Module MATH31420: Bayesian Computation and Modelling

Department: Mathematical Sciences

MATH31420: Bayesian Computation and Modelling

Prerequisites

• Data Science and Statistical Computation and Statistical Inference

Corequisites

• None

Excluded Combination of Modules

• None

Aims

• 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.

Content

• 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.

Learning Outcomes

• 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.

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

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

Modes of Teaching, Learning and Assessment and how these contribute to the learning outcomes of the module

• 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.
• Computer practicals 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.

Teaching Methods and Learning Hours

Summative Assessment

Formative Assessment:

Eight written or electronic assignments to be assessed and returned. Other assignments are set for self-study and complete solutions are made available to students.

■ Attendance at all activities marked with this symbol will be monitored. Students who fail to attend these activities, or to complete the summative or formative assessment specified above, will be subject to the procedures defined in the University's General Regulation V, and may be required to leave the University