This course is now a Core Optional module and will run as ST407 which is a 4th year course in Statistics and ST911 which is a MASDOC module. Please note that the CY904 module will now be called ST407.
Aims:
A large number of scientists and engineers employ Monte Carlo techniques as an essential tool in their work. This module will address foundations and advances in Monte Carlo methodologies.

Learning Outcomes:
 Knowledge of a collection of simulation methods including Markov chain Monte Carlo (MCMC); understanding of Monte Carlo procedures, their advantages, disadvantages, strengths and pitfalls.
 Ability to develop and implement (in BUGS) an MCMC algorithm for a given probability distribution
 Ability to implement an MCMC algorithm in a programming language such as FORTRAN or C for a welldefined problem in a scientific application
 Ability to evaluate a stochastic simulation algorithm with respect to both its efficiency and the validity of the inference results produced by it.
 Ability to use Monte Carlo methods for scientific applications.

Prerequisites:
 A good working knowledge of a scientific programming language (as for example taught in PX270 C Programming).
 A basic background in Probability and Statistics (as thaught in CY900).
 A basic knowledge of the statistical programming language R (as taught in CY900).
Syllabus:
 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: MetropolisHastings 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; EM algorithm.
