**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”,
2 ^{nd} edition, Springer, 2001 *

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

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

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

Geoff Nicholls

nicholls@stats.ox.ac.uk