpret results obtained from empirical applications to actual data.
Specific Targets:
a) Knowledge and capability in understanding.
After attending the course, students know and understand main problems of Panel Data. In particular, the course will account for the logic for building empirical models, related to the underlying economic theory (and the consequent subdivisions in endogenous and exogenous variables), with one or more equations in order to evaluate the degree of efficiency of a typical Decisional Making Unit (here the bank and possibly the insurance company). We will study the main estimation methods of Panel Data for solving efficiency problems pertaining a firm traditionally operating in the private sector.
b) Capability of applying knowledge and comprehension
At the end of the course students are able to formalize and solve problems by means of specific methods as well as treating fundamental models of Panel Data to answer questions on the Efficiency and Productivity Analysis for the banking system. Finally, students will be able to apply the methods studied to real data and interpret results correctly also from a theoretical point of view.
c) Autonomy in assessment.
Students develop analytical skills and capacity of facing different alternative approaches for solving actual empirical problems.
d) Communication ability.
Students learn technical language which is appropriate for the subject studied and that will be used at the oral and written exam, by means of practical exercises.
e) Learning capacity.
Students passing the exam are capable to extend the methodology studied also to other fields and derive conclusions.

Educational objectives

General learning goals
- Define what subset of Big Data can be used in Official Statistics and what domains of Official Statistics can be enriched through the availability of new data sources
- Establish how new data sources can be used in Official Statistics, by taking into account challenges, needs and risks in this exercise
- Definition of the role of Big Data in the context of Official Statistics
- Establish how to frame the measurement of social, demographic and economic phenomena through Big Data by considering challenges, needs and risks

Knowledge and understanding
Knowledge and understanding of statistical methods to handle Big Data in official statistics

Applying knowledge and understanding
Ability to apply statistical methods for official statistics problems with emphasis on Big Data

Making judgements
Ability of choosing appropriate methods in different problems in official statistics with emphasis on Big Data

Communication skills
Ability of communicating results of the analyses in official statistics with emphasis on Big Data

Learning skills
Students acquire skills useful to approach more advanced topics in official statistics and Big Data management

Educational objectives

General objectives

The primary objective is to study algorithms and data structures that efficiently solve problems whose solution, using trivial approaches, would require very high resources. The algorithms studied will be implemented in Java language.

Specific objectives

Knowledge and ability to understand
Basic data structures and their use in solving sorting, searching, and graph problems will be shown. It will be shown how the data structures described are made available in Java language. The student will be able to determine the computational complexity of algorithms, and associate them with the appropriate complexity class.

Ability to apply knowledge and understanding
At the end of the course the students will be able to determine algorithms to efficiently solve complex problems, in particular problems on graphs, and choose the most suitable data structures to obtain an efficient implementation of the algorithm. They will also be able to use the Java classes that implement the data structures studied.

Autonomy of judgment
Students will be able to distinguish the computational complexity of problems and algorithms, and to identify the computationally more costly steps in solving a problem.

Communication skills
Students will be able to describe, in appropriate terms, the characteristics of the main data structures, and identify the primitives needed to efficiently implement an algorithm.

Learning ability
Students who pass the exam will be able to take advanced courses, of an applicative nature, that require the use of sophisticated algorithms. They will also be able to appreciate software engineering and computational complexity theory teachings.

Educational objectives

Finally, some statistical learning models, supervised and unsupervised, for the analysis of Big Data, will be presented.
Real-world problems will be addressed during the course using suitable software.

Knowledge and understanding.
The student will learn as to apply some statistical learning techniques for dimensionality reduction, based on feature extraction and feature selection.
Moreover, he will know and understand some powerful statistical learning models, supervised and unsupervised, to analyse Big Data.

Applying knowledge and understanding.
The student will be able to manage Big Data collected from various sources.
He will learn as to apply dimensionality reduction techniques, based on feature extraction and feature selection.
Moreover, he will be able to choose and apply some powerful statistical learning models to analyse Big Data.

