58勛圖

MT2508 Statistical Inference

Academic year

2026 to 2027 Semester 2

Further information on which modules are specific to your programme.

Key module information

SCOTCAT credits

15

The Scottish Credit Accumulation and Transfer (SCOTCAT) system allows credits gained in Scotland to be transferred between institutions. The number of credits associated with a module gives an indication of the amount of learning effort required by the learner. European Credit Transfer System (ECTS) credits are half the value of SCOTCAT credits.

SCQF level

SCQF level 8

The Scottish Credit and Qualifications Framework (SCQF) provides an indication of the complexity of award qualifications and associated learning and operates on an ascending numeric scale from Levels 1-12 with SCQF Level 10 equating to a Scottish undergraduate Honours degree.

Planned timetable

12.00 noon Mon (weeks 2, 4, 6, 8, 11), Tue and Thu

This information is given as indicative. Timetable may change at short notice depending on room availability.

Module coordinator

Prof L J Thomas

Prof L J Thomas
This information is given as indicative. Staff involved in a module may change at short notice depending on availability and circumstances.

Module Staff

TBD

This information is given as indicative. Staff involved in a module may change at short notice depending on availability and circumstances.

Module description

This module provides an introduction to the mathematical models of randomness. These models are used to perform statistical analysis, where the aim is to evaluate our uncertainty on a certain quantity after observing data. Important topics in statistics are described including maximum likelihood estimation, confidence intervals and hypothesis testing, permutation tests, and linear regression. It forms a prerequisite for the statistics modules in the Honours programme. It is recommended that students in the Faculties of Arts and Divinity take an even number of the 15-credit 2000-level MT modules.

Relationship to other modules

Pre-requisites

BEFORE TAKING THIS MODULE YOU MUST PASS MT2504

Anti-requisites

YOU CANNOT TAKE THIS MODULE IF YOU TAKE EC2203

Assessment pattern

2-hour Written Examination = 70%, Coursework = 30%

Re-assessment

2-hour Written Examination = 100%

Learning and teaching methods and delivery

Weekly contact

2.5 hours of lectures (x 10 weeks), 1-hour tutorial (x 5 weeks), 1-hour examples class (x 5 weeks)

Scheduled learning hours

35

The number of compulsory student:staff contact hours over the period of the module.

Guided independent study hours

115

The number of hours that students are expected to invest in independent study over the period of the module.

Intended learning outcomes

  • Define estimators and determine whether they are unbiased and/or consistent. Understand and estimate the variability of estimators. Calculate point estimates from data and quantify uncertainty through confidence intervals
  • Identify, perform and interpret relevant hypothesis tests using both parametric and nonparametric methods
  • Construct likelihoods and apply the method of maximum likelihood to basic examples including the mean and variance of the normal distribution
  • Fit, interpret, compare and assess linear models including simple, multiple and polynomial regression with continuous covariates
  • Appreciate the importance of testing assumptions and limitations of statistical methods. Appreciate and practice the conveying of statistics to a non-technical audience
  • Develop basic skills in computational statistics using R including working with common distributions, reading in data, basic simulation methods, programming computational randomisation tests, fitting linear models and interpreting model output

Additional information from school

For guidance on module choice at 2000-level in Mathematics and Statistics see our Module choices at 1000 and 2000 level page.

Syllabus

  • Difference between population and sample: Sample mean and variance as estimates of population mean and variance; sample covariance and correlation.
  • Likelihood and maximum likelihood estimation: Discrete data and examples (sequence of binary trials, Poisson counts all with the same mean, Poisson with mean a function of a covariate); continuous data and example (n observations from N(m,s2), m.l.e.s of mean and variance); invariance of m.l.e.s
  • Confidence intervals and hypothesis testing: Unbiased and consistent estimators, interval estimation, hypothesis testing
  • Basic properties of Normal distributions, Central Limit Theorem (statement and application to binomial and Poisson), assessing normality (normal scores)
  • Hypothesis testing and interval estimation for normal distributions with s2 known; c2, t and F distributions and their basic properties; one-sample t-test, paired t-test; two-sample t-tests and confidence intervals for means of normal distributions; F-tests for equality of variances of normal distributions; permutation tests: 2-sample permutation test; perm test for matched pairs and one-sample test; randomization tests.
  • Simple linear regression: Intro and least squares, normal linear regression, regression in R, CIs and PIs, checking assumptions.