## BS2a Statistical Inference

### Lecture Notes 2011

Overheads for L1,2 Exponential Families, Sufficient and Minimal Sufficient Statistics

Overheads for L3,4 Estimators, the Cramer-Rao Bound and the Rao-Blackwell Theorem

Overheads for L5,6 Complete Sufficient Statistics, Method of Moments; Likelihood principle, Bayesian Inference

and some revision material on Hypothesis testing.

Overheads for L7,8 Asymptotic Normality of posterior distribution, Conjugate priors, Marginals, Predictive Distributions

Overheads for L9,10 Hierarchical Models. Constructing Priors. Uniform, Jeffreys, MaxEnt. HPD intervals.

Overheads for L11,12 Bayesian Hypothesis tests. The Bayes factor.

Overheads for L13,14 Decision Theory. Hypothesis testing as decision problem.

Overheads for L15,16 and accompanying R-code. The Stein paradox. Empirical Bayes. Markov Chain Monte Carlo.

### Problem sheets 2011

Classes are 3-4pm and 4-5pm on Fridays in the lecture room in SPR1, starting in week 3.

Hand in your work to the appropriate BS2a tray in SPR1 by midday on Wednesdays.

Classes have been assigned.

Week 3 classes - Problem Sheet 1

Week 4 classes - Problem Sheet 2

Week 5 classes - Problem Sheet 3

Week 6 classes - Problem Sheet 4

Week 7 classes - Problem Sheet 5

Week 8 classes - Problem Sheet 6 (due 12 midday Wednesday of Week 8 at SPR1).

(In Q2, time starts at 0, Q2b.i means 'calculate the Bayes risk for the new cost' and Q4b it is a1/(a0+a1) not a0/(a0+a1)).

### Other resources

Some material from MT10 can be found at Prof Griffiths' 10-11 BS2a page

*nicholls@stats.ox.ac.uk*