Making judgements.
Students will develop critical skills through the application of a wide range of machine learning and statistical models.
They also will develop the critical sense through the comparison between alternative solutions to the same problem obtained using different learning logics.
They will learn to critically interpret the results obtained by applying the procedures to real data sets.

Communication skills.
Students, through the study and execution of practical exercises, acquire the technical-scientific language of the discipline, which must be used appropriately in both the intermediate and final written tests and in the oral tests.
Communication skills are also developed through group activities.

Learning skills.
Students who pass the exam will have learned an analytical approach that allows them to tackle Big Data analysis with statistical models and machine learning methods.

Educational objectives

Finally, some statistical learning models, supervised and unsupervised, for the analysis of Big Data, will be presented.
Real-world problems will be addressed during the course using suitable software.

Knowledge and understanding.
The student will learn as to apply some statistical learning techniques for dimensionality reduction, based on feature extraction and feature selection.
Moreover, he will know and understand some powerful statistical learning models, supervised and unsupervised, to analyse Big Data.

Applying knowledge and understanding.
The student will be able to manage Big Data collected from various sources.
He will learn as to apply dimensionality reduction techniques, based on feature extraction and feature selection.
Moreover, he will be able to choose and apply some powerful statistical learning models to analyse Big Data.

Making judgements.
Students will develop critical skills through the application of a wide range of machine learning and statistical models.
They also will develop the critical sense through the comparison between alternative solutions to the same problem obtained using different learning logics.
They will learn to critically interpret the results obtained by applying the procedures to real data sets.

Communication skills.
Students, through the study and execution of practical exercises, acquire the technical-scientific language of the discipline, which must be used appropriately in both the intermediate and final written tests and in the oral tests.
Communication skills are also developed through group activities.

Learning skills.
Students who pass the exam will have learned an analytical approach that allows them to tackle Big Data analysis with statistical models and machine learning methods.

Educational objectives

Finally, some statistical learning models, supervised and unsupervised, for the analysis of Big Data, will be presented.
Real-world problems will be addressed during the course using suitable software.

Knowledge and understanding.
The student will learn as to apply some statistical learning techniques for dimensionality reduction, based on feature extraction and feature selection.
Moreover, he will know and understand some powerful statistical learning models, supervised and unsupervised, to analyse Big Data.

Applying knowledge and understanding.
The student will be able to manage Big Data collected from various sources.
He will learn as to apply dimensionality reduction techniques, based on feature extraction and feature selection.
Moreover, he will be able to choose and apply some powerful statistical learning models to analyse Big Data.

Making judgements.
Students will develop critical skills through the application of a wide range of machine learning and statistical models.
They also will develop the critical sense through the comparison between alternative solutions to the same problem obtained using different learning logics.
They will learn to critically interpret the results obtained by applying the procedures to real data sets.

Communication skills.
Students, through the study and execution of practical exercises, acquire the technical-scientific language of the discipline, which must be used appropriately in both the intermediate and final written tests and in the oral tests.
Communication skills are also developed through group activities.

Learning skills.
Students who pass the exam will have learned an analytical approach that allows them to tackle Big Data analysis with statistical models and machine learning methods.

Educational objectives

General goals
Learning problems and principles of survey methodology

Knowledge and understanding
Knowledge and understanding of principles and of operational phases of statistical surveys (with specific emphasis in official statistics)

Applying knowledge and understanding
Ability to plan a statistical survey

Making judgements
Ability of understanding existing statistical surveys and of proposing improvements

Communication skills
Ability of using appropriate scientific and technical language of survey methodology; students are also trained in team-work

Learning skills
Students acquire skills useful to approach more advanced topics in official statistics

Educational objectives

Learning goals
The main goal of the course is to learn about common general computational tools and methodologies to perform reliable statistical analyses. Students will be able
- to understand the theoretical foundations of the most important methods;
- to appropriately implement and apply computational statistical procedures;
- to interpret the results deriving from their applications to real data.

