ST21912 Mathematical Statistics Part B
Introductory description
This module runs in Term 2 and is core for students with their home department in Statistics. It is not available to other students who should consider ST220: Introduction to Mathematical Statistics as an alternative.
Prerequisite(s): ST218 Mathematical Statistics Part A
Leads To: many ST3 and ST4 modules
Module aims
To introduce the major ideas of statistical inference with an emphasis on likelihood methods of estimation and testing.
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.
The notion of a parametrized statistical model for data.
The definition of likelihood and examples of using it compare possible parameter values.
Parameter estimates and in particular maximum likelihood estimates. Examples including estimated means and variances for Gaussian variables.
The repeated sampling principle: the notion of estimator and its sampling distribution. Bias and MSE. Examples of calculating sampling distributions.
Construction of confidence intervals.
Notion of a hypothesis test. Likelihood ratio tests. NeymanPearson Lemma. Pvalue.
Principle of data reduction: sufficient statistics, and applications to point estimation and hypothesis testing.
Asymptotic normality of MLEs. Examples.
Learning outcomes
By the end of the module, students should be able to:
 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 use likelihood ratios to construct hypothesis tests in a variety of examples including the classical t and F tests.
 Be able to derive properties of sampling distributions of estimators in a variety of examples.
Indicative reading list
The main reference books for the course are:
 Statistical Inference, G. Casella and R. L. Berger.
 Introduction to the theory of Statistical Inference, H. Liero and S. Zwanzig.
Other possible books that you can refer at:
3. Probability and statistics by example: 1: Basic probability and statistics, Y. M. Suhov, M. Kelbert (available online through Warwick Reading Lists)
4. Introductory Statistics, S.M. Ross.
5. Introduction to Probability and Statistics for Engineers and Scientists, S. M. Ross
Note that 13 are already available through "Talis Aspire link"
View reading list on Talis Aspire
Subject specific skills
Among others, ability to recognise sufficient/complete statistics, computing the Fisher information about a parameter of a given statistical model
Transferable skills
Among others, ability to derive methods for standard point estimation, hypothesis tests and confidence intervals in different setting that the statistical models considered in the module, e.g., for linear models or for stochastic processes.
Study time
Type  Required  Optional 

Lectures  30 sessions of 1 hour (25%)  2 sessions of 1 hour 
Tutorials  4 sessions of 1 hour (3%)  
Private study  62 hours (52%)  
Assessment  24 hours (20%)  
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.
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 D2
Weighting  Study time  

Multiple Choice Quiz 1  3%  4 hours 
A multiple choice quiz which will take place during the term that the module is delivered. 

Multiple Choice Quiz 2  3%  4 hours 
A multiple choice quiz which will take place during the term that the module is delivered. 

Multiple Choice Quiz 3  4%  4 hours 
A multiple choice quiz which will take place during the term that the module is delivered. 

Written assignment  10%  12 hours 
The assignment will contain a number of questions for which solutions and / or written responses will be required. The preparation and completion time noted below refers to the amount of time in hours that a wellprepared student who has attended lectures and carried out an appropriate amount of independent study on the material could expect to spend on this assignment. You will write your answers on paper and submit to the Statistics Support Office. 

2 hour examination (Summer)  80%  
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 R1
Weighting  Study time  

2 hour examination (September)  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 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:
 EC33815 Econometrics 2: Microeconometrics
 EC30615 Econometrics 2: Time Series
 ST40915 Medical Statistics with Advanced Topics
 ST33215 Medical Statistics
Antirequisite modules
If you take this module, you cannot also take:
 ST22012 Introduction to Mathematical Statistics
Courses
This module is Core for:
 Year 2 of USTAG302 Undergraduate Data Science
 Year 2 of USTAG304 Undergraduate Data Science (MSci)
 Year 2 of USTAG300 Undergraduate Master of Mathematics,Operational Research,Statistics and Economics
 Year 2 of USTAG1G3 Undergraduate Mathematics and Statistics (BSc MMathStat)
 Year 2 of USTAGG14 Undergraduate Mathematics and Statistics (BSc)
 Year 2 of USTAY602 Undergraduate Mathematics,Operational Research,Statistics and Economics
This module is Optional for:
 Year 3 of UMAAGL11 Undergraduate Mathematics and Economics
 Year 4 of UECAGL12 Undergraduate Mathematics and Economics (with Intercalated Year)
This module is Option list B for:
 Year 2 of UCSAG4G1 Undergraduate Discrete Mathematics
 Year 2 of UCSAG4G3 Undergraduate Discrete Mathematics