This module is not currently running in 2024 to 2025.
This 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.
Total contact hours: 36
Private study hours: 114
Total study hours: 150
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.
See the library reading list for this module (Canterbury)
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.
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