MATH3421: Bayesian Computation and Modelling III

• Data Science and Statistical Computation (MATH2687) and Statistical Inference (MATH2711)

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• To provide advanced methodological and practical knowledge in the field of Bayesian statistics, specifically Bayesian approaches to statistical modelling, and to the computational techniques needed to extract information from those models.

• Computation: o Importance sampling. o Markov chains and Markov chain Monte-Carlo methods. o Gibbs and Metropolis-Hastings samplers. o Analysis of MCMC output. o Variants of Metropolis-Hastings. o Sequential Monte-Carlo. o Other topics: simulated annealing, Laplace approximation, variational methods.
• Modelling: o Directed graphical models, Bayesian networks, exchangeability. o Hierarchical models: multilevel, linear, multinomial/Dirichlet. o Undirected graphical models, HMMs, MRFs. o Model selection, averaging. o Probabilistic programming.

Subject-specific Knowledge:

• By the end of the module students will:
• be able to formulate a given problem in Bayesian terms, and bring it to a point at which modelling becomes possible;
• know a number of methods for building statistical models, and be able to choose, combine, and apply them to any given problem;
• know a number of methods for assessing the suitability of a given model, and for comparing it with competing models;
• be able to explain, justify, and compare the theoretical and practical properties of specific Bayesian computational methods, in particular Markov chain Monte Carlo;
• be able to implement these models and methods in an appropriate programming language, assess their correctness and efficacy, interpret their output, and draw practical conclusions from them.
• have acquired a coherent body of knowledge on Bayesian computation and modelling, based on which modern developments in the field can be followed and understood.

Subject-specific Skills:

• Students will have advanced mathematical skills in the following areas: Bayesian inference techniques for complex models, computational techniques for Bayesian inference.

Key Skills:

• Students will have advanced skills in the following areas: problem solving, synthesis of data, critical and analytical thinking, computer skills.

• Lectures demonstrate what is required to be learned and the application of the theory to practical examples.
• Problem classes show how to solve example problems in an ideal way, revealing also the thought processes behind such solutions.
• Workshops consolidate the studied material, explore theoretical ideas in practice, enhance practical understanding, and develop practical data analysis skills.
• Assignments for self-study develop problem-solving skills and enable students to test and develop their knowledge and understanding.
• Formative assessments provide feedback to guide students in the correct development of their knowledge and skills in preparation for the summative assessment.
• Computer-based examinations assess the ability to use statistical software and basic programming to solve predictable and unpredictable problems.
• The end-of-year examination assesses the knowledge acquired and the ability to solve predictable and unpredictable problems.

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