ST40715 Monte Carlo Methods
Introductory description
This module runs in Term 1 and will provide students with the tools for advanced statistical modelling and associated estimation procedures based on computerintensive methods known as Monte Carlo techniques.
Prerequisites:
Statistics Students: ST218 Mathematical Statistics A AND ST219 Mathematical Statistics B
NonStatistics Students: ST220 Introduction to Mathematical Statistics
Module aims
When modelling real world phenomena statisticians are often confronted with the following dilemma: should we choose a standard model that is easy to compute with or use a more realistic model that is not amenable to analytic computations such as determining means and pvalues. We are faced with such choice in a vast variety of application areas, some of which we will encounter in this module. These include financial models, genetics, polymer simulation, target tracking, statistical image analysis and missing data problems. With the advent of modern computer technology we are no longer restricted to standard models as we can use simulationbased inference. Essentially we replace analytic computation with sampling of probability models and statistical estimation. In this module we discuss a variety of such methods, their advantages, disadvantages, strengths and pitfalls.
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: 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; Metropolisadjusted Langevin algorithms.
Learning outcomes
By the end of the module, students should be able to:
 Knowledge of a collection of simulation methods including Markov chain Monte Carlo (MCMC); understanding of Monte Carlo procedures.
 Ability to develop and implement an MCMC algorithm for a given probability distribution
 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.
Indicative reading list
View reading list on Talis Aspire
Subject specific skills
TBC
Transferable skills
TBC
Study time
Type  Required  Optional 

Lectures  30 sessions of 1 hour (20%)  2 sessions of 1 hour 
Practical classes  10 sessions of 1 hour (7%)  
Private study  110 hours (73%)  
Total  150 hours 
Private study description
Weekly revision of lecture notes and materials, wider reading, practice exercises and preparing for the examination.
Costs
No further costs have been identified for this module.
You do not need to pass all assessment components to pass the module.
Students can register for this module without taking any assessment.
Assessment group D5
Weighting  Study time  

Assignment 2  10%  
The assignment will contain a number of questions for which solutions and / or written responses will be required. 

Assignment 1  10%  
The assignment will contain a number of questions for which solutions and / or written responses will be required. 

Inperson Examination  80%  
The examination paper will contain four questions, of which the best marks of THREE questions will be used to calculate your grade.

Assessment group R2
Weighting  Study time  

Inperson Examination  Resit  100%  
The examination paper will contain four questions, of which the best marks of THREE questions will be used to calculate your grade.

Feedback on assessment
Marked assignments will be available for viewing at the support office within 20 working days of the submission deadline. Cohort level feedback and solutions will be provided.
Solutions and cohort level feedback will be provided for the examination.
Courses
This module is Optional for:
 Year 1 of TMAAG1PE Master of Advanced Study in Mathematical Sciences
 Year 1 of TMAAG1PD Postgraduate Taught Interdisciplinary Mathematics (Diploma plus MSc)
 Year 1 of TMAAG1PC Postgraduate Taught Mathematics (Diploma plus MSc)
 Year 1 of TSTAG4P1 Postgraduate Taught Statistics

USTAG300 Undergraduate Master of Mathematics,Operational Research,Statistics and Economics
 Year 3 of G300 Mathematics, Operational Research, Statistics and Economics
 Year 4 of G300 Mathematics, Operational Research, Statistics and Economics
This module is Option list A for:
 Year 4 of UCSAG4G3 Undergraduate Discrete Mathematics

USTAG1G3 Undergraduate Mathematics and Statistics (BSc MMathStat)
 Year 3 of G1G3 Mathematics and Statistics (BSc MMathStat)
 Year 4 of G1G3 Mathematics and Statistics (BSc MMathStat)

USTAG1G4 Undergraduate Mathematics and Statistics (BSc MMathStat) (with Intercalated Year)
 Year 4 of G1G4 Mathematics and Statistics (BSc MMathStat) (with Intercalated Year)
 Year 5 of G1G4 Mathematics and Statistics (BSc MMathStat) (with Intercalated Year)
This module is Option list B for:
 Year 4 of USTAG304 Undergraduate Data Science (MSci)

UMAAG105 Undergraduate Master of Mathematics (with Intercalated Year)
 Year 4 of G105 Mathematics (MMath) with Intercalated Year
 Year 5 of G105 Mathematics (MMath) with Intercalated Year
 Year 3 of UMAAG100 Undergraduate Mathematics (BSc)

UMAAG103 Undergraduate Mathematics (MMath)
 Year 3 of G103 Mathematics (MMath)
 Year 4 of G103 Mathematics (MMath)

UMAAG106 Undergraduate Mathematics (MMath) with Study in Europe
 Year 3 of G106 Mathematics (MMath) with Study in Europe
 Year 4 of G106 Mathematics (MMath) with Study in Europe
 Year 4 of UMAAG101 Undergraduate Mathematics with Intercalated Year
This module is Option list D for:
 Year 4 of USTAG300 Undergraduate Master of Mathematics,Operational Research,Statistics and Economics
 Year 5 of USTAG301 Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (with Intercalated
This module is Option list E for:
 Year 4 of USTAG300 Undergraduate Master of Mathematics,Operational Research,Statistics and Economics
 Year 5 of USTAG301 Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (with Intercalated