STATISTICAL MODELING

Description

Objectives: The course introduces the main concepts of probability and statistics, providing the methodological foundations for data collection and analysis. Assessment: Students will be evaluated through the final written exam, covering the whole course program. The final written exam consists of theoretical questions and practical problems aimed at verifying the student’s mastering of the basic notions and their application. In general, the exam will be formed by 5-6 questions. During the semester, there will be an intermediate test covering the first part of the program, which will count for 1/3 of the final grade. NOTE: the intermediate test grade will be effective only if the final exam is taken during the summer session. Teaching Methods: Lectures with at least three intermediate tests. Prerequisites: One semester of Math prior to taking the course. Contents: Elements of probability theory and main probability models. Descriptive statistics: data sets description and summarization; correlation in bivariate data sets. Statistical inference: sampling statistics; point estimation and confidence intervals; hypothesis testing. Reference Texts: First part of the course: 1. Ross, Sheldon M. Introductory statistics. Elsevier/Academic Press. Second part of the course: 2. Ross, Sheldon M. Introduction to probability and statistics for engineers and scientists. Elsevier/Academic Press. Thesis assignment criteria: Not relevant. Extended Program And Reference Reading Material: Week 1: Book 1 Ch 1: Introduction, data collection. Statistical models and parameters. The population and the sample. Book 1 Ch 4: Basic probability, events, experiments, conditional probability, independence, uniform spaces and notions of combinatorics. Extended Program And Reference Reading Material: Week 10: Book 2 Ch 7: Confidence intervals for the difference of expectations. Asymptotic confidence intervals based on Central Limit Theorem approximation. Extended Program And Reference Reading Material: Week 11: Book 2 Ch 8: Hypothesis testing. Extended Program And Reference Reading Material: Week 12: Review. Extended Program And Reference Reading Material: Week 2: Book 1 Ch 2-3: Descriptive statistics: tables, line plots, histograms, etc. Data examples. Summary statistics, mean, median, variance, standard deviation, covariance and correlation coefficient and percentiles Extended Program And Reference Reading Material: Week 3: Book 1 Ch 4 Bayes' formula. Ch 5 Discrete random variables, Bernoulli sequences, Bernoulli and Binomial distributions. Extended Program And Reference Reading Material: Week 4: Book 1 Ch 5: Expectation and variance for discrete random variables. Transformations of discrete random variables. Linear transformations. Joint distributions, covariance, correlation and independence. Hypergeometric and Poisson random variables. Extended Program And Reference Reading Material: Week 5: Book 2 Ch 4: Continuous random variables, densities and their features. Expectations for continuous random variables. Jointly continuous random variables. Extended Program And Reference Reading Material: Week 6: Book 2 Ch 4: Independence. Book 2 Ch 5: Probability models: Binomial, Poisson, Uniform, Exponential, Normal. Properties of normal random variables. chi-square and T distributions. Extended Program And Reference Reading Material: Week 7: Book 2 Ch 6: Introduction to statistical inference. Distribution of Sample statistics. Main convergence theorems. Extended Program And Reference Reading Material: Week 8: Book 2 Ch 7: Maximum likelihood estimators, moment estimators. Estimators’ sampling properties MSE and bias). Extended Program And Reference Reading Material: Week 9: Book 2 Ch 7: Confidence intervals for the parameters of a normal population. Intended learning outcomes: Knowledge and understanding: The course develops students' ability in collecting, analyzing and critically interpreting data related to economics, finance, management as well as everyday situations. The course also contributes to students' mathematical skills. Applying knowledge and understanding: The course provides the student the knowledge of a series of tools such as probabilistic models to model phenomena whose outcomes are uncertain, estimation techniques for understanding and prediction, hypothesis testing for decision making. During the final exam, students are required to use mathematical thinking to formalize complex problems and to apply analytical tools to solve them. Making judgements: When facing complex problems, students are encouraged to apply analytical tools in an independent way and to give original interpretations to the results they obtain. This is also a requirement for the final exam. Communication skill: The course contributes to students' mathematical reasoning and ability to communicate in mathematical language. Learning skills: The knowledge in Probability and Statistics acquired during the course will allow the student to autonomously understand and interpret new more advanced techniques and adapt them to the specific reference context.