Statistics

This course examines modern predictive modelling techniques, with application to realistically large data sets. Case studies will be drawn from business, industrial, and government applications.

The course covers several current and advanced topics in optimization, with an emphasis on efficient algorithms for solving large scale data-driven inference problems. Topics include first and second order methods, stochastic gradient type approaches and duality principles. Many relevant examples in statistical learning and machine learning are covered in detail. The algorithms uses the Python programming language. The course requires students to take prerequisites.

This course introduces students to several computer intensive statistical methods and the topics include: empirical distribution and plug-in principle, general algorithm of bootstrap method, bootstrap estimates of standard deviation and bias, jack-knife method, bootstrap confidence intervals, the empirical likelihood for the mean and parameters defined by simple estimating function, Wilks theorem, and EL confidence intervals, missing data, EM algorithm, and Markov Chain Monte Carlo methods. This course has a prerequisite of Mathematical Statistics. 

The course is a rigorous introduction to probability. Students gain a solid grounding on the its foundations, learn how to deal with randomness with the correct mathematical tools and how to solve problems. Course topics include probability; definition and properties; conditional probability and independence; random variables and random vectors; joint and conditional distributions; expectation and moments; integral tranforms; convergence in distribution and the Central Limit Theorum; and modes of convergence and the laws of large numbers. Prerequisites: Set theory, sequences and series, continuous and differentiable functions, and integrals.

The course gives an introduction to probability theory in a measure-theoretic setting. Among the topics discussed are: Probability measures, σ-algebras, conditional expectations, convergence of random variables, the law of large numbers, characteristic functions, the central limit theorem, filtrations, and martingales in discrete time. Recommended prerequisites include calculus, linear algebra, and probability and statistical modeling. 

This course focuses on the theory of linear models. Topics include: linear regression model, general linear model, prediction problems, sensitivity analysis, analysis of incomplete data, robust regression, multiple comparisons, and an introduction to generalized linear models. This course has a prerequisite of Regression Analysis.

This course introduces the theoretical underpinnings of statistical methodology and concentrates on inferential procedures within the framework of parametric models. Topic include: random sample and statistics, method of moments, maximum likelihood estimate, Fisher information, sufficiency and completeness, consistency and unbiasedness, sampling distributions, x2-, t- and F distributions, confidence intervals, exact and asymptotic pivotal method, concepts of hypothesis testing, likelihood ratio test, and Neyman-Pearson lemma. The course has a prerequisite of Probability and Statistics.

This course offers an introduction to the tools for the estimation, detection, and prediction of discrete-time random signals. It is divided into three units: stochastic processes; estimation theory; detection theory.

The course enables students to understand and use multilevel models mainly in the context of social science, but examples are also given from medicine and some aspects of biological science. The focus is on multilevel models for quantitative, binary, and multinomial outcomes, with further sessions on models for ordinal and count outcomes. The importance of multilevel modelling for longitudinal data is explained. Analysis is conducted using the Noteable service and the R Stan statistical modelling package, which is free to all users.

This course examines components, decompositions, smoothing and filtering, modelling and forecasting.