Markov Chain Monte Carlo

MATH68122 Markov Chain Monte Carlo 15 Semester 2 Postgraduate Taught Level 6 Theodoros Papamarkou Unit coordinator Timothy Waite Unit coordinator 1 FHEQ level (Framework for Higher Education Qualifications) ' Masters/Integrated Masters P4 ' European Credit Transfer & Accumulation System Rating : 7.5 The unit aims to introduce the student to computational Bayesian statistics, in particular Markov chain Monte Carlo (MCMC) and Approximate Bayesian Computation (ABC).  The unit aims to introduce the student to computational Bayesian statistics, in particular Markov chain Monte Carlo (MCMC) and Approximate Bayesian Computation (ABC).  The unit aims to introduce the student to computational Bayesian statistics, in particular Markov chain Monte Carlo (MCMC) and Approximate Bayesian Computation (ABC).  On successful completion of this course unit students will be able to: <ul><li>apply various MCMC algorithms, such as the Metropolis-Hastings algorithm and the Gibbs sampler, to obtain samples from complex distributions and for parameter estimation in standard problems, such as regression modelling;</li><li>employ the Approximate Bayesian Computation (ABC) algorithm for parameter estimation in various problems, including population genetic models;</li><li>describe the various algorithms in words but also implement the algorithms through statistical software;</li><li>evaluate the performance of the algorithms using diagnostics and explain how to improve performance when necessary;</li><li>formulate MCMC/ABC algorithms to perform model selection.</li></ul>   SyllabusIntroduction: Monte Carlo, Bayesian statistics, Markov chains. [2]Gibbs Sampler: data augmentation, burn-in, convergence. [4]Metropolis-Hastings algorithm: independent sampler, random walk Metropolis, scaling, multi- modality. [4]MCMC Issues: Monte Carlo Error, reparameterisation, hybrid algorithms, convergence diagnostics. [4]Reversible jump MCMC: known number of parameters. [2]Hamiltonian Monte Carlo. [2]Approximate Bayesian Computation: simulation based inference. [4]   The course is delivered in 2hr lectures followed by a 1hr computer class each week. The material for each week is uploaded ahead of time on the VLE and includes lecture notes, an example sheet and often datasets for the practical implementation.In terms of e-learning, there are weekly (non-assessed) quizzes available on the VLE and the pre-recorded videos from 2021 are also provided as an additional resource. Lecture podcasts are made available after the lecture, along with copies of any handwritten notes from the lecture. A discussion board is also set up for the course.In the final week, the lecture is replaced by a 2hr revision class where worked solutions of last year’s exam paper are demonstrated to students.   0 Other 50% 1 Written exam 50% <ul><li>Three take home courseworks: 50%</li><li>End of semester written examination: 50%</li></ul> Feedback tutorials will provide an opportunity for students' work to be discussed and provide feedback on their understanding.  Coursework or in-class tests (where applicable) also provide an opportunity for students to receive feedback.  Students can also get feedback on their understanding directly from the lecturer, for example during the lecturer's office hour. MATH48091 Statistical Computing Pre-Requisite Optional MATH27720 Probability and Statistics 2 Pre-Requisite Compulsory Students are not permitted to take, for credit, MATH48122 in an undergraduate programme and then MATH68122 in a postgraduate programme at the University of Manchester, as the courses are identical. N <ul> <li> W. R. Gilks, S. Richarson and D. Spiegelhalter, Markov chain Monte Carlo methods in Practice, Chapman and Hall</li> <li> A. Gelman, J. B. Carlin, H. S. Stern, D. B. Dunson, A. Vehtari and D. B. Rubin, Bayesian Data Analysis, Chapman and Hall.</li> </ul> Lectures 22 Practical classes & workshops 11 117 Total scheduled hours 35 hrs:  2 Lectures + 1 Computer class each week (11 weeks), + 2 Revision classes in Week 12.