Knowledge and understanding
After attending the course, students will know and understand the most important computational techniques in statistical analysis. In addition, students will be able to appropriately implement the learned tools with the statistical software R and to develop original ideas often in a research context.

Applying knowledge and understanding
At the end of the course, students will be able to formalize statistical problems from a computational point of view, to apply the learned methods to solve them, also in contexts not covered in the lessons, and to interpret the results deriving from their applications to real data.

Making judgements
Students will develop critical skills through the application of computational methodologies to a wide range of statistical problems and through the comparison of alternative solutions to the same problem by using different tools. Furthermore, they will learn to interpret critically the results obtained by applying procedures to real datasets.

Communication skills
By studying and carrying out practical exercises, students will acquire the technical-scientific language of the discipline, which must be suitably used in the final written test.
Communication skills will be also developed through group activities.

Learning skills
Students who pass the exam have learned computational techniques useful in the statistical analysis and to work self-sufficiently to face with the complexity of the statistical problems.

Educational objectives

General Aim
The primary educational goal of the course is students' learning of the main concepts and basic methods of
Demography.

Knowledge and understanding
After attending the course, the students know and understand the main international demographic sources and the
measures to describe the population processes.

Applying knowledge and understanding
At the end of the course, the students are able to apply the learned methods to the real data, and to understand the
results of these applications.

Making judgements
Students develop critical skills through the application of different indicators and measures to a wide range of case
studies from different countries, and learn to critically interpret the results.

Communication skills
Students, through the study and the carrying out of practical exercises, acquire the technical-scientific language of
the discipline, which must be opportunely used in the final oral examination. Communication skills are also
developed through group activities.

Learning skills
Students who pass the exam have learned the skills necessary to address the study of more complex methods and
models in subsequent teachings of demographic area.

Educational objectives

Learning goals
The main goal is acquiring advanced modelling techniques for mutivariate economic data. Students are expected to understand the theoretical foundations of the methods studied and to apply them to real datasets.

Knowledge and understanding
The focus of the course will on the Vector Autoregressive (VAR) model in stationary and non stationary settings, using both asymptotic and simulation (bootstrap) inference

Applying knowledge and understanding
After the course students will be able to specify a VAR model, evaluate if is adequate to the dataset of interest , use for estimating causal relationship and formatulate forecasts

Making judgements
Learning how to judging the adequacy of the models and assessing the uncertainty of the estimated relationships and forecasts will be an essential part of the course

Communication skills
Learning to communicate the results of the estimation process both in oral and written form will be an essential part of the course

Learning skills
The models object of the course are essential parts of the most advanced and complex models used in quantitative economic analysis, which the students will then be able to tackle.

Educational objectives

General Targets:
Prior educational teaching concern is the students’ understanding of the main (Economic Statistics Modeling) problems and methods for Panel Data making use of parametric estimation. Here the empirical focus is on individuals represented by Decisional Making Units (DMU). More specifically, these are banks typically involved in the European (and also international) banking system. The course will focus on managerial problems of these firms by studying equations such as cost (mostly) and profit functions which are relevant to asses on the Efficiency of banks. Furthermore, students should know both how to solve analytical problems, in order to apply the appropriate methodology, and to interpret results obtained from empirical applications to actual data.
Specific Targets:
a) Knowledge and capability in understanding.
After attending the course, students know and understand main problems of Panel Data. In particular, the course will account for the logic for building empirical models, related to the underlying economic theory (and the consequent subdivisions in endogenous and exogenous variables), with one or more equations in order to evaluate the degree of efficiency of a typical Decisional Making Unit (here the bank and possibly the insurance company). We will study the main estimation methods of Panel Data for solving efficiency problems pertaining a firm traditionally operating in the private sector.
b) Capability of applying knowledge and comprehension
At the end of the course students are able to formalize and solve problems by means of specific methods as well as treating fundamental models of Panel Data to answer questions on the Efficiency and Productivity Analysis for the banking system. Finally, students will be able to apply the methods studied to real data and interpret results correctly also from a theoretical point of view.
c) Autonomy in assessment.
Students develop analytical skills and capacity of facing different alternative approaches for solving actual empirical problems.
d) Communication ability.
Students learn technical language which is appropriate for the subject studied and that will be used at the oral and written exam, by means of practical exercises.
e) Learning capacity.
Students passing the exam are capable to extend the methodology studied also to other fields and derive conclusions.

