Statistics

This course examines the practical knowledge and skills of some advanced analytics and statistical modeling problems.

The course is devoted to understanding the fundamentals of descriptive and inferential statistics (concepts, rationale of analyses, and their assumptions), and to the application of techniques on data sets. It starts with a definition of basic concepts relevant to all statistical tests, eg chance and odds, randomness, data levels, and probability distributions. Systematic errors and random errors are discussed concerning their impact on the reliability and validity of data. Concepts explained include the sampling distribution, standard error, test statistics, chosen (alpha) and observed (p-value) significance level, type I and type II error, the power of a test, confidence intervals, and effect size measures. Research designs that are widely used in applied science research and relate these to different types of samples are used. The lab sessions include data sets to be checked and summarized using appropriate descriptive statistical techniques. Data transformations are applied where needed.

This course is part of the Laurea Magistrale degree program and is intended for advanced level students. Enrolment is by permission of the instructor. The course is graded P/NP only. The course covers the main skills related to data communication: design of a data communication product, from the sourcing and interpretation of data to their graphic representation; and the creation of data visualizations, charts, and dashboards using the main tools of the industry. For both of these points, there are practical exercises, to gain mastery in specific data visualization tools or to favor a creative design process. The course discusses key topics related to these two skills, such as: evaluating accessibility and inclusivity of data communication products; the elements of visual and info design; audience-driven design; perception and bias, and their influence in data communication; exercises of creativity in the representation of data; a focus on maps and geo data; and a critical evaluation of data visualizations, to improve the efficiency and clarity communication products.

This course establishes the foundation of a wide range of statistical learning methods. It aims to understand and utilize the fundamentals of various statistical learning models. 

The course covers:

• statistical learning;
• classical linear methods for regression and classification; 
• cross-validation;
• bootstrap; 
• modern linear methods;
• nonlinear methods; 
• tree-based methods;
• support vector machines;
• unsupervised learning;
• neural networks, and
• deep learning. 

These topics are the basics of statistical learning, but the core of machine learning. By the end of this course, students will have easier access to and understanding of deep learning and artificial intelligence.

The course requires the following prerequisites: 

• Python Basic – this course assumes a basic knowledge of Python
• STAT 241: Matrix Theory or Linear Algebra - provides a computational foundation for understanding statistical models.
• STAT 232: Mathematical Statistics- knowledge of probability theory and asymptotic evaluations. 

Stochastic processes find applications in a wide variety of fields and offer a refined and powerful framework to examine and analyze time series. This course presents the basics for the treatment of stochastic signals and time series. Topics covered include models for stochastic dependence; concepts of description of stationary stochastic processes in the time domain including expectation, covariance, and cross-covariance functions; concepts of description of stationary stochastic processes in the frequency domain including effect spectrum and cross-spectrum; Gaussian process, Wiener process, white noise, and Gaussian fields in time and space; Stochastic processes in linear filters including relationships between in- and out-signals, autoregression and moving average (AR, MA, ARMA), and derivation and integration of stochastic processes; the basics in statistical signal processing, estimation of expectations, covariance function, and spectrum; and application of linear filters: frequency analysis and optimal filters.

Time series analysis concerns the mathematical modeling of time-varying phenomena, e.g., ocean waves, water levels in lakes and rivers, demand for electrical power, radar signals, muscular reactions, ECG signals, or option prices at the stock market. The structure of the model is chosen both concerning the physical knowledge of the process, as well as using observed data. Central problems are the properties of different models and their prediction ability, estimation of the model parameters, and the model's ability to accurately describe the data. Consideration must be given to both the need for fast calculations and the presence of measurement errors. The course gives a comprehensive presentation of stochastic models and methods in time series analysis. Time series problems appear in many subjects and knowledge from the course is used in, i.e., automatic control, signal processing, and econometrics.

This course offers a study of the basic concepts of statistical multivariate analysis and its applications in the social sciences. Topics include: linear regression; binomial logistic regression; principal component analysis; cluster analysis.

This course provides an introduction to the Bayesian approach to statistics.

This course is part of the Laurea Magistrale degree program and is intended for advanced level students. Enrolment is by permission of the instructor. The course discusses the fundamental principles of the relational data model and of the relational database management systems. In particular, the course examines the structure of a relational database, the integrity constraints on data, and the SQL query language. Course contents include: data modelling, database management, language to query databases, and data analysis.

The growth in computational power and availability of all sorts of data has led society to become bombarded with a variety of statistics. How much of this information is trustworthy, how much is noise - and how might it affect one’s decision-making? 
 
This course looks at the mathematical foundations of probability and randomness, and how they inform our understanding of how real-world data may be generated. Next, the course discusses what statistics are; how they are generated; when they are meaningful and when they are not. In parallel with theoretical study, the class will utilize statistical software to get a practical understanding of data processing and statistical analysis.