**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)

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”,
2 ^{nd} edition, Springer, 2001 *

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

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

Geoff Nicholls

nicholls@stats.ox.ac.uk