This course introduces the statistical theory of estimation and testing. Both non-parametric and parametric approaches are used, although much of the course is focused on likelihood-based inference.

20 lectures (typically 2 each week in Weeks 2-11)

5 tutorials

2, 2-hour practical sessions

STATS4012 Inference

STATS3015 Statistics 3I: Inference

STATS5024 Probability (Level M)

90-minute, end-of-course examination (90%), coursework (10%)

The aims of this course are:

■ to introduce students to parametric and non-parametric approaches to statistical inference;

■ to present the fundamental principles of likelihood-based inference, with emphasis on the large sample results that are widely used in practice;

■ to introduce Bayesian inference;

■ to compare and contrast these different approaches to inference;

■ to show students how to implement these statistical methods using the R computer package.

By the end of this course students will be able to:

■ define and contrast population and sample, parameter and estimate;

■ write down and justify criteria required of 'good' point estimators, and check whether or not a proposed estimator within a stated statistical model satisfies these criteria;

■ apply the principle of maximum likelihood to obtain point and interval estimates of parameters in one-parameter and multi-parameter statistical models, making appropriate use of the Newton-Raphson method of optimisation;

■ use pivotal functions to obtain confidence intervals with exact coverage properties within Normal models;

■ justify and make use of the large sample properties of maximum-likelihood estimators to obtain confidence intervals with approximate coverage properties in a range of statistical models;

■ formulate hypothesis tests in some common models (including Normal models), correctly using the terms null hypothesis, alternative hypothesis, test statistic, rejection region, significance level, power, p-value;

■ justify and make use of the Likelihood Ratio Test and the Generalised Likelihood Ratio tests;

■ describe the rules for updating prior distributions in the presence of data, and for calculating posterior predictive distributions;

■ derive posterior distributions corresponding to simple low-dimensional statistical models, with conjugate priors;

■ carry out a range of non-parametric tests, with due regard to the underlying assumptions;

■ implement these statistical methods using the R computer package;

■ frame statistical conclusions from interval estimates and hypothesis tests clearly.

Students must submit at least 75% by weight of the components (including examinations) of the course's summative assessment.