**SC7/SM6 Bayes Methods**

**Course details**

Sixteen lectures in LLT.

Part C classes: in LG04/Seminar room 1, Thursday 3-4:30pm weeks 3, 5, 8 and Trinity term week 1.

MSc Classes: in LLT, Friday 11am - 12 midday, weeks 2, 5, 8 and Trinity week 0.

MSc practical sessions: in the IT teaching Suite, Friday 2-4pm weeks 2, 4 (assessed) and 7.

**Mock Exam Questions**

Here are some mock exam questions: Mock 1; Mock 2; Mock 3 [M1 error corrections 04-05-17].

Each question should take approximately 45 minutes. The third mock has just one question in it.

Sample answer Mock 2.

**Lecture notes (posted below, subject to possible adjustment)**

**Week 1**

L1 The Bayesian inferential pipeline and R-code

L2 Monte Carlo Methods and R-code

**Week 2**

L3 Markov Chain Monte Carlo and R-code

L4 MCMC; Model averaging, Model selection

Bayesian inference for a thumbtack experiment (solutions and R-file)

**Week 3**

L5 Model selection and averaging and R-code

L6 Prior Elicitation and Example: radiocarbon dating. R-code plus mcmc and calibration data file

Problem Sheet 1 and data – Applied Bayesian inference

**Week 4**

L7 Prior elicitation (continued) and ABC (Approximate Bayesian Computation) and R-code

L8 ABC Examples: Ising model and Population genetics and R-code

(Non-Assessed Q1
data),* *Bradley-Terry, sample answer Q1;

(Assessed Q2 data), Spatial data, sample answer Q2

**Week 5**

L9 ABC examples continued; Reversible Jump MCMC (we just made a start).

L10 Reversible Jump (continued, simple example) and R-Code.

__Problem
Sheet 2__ – and ProblemSheet2Outliers.R
- advanced Applied Bayesian inference

**Week 6**

L11 Reversible Jump (updated, advanced examples), R-Code and data (insurance and galaxies).

L12 Reversible Jump (continued). Decision theory (review); Admissibility of Bayes Estimators

**Week 7**

L13 Utility; Paradoxes of inference; the Savage axioms and coherence

L14
Exchangeability
and Bayesian Non-Parameterics (BNP) – fundamentals
[*updated* 04-05-17]

Problem Sheet 3 and R-Code – ABC; Reversible jump; Axioms and paradoxes.

data, R-solutions, R for auxiliary functions – ABC fitting Strauss process using RJ-MCMC

**Week 8**

L15-16 BNP models: Dirichlet-process. Rcode for L15-16

L15-16
BNP models and fitting: [*updated 1/4/17*] CRP and Normal-Dirichlet
mixture; Galaxy data.

Problem Sheet 4 – [solutions to optional R q’s] Exchangeability; BNP theory and examples.

**Reading**

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

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

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

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

*JM Bernardo and AFM Smith, “Bayesian Theory”, Wiley, 2000*

Geoff Nicholls

nicholls@stats.ox.ac.uk