Statistical Inference (Level M) STATS5028
- Academic Session: 2023-24
- School: School of Mathematics and Statistics
- Credits: 10
- Level: Level 5 (SCQF level 11)
- Typically Offered: Either Semester 1 or Semester 2
- Available to Visiting Students: Yes
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)
2, 2-hour practical sessions
Requirements of Entry
Some optional courses may be constrained by space and entry to these is not guaranteed unless you are in a programme for which this is a compulsory course.
STATS3015 Statistics 3I: Inference
STATS5024 Probability (Level M)
90-minute, end-of-course examination (90%), coursework (10%)
Main Assessment In: December and April/May
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.
Intended Learning Outcomes of Course
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.
Minimum Requirement for Award of Credits
Students must submit at least 75% by weight of the components (including examinations) of the course's summative assessment.