# 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, 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.

Recommended

• Morris DeGroot and Mark J. Schervish, Probability and Statistics, 3rd Ed,. Addison Wesley, 2002
• John A. Rice, Mathematical Statistics and Data Analysis, 2nd Ed., Duxbery Press, 2007

Unit code: MATH20800
Level of study: I/5
Credit points: 20
Teaching block (weeks): 1 (1-12)
Lecturer: Dr Anthony Lee & Dr Skevi Michael

## Pre-requisites

MATH10013 Probability and Statistics

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
• 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.