ST22012 Introduction to Mathematical Statistics
Introductory description
This module runs in Term 1 and is optional for students from outside the Statistics department. It is of particular relevance to students who may be interested in taking third year Statistics modules.
This module is not available to students who have their home department in Statistics, who take equivalent modules.
Prerequisites: ST111 Probability A and ST112 Probability B
Leads to: Many ST3 modules.
Module aims
This module is designed for students in the Mathematics, Computer Science and other nonStatistics departments. It will introduce the main ideas of statistical inference emphasising the use of likelihood for estimation and testing. These ideas are fundamental to the use of statistics in modern applications such as mathematical finance, telecommunications, bioinformatics as well as more traditional areas such as insurance, engineering and the social sciences.
Outline syllabus
This is an indicative module outline only to give an indication of the sort of topics that may be covered. Actual sessions held may differ.
 Standard families of Probability distributions: Binomial, Geometric, Poisson, Exponential, Gamma, Gaussian.
 The weak law of large numbers and central limit theorem.
 The Multivariate Gaussian distribution. Orthogonality and Independence for jointly Gaussian random variables.
Distributions derived from the Gaussian: Chisquared, t and F.  The notion of a parametrized Statistical model, and examples.
 Likelihood including maximum likelihood estimates and use of likelihood ratios to compare hypotheses.
 The repeated sampling principle: bias and MSE, confidence intervals and pvalues.
 Fisher's theorem on Gaussian sampling, and its extension to linear regression.
Learning outcomes
By the end of the module, students should be able to:
 Understand more advanced notions of probability needed in mathematical statistics including properties of multivariate Gaussian distributions, the law of large numbers, and the central limit theorem.
 Understand the main notions of statistical inference including a (parametrized) statistical model, an estimator and its sampling distribution, and hypothesis tests.
 Be able to calculate maximum likelihood estimators in a variety of examples. Be able to derive properties of sampling distributions of estimators in a variety of examples, and thereby construct confidence intervals.
 Be able to use likelihood ratios to construct hypothesis tests in a variety of examples including the classical t and F tests.
Indicative reading list
View reading list on Talis Aspire
Subject specific skills
TBC
Transferable skills
TBC
Study time
Type  Required  Optional 

Lectures  30 sessions of 1 hour (25%)  2 sessions of 1 hour 
Tutorials  5 sessions of 1 hour (4%)  
Private study  73 hours (61%)  
Assessment  12 hours (10%)  
Total  120 hours 
Private study description
Weekly revision of lecture notes and materials, wider reading and practice exercises, working on problem sets and preparing for examination.
There will be fortnightly problem sets which will be marked and returned with feedback in tutorials.
Costs
No further costs have been identified for this module.
You do not need to pass all assessment components to pass the module.
Assessment group D
Weighting  Study time  

Multiple Choice Quizzes  10%  12 hours 
A number of multiple choice quizzes which will take place during the term that the module is delivered. 

Online Examination  90%  
The examination paper will contain four questions, of which the best marks of THREE questions will be used to calculate your grade. ~Platforms  Moodle

Assessment group R
Weighting  Study time  

Online Examination  Resit  100%  
The examination paper will contain four questions, of which the best marks of THREE questions will be used to calculate your grade. ~Platforms  Moodle

Feedback on assessment
Answers to the formative problems sets will be marked and returned to students in a tutorial or seminar taking place the following week when students will have the opportunity to discuss it.
Solutions and cohort level feedback will be provided for the examination.
Postrequisite modules
If you pass this module, you can take:
 ST40915 Medical Statistics with Advanced Topics
 ST33215 Medical Statistics
Antirequisite modules
If you take this module, you cannot also take:
 ST21812 Mathematical Statistics Part A
 ST21912 Mathematical Statistics Part B
Courses
This module is Optional for:
 Year 3 of UMAAG1NC Undergraduate Mathematics and Business Studies
 Year 3 of UMAAGL11 Undergraduate Mathematics and Economics
This module is Option list A for:
 Year 2 of UMAAG105 Undergraduate Master of Mathematics (with Intercalated Year)

UMAAG100 Undergraduate Mathematics (BSc)
 Year 2 of G100 Mathematics
 Year 2 of G100 Mathematics

UMAAG103 Undergraduate Mathematics (MMath)
 Year 2 of G103 Mathematics (MMath)
 Year 2 of G103 Mathematics (MMath)
 Year 2 of UMAAG106 Undergraduate Mathematics (MMath) with Study in Europe
 Year 2 of UMAAG1NC Undergraduate Mathematics and Business Studies
 Year 2 of UMAAG1N2 Undergraduate Mathematics and Business Studies (with Intercalated Year)
 Year 2 of UMAAGL11 Undergraduate Mathematics and Economics
 Year 2 of UECAGL12 Undergraduate Mathematics and Economics (with Intercalated Year)
 Year 2 of UMAAG101 Undergraduate Mathematics with Intercalated Year
This module is Option list B for:
 Year 2 of UCSAG4G1 Undergraduate Discrete Mathematics
 Year 2 of UCSAG4G3 Undergraduate Discrete Mathematics
 Year 3 of UMAAG105 Undergraduate Master of Mathematics (with Intercalated Year)

UMAAG100 Undergraduate Mathematics (BSc)
 Year 3 of G100 Mathematics
 Year 3 of G100 Mathematics

UMAAG103 Undergraduate Mathematics (MMath)
 Year 3 of G103 Mathematics (MMath)
 Year 3 of G103 Mathematics (MMath)
 Year 3 of UMAAG106 Undergraduate Mathematics (MMath) with Study in Europe
 Year 4 of UMAAG101 Undergraduate Mathematics with Intercalated Year