OverviewThis course introduces (and revises for some students) the essentials of probability and classical (frequentist) statistical inference, which provide the backbone for later modules.
Syllabus: Probability: axioms, marginal, joint and conditional distributions, Bayes theorem, important distributions, generating functions and various modes of convergence. Classical Inference: Sampling
distributions. Point estimation: consistency, Cramer-Rao inequality, efficiency, sufficiency, minimum variance unbiased estimators. Likelihood. Methods of estimation. Hypothesis tests: maximum likelihood-ratio test, Wald and score tests, profile and test-based confidence intervals.
This module appears in:
Method of assessment
80% Examination, 20% Coursework
BICKEL, P.J. and DOKSUM, K. (2001). Mathematical Statistics: Basic Ideas and Selected Topics, Volume 1, 2nd edition. London: Prentice-Hall International
CASELLA, G. and BERGER, R. L. (2002). Statistical Inference, 2nd Edition. Pacific Grove, CA: Duxbury.
FELLER, W. (1967). An Introduction to Probability Theory and its Applications, Volume 1, New York: Wiley.
HOGG, R., McKEAN, J. and CRAIG. A. (2014). Introduction to Mathematical Statistics. 7th International Edition. Harlow, Essex: Pearson Education.
ROSS, S.M. (2014). A First Course in Probability, 9th International Edition. Harlow, Essex: Pearson Education.
The intended subject specific learning outcomes. On successfully completing the module students will be able to:
1 demonstrate a systematic understanding of probability and frequentist statistical inference;
2 use a comprehensive range of relevant concepts and principles;
3 select and apply these to solve advanced problems in probability and statistical inference, using a variety of methods.
The intended generic learning outcomes. On successfully completing the module students will be able to:
1 apply a logical, mathematical approach to their work, identifying the assumptions made and the conclusions drawn;
2 solve challenging problems;