Please note: there may be some adjustments to the teaching arrangements published in the course catalogue for 2020-21. Given current circumstances related to the Covid-19 pandemic it is anticipated that some usual arrangements for teaching on campus will be modified to ensure the safety and wellbeing of students and staff on campus; further adjustments may also be necessary, or beneficial, during the course of the academic year as national requirements relating to management of the pandemic are revised.

Statistical Inference (Level M) STATS5028

  • Academic Session: 2021-22
  • 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
  • Available to Erasmus Students: Yes

Short Description

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

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.

Excluded Courses

STATS4012 Inference

STATS3015 Statistics 3I: Inference


STATS5024 Probability (Level M)


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

Main Assessment In: December and April/May

Course Aims

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.