SC7/SM6 Bayes Methods HT18

 

Course details

Sixteen lectures in LLT.

SC7 Part C classes: LG.05, Thurs 2-3:30/Fri 10:30-12, week 3,5,7, TT1 (due Tues 5pm at department)

SM6 MSc classes: LLT, Thursday 5-6pm weeks 3,5,7,TT0/1

MSc practical sessions: in the IT teaching Suite, Friday 11-1pm weeks 2, 5 (assessed) and 7.

 

Lecture notes

Here are all the lecture notes in one document

 

Lecture schedule and slides

Week 1

L1 The Bayesian inferential pipeline; lecture; R-code; (for data see R-code)

L2 Monte Carlo Methods; lecture; R-code

Week 2

L3 Markov Chain Monte Carlo; lecture; R-code

L4 Data Augmentation; Model selection; lecture; R-code

Week 3

L5 Estimating Bayes Factors; Model averaging; regression case study; lecture; R-code

L6 Prior Elicitation; Multiple testing; case study radiocarbon dating; lecture; R-code; calibration data

Week 4

L7 ABC (Approximate Bayesian Computation); lecture; R-code

L8 ABC case studies: Ising model and Kingman Coalescent; lecture; R-code

Week 5

L9 ABC Case study (cont); Reversible Jump MCMC; lecture and R-Code

L10 Reversible Jump MCMC (cont); lecture; R-Code and galaxy data

Week 6

L11 Reversible Jump MCMC case study (cont); Loss and Utility; lecture; R-code

L12 The Savage axioms and coherent belief; lecture

Week 7

L13 Exchangeability and de Finetti’s Theorem; lecture

L14 Bayesian Non-Parametric models: Dirichlet-Process; lecture; R-code

Week 8 

L15 Chinese Restaurant Process; Normal-Dirichlet mixture; collapsed Gibbs sampler;

       Galaxy data revisited; lecture; R-code

L16 Laplace Approximation and the BIC; lecture.

 

Problem sheets

Week 3: Problem Sheet 1 & data; Applied Bayesian inference and MCMC (soln Q4 R-code)

Week 5: Problem Sheet 2; & R-code soln Q4 Outliers; Applied Bayesian inference; ABC

Week 7: Problem Sheet 3 & R-code for Q1,3; ABC; Reversible jump; Axioms and paradoxes

Week 8: Problem Sheet 4; Exchangeability; BNP theory and examples.

MSc Lab sessions

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

Week 5:  Assessed practical Bayesian inference (in sport), sample answer Q1, data Q1, data Q2

Week 7: practical, towns data, Spatial Statistics - ABC fitting Strauss process using RJ-MCMC

               ABC R-solutions to Q2 (main file, start here), RJ MCMC R-solutions to Q1, and

               parallel MCMC R-solutions to Q3.

              

Mock Exam Questions

Here are some mock exam questions: Mock 1; Mock 2; Mock 3. Each question should take approximately 45 minutes. The third mock has just one question in it. Sample answer Mock 2.

[Note – I am absorbing some of these 2017 mock questions into the 2018 problem sheets, and will replace these in updated mocks prior to TT18]

 

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. P Hoff, “A First Course in Bayesian Statistical Methods”, Springer, 2010

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

 

Geoff Nicholls

nicholls@stats.ox.ac.uk