Part B Foundations of
Statistical Inference (SB2.1) MT 2019 (first half)
Julien Berestycki (lectures 1-8) and Dino Sejdinovic (Lectures 9-16)
data can be interpreted in the context of a statistical
model. Working knowledge and understanding of key-elements
of model-based statistical inference, including
awareness of similarities, relationships
and differences between Bayesian and frequentist
Curved and linear exponential families; canonical parametrization;
Sufficiency: Factorization theorem; sufficiency in exponential
Frequentist estimation: unbiasedness; method of moments; the
Cramer-Rao information inequality;
Rao-Blackwell theorem, Lehmann-Scheffe Theorem and
Statement of complete sufficiency for Exponential families.
The Bayesian paradigm: likelihood principle; subjective
probability; prior to posterior analysis; asymptotic normality;
conjugacy; examples from exponential families. Choice of prior
distribution: proper and improper priors;
Jeffreys and maximum entropy priors. Hierarchical Bayes models.
Decision theory: risk function; Minimax rules, Bayes rules. Point
estimators and admissibility of Bayes rules.
The James-Stein estimator, shrinkage estimators and Empirical
Bayes. Hypothesis testing as decision problem.
A brief revision of the
material covered in Part A Statistics course would be a good idea.
Course notes for Part A Statistics can be found here.
Lectures (all in Stats LG 0.1)
Tuesdays 3 pm and Thursdays 10 am weeks 1-4.
Mondays 11 am and Tuesdays 1 pm weeks 5-8.
( Part B timetable )
Copies of lecture slides will usually appear here before each lecture.
It is recommended that you bring copies of the slides to each lecture.
The 4-up slides would be best for this purpose.
|Sufficiency, Factorization Theorem, Minimal sufficiency
|Estimators, Minimum Variance Unbiased Estimators (MVUE)
The Cramér-Rao Lower Bound.
|Consequences of the Cramér-Rao Lower Bound.
Searching for a MVUE. Rao-Blackwell Theorem,
|The method of moments
|Prior distributions. Hierarchical models. Predictive
There will be UG classes
in weeks 3,5,7,8 (time and rooms on Minerva) .
Work should be handed in to the appropriate SB2.1 pigeon hole 48h before the class.
There will be MSc classes
in weeks 3,5,7,8 (Tuesday 10 am in LG.01) .
No work to be handed in.
- P. H. Garthwaite, I.
T. Jolliffe and Byron Jones, Statistical Inference, Second ed.
Oxford University Press, 2002
- G.A.Young and R.L.
Smith, Essentials of Statistical Inference, Cambridge
University Press, 2005.
- T. Leonard and
J.S.J. Hsu, Bayesian Methods, Cambridge University Press,
- D. R. Cox,
Principles of Statistical Inference, Cambridge University
- H. Liero and S
Zwanzig, Introduction to the Theory of Statistical Inference,
CRC Press, 2012
- D. Barber, Bayes
Reasoning and Machine Learning, Cambridge University Press,