STATG012 - STATISTICAL INFERENCE

Aims of course:
To provide a grounding in the theoretical foundations of statistical inference and, in particular, to introduce the theory underlying statistical estimation and hypothesis testing.

Objectives of course:
On successful completion of the course, a student should be able to

• describe the principal features of, and differences between, frequentist, likelihood and Bayesian inference;
• define and derive the likelihood function based on data from a parametric statistical model, and
describe its role in various forms of inference;
• define a sufficient statistic; describe, calculate and apply methods of identifying a sufficient statistic;
• define, derive and apply frequentist criteria for evaluating and comparing estimators;
• describe, derive and apply lower bounds for the variance of an unbiased estimator;
• define and derive the maximum likelihood estimate, and the observed and expected information;
• describe, derive and apply the asymptotic distributions of the maximum likelihood estimator and related quantities;
• conduct Bayesian analyses of simple problems using conjugate prior distributions, and asymptotic Bayesian analyses of more general problems;
• define, derive and apply the error probabilities of a test between two simple hypotheses; define and conduct a likelihood ratio test; state and apply the Neyman-Pearson lemma;

Applications:
The theory of statistical inference underpins statistical design, estimation and hypothesis testing. As such it has fundamental applications to all fields in which statistical investigations are planned or data are analysed. Important areas include engineering, physical sciences and industry, medicine and biology, economics and finance, psychology and the social sciences.

Prerequisites:
Foundation Course (STATG000), or equivalent

Course content
Frequentist and Bayesian approaches to statistical inference.
Summary statistics, sampling distributions.
Sufficiency, likelihood, and information.
Asymptotic properties of estimators.
Bayesian inference.
Hypothesis testing.
Likelihood ratio tests, application to linear models.

Texts
D.R. Cox, Principles of Statistical Inference, Cambridge University Press (2006).
P.H.Garthwaite, I.T.Jolliffe & B.Jones, Statistical Inference (2nd edition, 2002, Oxford University Press).
P.M.Lee, Bayesian Statistics: An Introduction (2nd edition, 1997,Arnold).
J.A Rice, Mathematical Statistics and Data Analysis (3rd edition, 2006, Duxbury).
G.A. Young and R.L. Smith, Essentials of Statistical Inference (2005, Cambridge University Press).

Assessment for examination grading
Two-hour written examination in term 3.

Other set work
About 8 sets of exercises. These will not count towards the examination grading.

Timetabled workload
Lectures: 2 hours per week in term 1.
Workshops: 2 two-hour classes in term 1.
Tutorials: 1 hour per week in term 1.