Course co-ordinator(s): Prof George Streftaris (Edinburgh), Prof Gavin Gibson (Edinburgh).
Aims:
To provide students with knowledge of modern Bayesian Statistical inference, an understanding of the theory and
application of computational methods in statistics and stochastic simulation methods including MCMC, and experience of
implementing the Bayesian approach in practical situations.
Detailed Information
Pre-requisites: none.
Location: Edinburgh.
Semester: 2.
Syllabus:
1. Statistical programming. This will include an introduction to the use of R (and/or, potentially, other languages and packages) for simple probabilistic and statistical calculations, including the use of built-in simulation capabilities, iterative procedures, solution of equations and maximisation of functions.
2. Philosophy of Bayesian inference. This will include treatment of subjective and frequentist probability; the role of likelihood as a basis for inference; comparative treatment of Bayesian and frequentist approaches.
3. Implementing the Bayesian approach. This will include: the formulation of likelihood for a range of statistical models and sampling designs; the incorporation of prior knowledge through prior density selection; conjugacy; the use of non-informative and non-subjective priors (including Jeffrey's prior); the interpretation of the posterior distribution as the totality of knowledge; predictive distributions.
4. Theory of stochastic processes. Markov chains, classification of states, irreducibility, aperiodicity etc., stationary distributions, generalised and detailed balance, convergence.
5. Markov-chain and other stochastic methods for investigating target distributions. Ideas covered will include: construction of MCMC methods using standard recipes - Metropolis (and Metropolis-Hastings) algorithm, Gibb's sampler, implementation of methods using R computing package; investigation of properties through simulation. Simpler simulation methods using transformations, distribution function inversion and rejection sampling will also be covered.
6. Application of MCMC methods in Bayesian inference Ideas covered will include: formulation of samplers for inferential problems in e.g. pattern recognition, signal classification, population dynamics; implementation of methods using R; application to problems involving missing data; informative methods of summarising posterior densities.
Learning Outcomes: Subject Mastery
After studying this module, students should be able to:
• Understand and use computational programming in statistics
• Understand the philosophy of Bayesian inference and implement it in the solution of practical problems
• Understand and implement the theory of stochastic simulation
• Understand and implement the theory of Markov processes as applied to MCMC
• Understand and implement solutions to the practical problems (burn-in, mixing, etc) involved in the use of MCMC
• Understand and use MCMC in a range of practical applications
Learning Outcomes: Personal Abilities
At the end of the module, students should be able to:
• Demonstrate the ability to learn independently
• Manage time work to deadlines and prioritise workloads
• Present results in a way which demonstrates that they have understood the technical and broader issues of Bayesian inference and computational methods in statistics and its applications
Assessment Methods: Due to covid, assessment methods for Academic Year 2021-22 may vary from those noted on the official course descriptor. Please see the Computer Science Course Weightings and the Maths Course Weightings for 2020-21 Semester 1 assessment methods.
SCQF Level: 11.
Credits: 15.
Other Information
Help: If you have any problems or questions regarding the course, you are encouraged to contact the lecturer
Canvas: further information and course materials are available on Canvas