30408 - ADVANCED MATHEMATICS AND STATISTICS - MODULE 2 (ADVANCED STATISTICAL METHODS)
Course taught in English
Go to class group/s: 25
Synchronous Blended: Lezioni erogate in modalità sincrona in aula (max 1 ora per credito online sincrona)
Solid knowledge of calculus and of basic programming tools in R facilitates students’ understanding of the topics covered during the course.
Data Science has recently emerged as one of the most exciting interdisciplinary research areas both in academia and among practitioners. The unprecedented availability of data is setting a variety of theoretical and computational challenges for statistics and is, thus, fueling novel groundbreaking developments in the field. Researchers and professional data scientists who want to play a leading role in such a new scenario must definitely have a solid mastery of topics in Probability and Statistics. The main aim of the course is to introduce students to more advanced topics in Probability Theory and Statistical Inference. The first part is devoted to investigating mathematical aspects of probability, with a special emphasis on multivariate distributions and limiting theorems. In the second part, students are guided through the methodological core of point estimation (both from a frequentist and Bayesian perspective) and hypothesis testing. These theoretical aspects are complemented by an in-depth presentation of elementary simulation and computational techniques that are routinely used within most popular statistical procedures.
- Review of discrete and continuous random variables.
- Moment generating function.
- Random vectors.
- Transformations of random vectors.
- Simulation of random variables.
- Laws of large numbers and the central limit theorem.
- Parametric statistical models.
- Parameter estimation: minimum variance and unbiased estimators, maximum likelihood and Bayesian methods.
- Hypothesis testing.
- Deal with intermediate statistical and probabilistic tools that lie at the foundations of modern Data Science and Machine Learning applications.
- Develop a multivariable thinking that is essential to understand and model large and complex datasets.
- Identify drawbacks and merits of both the frequentist and the Bayesian approaches to statistical inference.
- Profitably attend advanced courses in Probability and Stochastic Processes, Statistics and Machine Learning.
- Tailor statistical models to specific experiments, with the aim of addressing estimation and hypothesis testing problems.
- Study relationships among multivariate data, with the aim of drawing predictions and impacting decision-making processes.
- Interpret the output of basic statistical procedures in view of actual applications to real data.
- Face-to-face lectures
1) The exam consists of either two partial written tests or of a general written test.
Both partial and general exams are written tests with exercises. They aim at assessing the students' ability to solve simple problems in Probability and Mathematical Statistics. They require the application of analytical tools and univariate and multivariate calculus techniques that have been taught during the course. The probabilistic component of the course will be also relevant for solving exercises related to Statistics. The first mid-term exam covers the part on Probability Theory of the program, while the second partial exam focuses on Mathematical Statistics topics. The general exam is on the whole program.
F.J. SAMANIEGO, Stochastic Modeling and Mathematical Statistics, Boca Raton, FL, CRC Press, 2014.