MT3507 Mathematical Statistics

Academic year

2025 to 2026 Semester 1

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 9

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

11.00 am Mon (weeks 1, 3, 5, 8, 10), Wed & Fri

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

Module coordinator

Dr G Minas

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

Module Staff

Dr Giorgos Minas

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

Module description

Together with MT3508, this module provides a bridge between second year and Honours modules in statistics. It will provide students with a solid theoretical foundation on which much of more advanced statistical theory and methods are built. This includes probability generating functions and moment generating functions, as well as widely used discrete distributions (binomial, Poisson, negative binomial and multinomial) and continuous distributions (gamma, exponential, chi-squared, beta, t-distribution, F-distribution, and multivariate normal). Hypothesis testing and confidence intervals for Binomial and Poisson data are derived. The module will also provide a foundation in methods of statistical inference (maximum likelihood and Bayesian), model selection methods based on information theory (AIC and BIC), and the General Linear Model.

Relationship to other modules

Pre-requisites

BEFORE TAKING THIS MODULE YOU MUST PASS MT2508

Assessment pattern

2-hour Written Examination = 90%, Class Test = 10%

Re-assessment

Oral examination = 100%

Learning and teaching methods and delivery

Weekly contact

2.5 hours of lectures and 1 tutorial.

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

  • Derive informative theoretical properties of continuous and discrete probability distributions and transformations of these distributions
  • Formulate appropriate likelihood functions and demonstrate understanding of the role of the likelihood in parameter estimation methods
  • Quantify the uncertainty of parameter estimates through the calculation of interval estimates using the likelihood function, frequentist and Bayesian methods
  • Conduct a range of statistical tests to evaluate hypotheses about unknown parameters, and the data distribution
  • Demonstrate knowledge of Bayesian methods by deriving posterior distributions for unknown parameters, and using them to derive parameter estimates
  • Formulate, compare, and interpret general linear models, and be able to perform statistical inference to obtain expressions for parameter estimators and their properties