Introductory description

This module will provide students with the tools for advanced statistical modelling and associated estimation procedures based on computer-intensive methods known as Monte Carlo techniques.

Pre-requisites

• Statistics UG Students:

  • ST230 Mathematical Statistics.

• Non-Statistics UG Students:

  • ST232/ST233 Introduction to Mathematical Statistics or ST352 Introduction to Mathematical Statistics (for Finalists).

• MSc in Statistics Students:

  • ST961 Statistical Methods and Practice.

Module web page

Module aims

Outline syllabus

This is an indicative module outline only to give an indication of the sort of topics that may be covered. Actual sessions held may differ.

Introduction and Examples: The need for Monte Carlo Techniques; history; example applications.
Basic Simulation Principles: Rejection method; variance reduction; importance sampling.
Markov chain theory: convergence of Markov chains; detailed balance; limit theorems.
Basic MCMC algorithms: Metropolis-Hastings algorithm; Gibbs sampling.
Implementational issues: Burn In; Convergence diagnostics, Monte Carlo error.
More advanced algorithms: Auxiliary variable methods; simulated and parallel tempering; simulated annealing; reversible jump MCMC; Metropolis-adjusted Langevin algorithms.

Learning outcomes

By the end of the module, students should be able to:

• demonstrate knowledge of a collection of simulation methods including Markov chain Monte Carlo (MCMC) and understanding of Monte Carlo procedures.
• develop and implement an MCMC algorithm for a given probability distribution
• evaluate a stochastic simulation algorithm with respect to both its efficiency and the validity of the inference results produced by it.
• use Monte Carlo methods for scientific applications.

Indicative reading list

Specific reading list for the module

Subject specific skills

• Demonstrate facility with rigorous Monte Carlo methods.

• Evaluate, select and apply appropriate Monte Carlo techniques.

• Demonstrate knowledge of and facility with formal Monte Carlo concepts, both explicitly and by applying them to the solution of problems.

• Create structured and coherent arguments communicating them in written form. 

• Construct logical mathematical arguments with clear identification of assumptions and conclusions.

• Reason critically, carefully, and logically and derive (prove) mathematical results.

Transferable skills

• Problem solving: Use rational and logical reasoning to deduce appropriate and well-reasoned conclusions. Retain an open mind, optimistic of finding solutions, thinking laterally and creatively to look beyond the obvious. Know how to learn from failure.

• Self awareness: Reflect on learning, seeking feedback on and evaluating personal practices, strengths and opportunities for personal growth.

• Communication: Present arguments, knowledge and ideas, in a range of formats.

• Professionalism: Prepared to operate autonomously. Aware of how to be efficient and resilient. Manage priorities and time. Self-motivated, setting and achieving goals, prioritising tasks.