# Probability and Classical Inference - MA881

Location Term Level Credits (ECTS) Current Convenor 2019-20
Canterbury
(version 2)
Autumn
View Timetable
7 15 (7.5) PROF M Ridout

None

None

2019-20

## Overview

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.

36 hours

## 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.

See the library reading list for this module (Canterbury)

## Learning outcomes

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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