# Statistics 2

## Unit aims

To develop the theory and practice of basic statistical inference, and statistical calculation.

## Unit description

Statistics is about inference under uncertainty, ie in situations where deductive logic cannot give a clearcut answer. In these situations our decisions must be assessed in terms of their probabilities of being correct or incorrect. Such decisions include estimating the parameters of a statistical model, making predictions, and testing hypotheses. It is often possible to identify 'optimal' or at least good decisions, and Statistics is about these decisions, and knowing where they apply. A thorough grounding in Statistics, as provided by this course, is crucial not only for anyone contemplating a career in finance or industry, but also for scientists and policymakers, as we realise that some of the biggest issues, like climate change, natural hazards, or health, are also some of the most uncertain.

## Relation to other units

This unit develops Level 4 probability and statistics material, and is a prerequisite for some statistics units at Levels 6 and 7, namely Bayesian Modelling A, Linear and Generalised Linear Models, and Financial Time Series.

## Learning objectives

By the end of the course the students should be able to:

• Design powerful tests for statistical hypotheses, and understand both the power and the limitations of such tests.
• Derive estimators of statistical parameters using Maximum Likelihood (ML), including assessment of their properties and measures of uncertainty.
• Apply the Bayesian approach to estimation, prediction, and hypothesis testing, in the special case of conjugate analysis.
• Use asymptotic arguments to understand the convergence of ML and Bayesian methods for large samples.
• Choose appropriate statistical models for many common situations, and validate them.
• Use the statistical computing enviroment R for routine statistical calculations, and plotting.

## Transferable skills

A clearer understanding of the logical constraints on inference; facility with the R environment for statistical computing.

## Syllabus

• Principles of Frequentist inference
• Maximum likelihood estimation: general and asymptotic properties, Fisher information, optimality, point prediction
• Hypothesis tests and confidence sets
• New distributions: Beta, Weibull, Hypergeometric, Pareto, Multinomial
• Bayesian statistics: principles, Bayes's theorem, point prediction, conjugate analysis, asymptotic properties.
• Statistical computing in R: implementation of techniques from throughout the course.

The main text is:

Rice, J. A. 1995 Mathematical statistics and data analysis, Duxbery Press, 2nd Ed.

This is now out in a 3rd edition, either one will be fine, but references will be to the second edition.

Also informative and useful:

Morris H, DeGroot, and Mark J Schervish. 2002 Probability & Statistics, Addison Wesley, 3rd Ed.

Other reading will be given on the unit homepage (see Unit Aims).

Unit code: MATH20800
Level of study: I/5
Credit points: 20
Teaching block (weeks): 2 (13-24)
Unit director: Anthony Lee
Lecturer: Anthony Lee

## Pre-requisites

MATH11300 Probability 1 and MATH11400 Statistics 1

None

## Methods of teaching

Three lectures a week, and one problems class. Weekly homework, and weekly/fortnightly office hours for statistics and for computing.

## Methods of Assessment

The pass mark for this unit is 40.

The final mark is calculated as follows:

• 80% from a 2 hour 30 minute exam in May/June
• 20% from two practical assignments*

*Three computer practical sessions are set in roughly the 4th, 7th & 10th weeks. The 2nd and 3rd count 10% each to the final unit mark.

NOTE: Calculators of an approved type (non-programmable, no text facility) are allowed.

Candidates may bring into the examination room one A4 double-sided sheet of notes.

Statistical tables will be provided.

For information resit arrangements, please see the re-sit page on the intranet.

Please use these links for further information on relative weighting and marking criteria.

Further exam information can be found on the Maths Intranet.