Statistics

Are you looking to develop the skills to solve real-world challenges in finance, risk management, and insurance? These fields often deal with unpredictable phenomena—like investment decisions, insurance claim patterns, or pricing derivatives—which require robust stochastic models and advanced machine learning techniques. To tackle these challenges effectively, it’s essential to use robust statistical techniques and calibration methodologies to ensure models are reliable. This course equips students with the tools to apply modern statistical and machine learning methods to these complex problems. Students start by exploring Monte Carlo methods, simulating stochastic processes, and applying Generative Adversarial Networks (GANs) in risk management. They then connect Generalized Linear Models to deep neural networks, discovering their practical applications in the insurance industry. The course also addresses the challenges of calibrating models to ensure their accuracy and reliability. Combining rigorous theory with hands-on coding exercises in Python, students gain experience implementing real-world case studies while strengthening their core data science skills.

This course provides an introduction to the basic mathematical aspects and associated data analysis of statistical design and survey sampling, and also to data ethics as a set of principles to guide the design of appropriate data use in academia and the public sector. 

This course examines the relationship between business and industrial applications and their associated operations research models. Software packages will be used to solve practical problems. Topics include: linear programming, transportation and assignment models, network algorithms, queues, inventory models, simulation, analytics and visualization.

This course examines stochastic modelling, with an emphasis on queues and models used in finance. Behavior of poisson processes, queues and continuous time markov chains will be investigated using theory and simulation.

This course examines an elegant unified theory that includes the estimation of model parameters, quadratic forms, hypothesis testing using analysis of variance, model selection, diagnostics on model assumptions, and prediction. Both full rank models and models that are not of full rank are considered. The theory is illustrated using common models and experimental designs.

This course covers recent statistical techniques in high dimensions and applies them to the analysis of real data. Students gain a broad understanding of various (non-convex) penalization techniques, dimensionality reduction, and more, with the goal of learning how to effectively summarize and interpret high-dimensional data and to systematically understand the challenges of analyzing data where the dimensionality of the data is comparable to or greater than the sample size.  

Topics include introduction to high-dimensional data, regression in high-dimensions, (non-convex) penalization methods in high-dimensions, regression in high-dimensional with real-data applications, matrix estimation with rank constraints, graphical models for high-dimensional data, spectral clustering in high-dimensions, principal component analysis in high-dimensions, and quantile regression in high-dimensions.