ST219-12 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. Neyman-Pearson Lemma. P-value.
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 1-3 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 (88%) | 2 sessions of 1 hour |
| Tutorials | 4 sessions of 1 hour (12%) | |
| Total | 34 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 D3
| Weighting | Study time | Eligible for self-certification | |
|---|---|---|---|
| Multiple Choice Quiz 1 | 3% | 4 hours | Yes (waive) |
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A multiple choice quiz which will take place during the term that the module is delivered. |
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| Multiple Choice Quiz 2 | 3% | 4 hours | Yes (waive) |
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A multiple choice quiz which will take place during the term that the module is delivered. |
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| Multiple Choice Quiz 3 | 4% | 4 hours | Yes (waive) |
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A multiple choice quiz which will take place during the term that the module is delivered. |
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| Written assignment | 10% | 12 hours | Yes (extension) |
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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 well-prepared 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. |
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| In-person Examination | 80% | No | |
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The examination paper will contain four questions, of which the best marks of THREE questions will be used to calculate your grade.
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Assessment group R2
| Weighting | Study time | Eligible for self-certification | |
|---|---|---|---|
| In-person Examination - Resit | 100% | No | |
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The examination paper will contain four questions, of which the best marks of THREE questions will be used to calculate your grade.
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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.
Post-requisite modules
If you pass this module, you can take:
- EC306-15 Econometrics 2: Time Series
- EC338-15 Econometrics 2: Microeconometrics
- ST404-15 Applied Statistical Modelling
- ST409-15 Medical Statistics with Advanced Topics
- ST332-15 Medical Statistics
Anti-requisite modules
If you take this module, you cannot also take:
- ST220-12 Introduction to Mathematical Statistics
Courses
This module is Core for:
- Year 2 of USTA-G305 Undergraduate Data Science (MSci) (with Intercalated Year)
- Year 2 of USTA-G300 Undergraduate Master of Mathematics,Operational Research,Statistics and Economics
This module is Optional for:
- Year 3 of UMAA-GL11 Undergraduate Mathematics and Economics
- Year 4 of UECA-GL12 Undergraduate Mathematics and Economics (with Intercalated Year)