# DEGREE REGULATIONS & PROGRAMMES OF STUDY 2017/2018

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# Postgraduate Course: Bayesian Theory (MATH11177)

 School School of Mathematics College College of Science and Engineering Credit level (Normal year taken) SCQF Level 11 (Postgraduate) Availability Not available to visiting students SCQF Credits 10 ECTS Credits 5 Summary This course will provide the underlying theory for Bayesian statistics. Students will understand the role of the prior distribution and be able to formulate a posterior distribution (up to proportionality). They will also be exposed to the ideas of summarising posterior distributions and associated statistics. The underlying theory of Markov chain Monte Carlo will be introduced (Metropolis-Hastings and Gibbs sampler) with associated issues of implementation. Course description 1. Bayes theorem (discrete and continuous) 2. Prior specification 3. Posterior distribution and associated summary statistics (point and interval) 4. Predictive distributions 5. Hypothesis testing (simple and composite hypotheses) 6. Monte Carlo integration 7. Markov chain Monte Carlo (MCMC): Metropolis-Hastings (MH) and Gibbs sampler
 Pre-requisites Students MUST have passed: Several Variable Calculus and Differential Equations (MATH08063) AND Likelihood (MATH10004) Co-requisites Prohibited Combinations Other requirements None
 Academic year 2017/18, Not available to visiting students (SS1) Quota:  None Course Start Semester 1 Timetable Timetable Learning and Teaching activities (Further Info) Total Hours: 100 ( Lecture Hours 20, Seminar/Tutorial Hours 5, Programme Level Learning and Teaching Hours 2, Directed Learning and Independent Learning Hours 73 ) Assessment (Further Info) Written Exam 90 %, Coursework 10 %, Practical Exam 0 % Additional Information (Assessment) Coursework 10%, Examination 90% Feedback Not entered Exam Information Exam Diet Paper Name Hours & Minutes Main Exam Diet S1 (December) Bayesian Theory (MATH11177) 2:00
 On completion of this course, the student will be able to: Understand the Bayesian philosophy.Ability to specify a prior distribution and derive a posterior distribution (up to proportionality).Ability to derive additional related posterior distributions and quantities algebraically.Understand the theory of Markov Chain Monte Carlo (MCMC) and associated implementation issues.
 Bayesian Statistics: An Introduction (4th edition). Lee. Wiley Markov chain Monte Carlo: Stochastic simulation for Bayesian Inference (2nd edition). Gamerman and Lopes. CRC Press Bayesian Data Analysis (3rd edition). Gelman, Carlin, Stern, Dunson, Vehtari and Rubin. CRC Press (earlier editions of the above are equally suitable)
 Graduate Attributes and Skills Not entered Keywords BTh,statistics,Bayesian,Markov chain Monte Carlo
 Course organiser Prof Ruth King Tel: (0131 6)50 5947 Email: Ruth.King@ed.ac.uk Course secretary Mrs Frances Reid Tel: (0131 6)50 4883 Email: f.c.reid@ed.ac.uk
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