Statistics

This course covers the concept of regression analysis. Students learn to perform statistical inferences in linear regressions and carry out regression analysis using data examples. The course examines the setting and suitability of regression models and model diagnosis. Simple linear regression, multilinear regression, variable selection, and nonlinear regression are included, and statistical package programs such as SAS are used. 

Topics include Simple Linear Regression, Simple Linear Regression, Multiple Linear Regression, Multiple LInear Regression, Regression Diagnostics, Regression Diagnostics, Qualitative Variables as Predictors, Transformation of Variables, Weighted Least Squares, The Problem of Correlated Errors, Analysis of Collinear Data, Variable Selection Procedures. 

This course is part of the Laurea Magistrale degree program and is intended for advanced level students. Enrollment is by permission of the instructor. The course focuses on the basic statistical techniques concerning the data analysis. In particular, the student is expected to learn: foundations of probability, descriptive and inferential statistics, and simple regression. By the end of the course, students are better prepared to interpret cultural data, understand its relevance for policy, and engage thoughtfully in data-informed policy discussions in the cultural and creative sectors. The course content is divided into the following elements: data collection, management and visualization; descriptive statistics; foundations of probability; and statistical inference.

This course develops a solid understanding of reinforcement learning, a major area within machine learning and artificial intelligence. Reinforcement learning is grounded in various probabilistic and statistical theories and has recently been widely applied to the training of large-scale machine learning models. The course covers the theoretical foundations, applications, and current research trends in this field. Topics include Finite Markov Decision Processes, Dynamic Programming, Temporal Difference Learning, Eligibility Traces, Generalization and Function Approximation, On-policy Approximation of Action Values, Off-policy Approximation of Action Values and Policy Approximation, Meta/Multi-task Learning and RL, and Foundation Model and RL. 

This course covers the essence of quantum computing and various quantum machine learning techniques. Quantum computing has the potential to outperform classical computing and to solve problems that were believed to be intractable otherwise. With rapid advances in quantum technology, current technology is expected to be disrupted in many ways. Quantum computing opens up tremendous opportunities for data science in the big data era where computational power is of critical importance.  

This course equips students with theoretical backgrounds to be able to apply the principles of quantum computing in solving various challenges of modern data science problems. Topics include Introduction to quantum data science & quantum machine learning, Machine learning basics & classical information, Quantum mechanics & quantum information, Circuit model of quantum computation & reversible computing, Black-box model of computation & related quantum algorithms, Quantum phase estimation & Quantum Fourier transform, Unstructured search & quantum amplitude estimation, Quantum linear systems solver & quantum support vector machine, Quantum kernel method, and Quantum neural network. 

Prerequisites: Linear algebra, calculus, probability theory and statistics, Quantum mechanics, Python or Matlab (or similar programming skills) 

This course focuses on practical statistics and computation in real-world scenarios. It covers how statistics are used, how to turn data into information, how to create statistical graphics, how to obtain data from surveys and designed experiments, probability theory, and random variables.

This course is part of the Laurea Magistrale degree program and is intended for advanced level students. Enrollment is by permission of the instructor. The course provides students with a fundamental understanding of the objectives, theory, and application of statistical methods for the production of health indicators. The learning process includes an updated overview of the aims and definitions adopted internationally to monitor population health and health care, particularly at EU level. The course provides detailed explanations on the statistical methods applied for the continuous improvement of health and social policies, with practical examples showing how to produce indicators from large databases using R software.

This course supports the student toward a fundamental understanding of the societal value of health information and the methods and tools used to report, evaluate, and continuously improve policies. In particular, the course presents solutions to current challenges involving the use of large scale routine databases available at the national and international level. Practical cases of data analysis are presented using relevant statistical software. Issues in the correct communication of health statistics are also discussed. At the end of the course, the student is able:

• to calculate and interpret health indicators used in regional, national and international reports (in particular, the EU European Core Health Indicators, European Sustainable Development Indicators and State of Health in the EU): from life expectancy to quality of care, access and efficiency measures.
• to apply advanced techniques for health systems performance evaluation: from risk adjustment and standardization through the use of multivariate models (generalized linear models, generalized estimating equations and multilevel models), to modern approaches using person-centered statistical models (risk prediction and stratification for population health management).
• to apply principles of study design (experimental vs observational) and analytical techniques (e.g. propensity scores, difference-in-difference) to plan and evaluate treatments and policies.

This course is part of the Laurea Magistrale degree program and is intended for advanced level students. Enrollment is by permission of the instructor. At the end of the course the student is able to choose and use recent methods for web and social mining. In particular the student is able to extract knowledge from the web and social media by applying machine learning techniques to analyze associations and carry out clickstream, sentiment, text mining, and network analysis. The student is able to: use methods for extracting knowledge from the web; use recent data mining software for solving practical problems of web mining; and has the experience to carry out independent study and research. Lectures and laboratory exercises using R software.

The course is divided into 4 parts: Aims and steps of web mining; Data extraction; Text mining; Analysis of Social Networks

The course equips practical experience and skills in analyzing data, using statistical techniques frequently used in the sciences. The skills include designing experiments, choosing appropriate statistical methods for visual display and statistical modelling of data, model checking, interpretation and reporting of statistical results, and understanding of limitations of statistical methods and data. Topics covered include Introduction to statistical notation, linear regression, design and analysis of experiments, generalized linear models. Strong emphasis on the practical application of the above methods, using open-source statistical software such as R.  Course entry requirements: A pass in STA1000F/S or STA1006S or STA1007S or STA1106H or STA1100S or STA1008F/S) and (MAM1000W or MAM1031F or MAM1033F or MAM1004F/S or MAM1005H or MAM1010F/S or MAM1020F/S or MAM1110F/H).

This course covers the fundamental algorithms for statistical computations and R packages that implement some of these algorithms or are useful for developing novel implementations. It develops the ability to implement, test, debug, benchmark, profile and optimize statistical software; select appropriate numerical algorithms for statistical computations; and evaluate implementations in terms of correctness, robustness, accuracy and memory, and speed efficiency. Topics include: maximum-likelihood and numerical optimization; the EM-algorithm; Stochastic optimization algorithms; simulation algorithms and Monte Carlo methods; nonparametric density estimation; bivariate smoothing; numerical linear algebra in statistics, sparse and structured matrices; practical implementation of statistical computations and algorithms; R/C++ and RStudio statistical software development. 

This course examines mathematical concepts for stochastic calculus. The topics include: introduction to continuous time stochastic processes; definition and properties of Brownian motion; semimartingales; Stochastic integration; Itô (change of variable) formula; theorems for applications (e.g., Girsanov’s theorem).