Educational objectives

Learning goals.
General learning targets:
The course is organised as a series of classes where the students will have the possibility to solve and discuss the solutions of a series of advanced exercises on the theory of stochastic processes.

Knowledge and understanding.
At the end of the course the students will acquire the ability to solve autonomously simple and more advanced exercises on the theory of stochastic processes.

Applying knowledge and understanding.
During the course the students will exercise the ability to grasp and formalize, in the language of stochastic processes, phenomena that evolve in time and space and to solve simple applied problems in new environments and broader contexts.

Making judgements At the end of the course the students will have the tools to evaluate critically and choose between different stochastic models to model phenomena that evolve in time and space.

Communication skills.
The students will exercise the intuition and the communication skills necessary to describe phenomena in the mathematical language of stochastic processes.
In particular the student will acquire familiarity with the main ideas that are behind the stochastic model, e.g., the ideas of Markovianity, transience, recurrence, equilibrium, stationarity, long and short-time behaviour. Learning skills.
The students will acquire autonomy in studying more advanced theoretical aspects of stochastic processes and in applying the main ideas of stochastic processes to the subsequent studies in the area of statistics and finance.

Educational objectives

The overall goal of these activities is to enable students to blend their academic knowledge with professional skills. By tackling practical, real-world problems, students develop judgment and communication skills.
Students can agree on internship-type activities with the study course coordinator or his delegate for a total of no less than 72 hours. Hackathons or similar types of challenges that require statistical expertise may also be offered. Occasionally, students can otherwise agree on some activities with the study program coordinator, such as in-depth studies on specific topics, sometimes linked to in-depth studies or extensions of teachings within the study program. Sometimes the study course coordinator proposes specifically organized thematic teaching modules.

Educational objectives

Learning goals.
The lab consists of the application of machine learning techniques to the analysis of images and/or textual documents.
The language used is Python 3.x with the Tensorflow package for the application of Convolutional and Recurrent Neural Networks (deep learning).

Knowledge and understanding.
Acquire the basics of machine learning techniques.
Understanding how and why to choose between alternative methods, or possibly how to combine different methods.
Ability to handle large amounts of images or text with the help of appropriate open source software.

Applying knowledge and understanding.
Students develop critical skills through the application of a wide range of statistical and machine learning models.
They also develop the critical sense through the comparison between alternative solutions to the same problem obtained using different learning logics.
They learn to critically interpret the results obtained by applying the procedures to real data sets.

Making judgements.
Students develop critical skills through the application of a wide range of machine learning and statistical models.
They also develop the critical sense through the comparison between alternative solutions to the same problem obtained using different learning logics.
They learn to critically interpret the results obtained by applying the procedures to real data sets.

Communication skills.
Students, through the study and execution of practical exercises, acquire the technical-scientific language of the discipline, which must be used appropriately in both the intermediate and final written tests and in the oral tests.
Communication skills are also developed through group activities.

Learning skills.
Students who pass the exam have learned a method of analysis that allows them to tackle the analysis of the images or text documents by machine learning techniques.

Educational objectives

Learning goals
Prepare students to proposing solutions to real statistical problems in many research areas.

Knowledge and understanding
At the end of the course the students have the ability to understand and solve real practical statistical problems and to propose adequate solutions.

Applying knowledge and understanding
Students are required to apply theoretical and computational skills to real problems and case-studies in a wide range of domains.

Making judgements
One of the main goals of practical activities is to develop the ability to understand problems and to propose and compare alternative statistical approaches to solve them.

Communication skills
Students acquire the ability of discussing problems and of presenting oral and written reports of their practical analyses.

Learning skills
The students acquire a series of skills useful for future academic and professional activities.