SC7/SM6 Bayes Methods HT20

 

Course details

Sixteen lectures in LLT.

SC7 Part C classes: see dept webpage

SM6 MSc classes: see canvas pages.

SM6 MSc practical sessions: see canvas pages.

 

Lecture schedule and slides

The following schedule is a sketch to give you a sense of where we are going. The material from last

year is available here. I do not promise to stick to this schedule. It is correct only as a record.

 

Week 1 – common ground I

L1 The Bayesian inferential pipeline - slides

L2 Case Study – radiocarbon dating – slides (for later main code, MCMC code)

Week 2 – common ground II

L3 Markov Chain Monte Carlo I – slides and code for this and next lect.

L4 Markov Chain Monte Carlo II – slides

Week 3 – back to the basics (in L6)

L5 Data Augmentation; Estimating Bayes Factors – slides and code

L6 Decision theory; Utility and the expected-utility hypothesis – slides

Week 4 - principles

L7 Coherence and the Savage axioms - slides (sorry still no page numbers)

L8 Exchangeability and de Finetti’s Theorem - slides

Week 5 – Approximate Bayesian Computation (ABC)

L9 ABC - slides and code

L10 Model averaging - slides and code

Week 6 – the number of unknowns is unknown

L11 MCMC with involutions and Jacobians - slides and code (slight changes after lecture)

L12 Reversible Jump MCMC – slides and code

Week 7 – the number of unknowns is infinite

L13 Reversible Jump MCMC case study; Bayesian Non-Parametric Models (intro) slides

(the slides for L13 and the code in L12.R were updated 6/3/20 – fix missing m! in the posterior).

L14 Bayesian Non-Parametric models: Dirichlet-Process slides and code

Week 8 – approximations

L15 Chinese Restaurant Process; Normal-Dirichlet mixture;

       Galaxy data revisited - slides and code

L16 Gibbs sampler for DP mixture (Galaxy data, cont); Laplace Approximation; slides

(the Laplace approximation material was covered briefly but is not examinable)

 

Problem sheets

Week 3: first problem sheet

Week 5: second problem sheet

Week 7: third problem sheet and related R-code for optional questions

Week 1 TT20: fourth problem sheet

 

MSc Lab sessions

Week 2: practical - Bayesian inference for a thumbtack experiment (solutions and R-file)

Week 5: practical – (marked with feedback) with solutions to Q1, chess data and CompRank data.

Week 7: practical – ABC for a variable dimension model of change points (R-file sample solutions)

 

Mock Exam Questions – correction mock 2 Q1(b) posted 19/05/20

Here are some mock exam questions:  Mock 1; Mock 2. Here are sample solutions to M1 and M2.

Each question should take approximately 45 minutes. MSc and Part C exams from 2017 and 2018

are available on OXAM (on weblearn).

 

Reading

1. C.P. Robert, “The Bayesian Choice: From Decision-Theoretic Foundations to Computational

Implementation”, 2nd edition, Springer, 2001

2. C.P Robert & G Casella, “Monte Carlo Statistical Methods”, 2nd edition, Springer, 2004

3. A. Gelman et al, “Bayesian Data Analysis”, 3rd edition, Boca Raton Florida: CRC Press, 2014

 

Geoff Nicholls

nicholls@stats.ox.ac.uk