SC7/SM6 Bayes Methods
lectures in LLT.
C classes: in LG04/Seminar room 1, Thursday 3-4:30pm weeks 3, 5, 8 and Trinity
term week 1.
Classes: in LLT, Friday 11am - 12 midday, weeks 2, 5, 8 and Trinity week 0.
practical sessions: in the IT teaching Suite, Friday 2-4pm weeks 2, 4
(assessed) and 7.
Mock Exam Questions
are some mock exam questions: Mock 1; Mock 2; Mock 3 [M1 error
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)
The Bayesian inferential pipeline and R-code
Carlo Methods and R-code
Chain Monte Carlo and R-code
averaging, Model selection
Bayesian inference for a thumbtack
selection and averaging and R-code
Elicitation and Example: radiocarbon dating. R-code plus mcmc and calibration data
Sheet 1 and data
– Applied Bayesian inference
elicitation (continued) and ABC (Approximate Bayesian Computation) and R-code
Examples: Ising model and Population genetics and
data), Bradley-Terry, sample answer Q1;
(Assessed Q2 data), Spatial data, sample answer Q2
ABC examples continued; Reversible
Jump MCMC (we just made a start).
Jump (continued, simple example) and R-Code.
Sheet 2 – and ProblemSheet2Outliers.R
- advanced Applied Bayesian inference
Jump (updated, advanced examples), R-Code and
Reversible Jump (continued). Decision
theory (review); Admissibility of Bayes Estimators
Paradoxes of inference; the Savage axioms and coherence
and Bayesian Non-Parameterics (BNP) – fundamentals
Sheet 3 and R-Code
– ABC; Reversible jump; Axioms and paradoxes.
R for auxiliary
functions – ABC fitting Strauss process using RJ-MCMC
BNP models: Dirichlet-process. Rcode for 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.
C.P. Robert, “The Bayesian Choice: From
Decision-Theoretic Foundations to Computational
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