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

MSc Lab

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

MSc Lab;

(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.

MSc Lab

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”, 2nd edition, Springer, 2001

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

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

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

 

Geoff Nicholls

nicholls@stats.ox.ac.uk