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Statistics 2 (MATH 20800)

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Administrative Information

  1. Unit number and title: MATH 20800 Statistics 2
  2. Level: I/5
  3. Credit point value: 20 credit points
  4. Year: 12/13
  5. First Given in this form: 1999/2000
  6. Unit Organiser: Christophe Andrieu
  7. Lecturer: Prof. Christophe Andrieu
  8. Teaching block: 1
  9. Prerequisites: MATH11300 Probability 1 and MATH 11400 Statistics 1

Unit aims

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

Unit homepage: http://www.maths.bris.ac.uk/~maxca/stats2/

 

General Description of the Unit

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 the Level 4 Probability & Statistics material, and is a prerequisite for some statistics units at Levels 6 and 7, namely Bayesian Modelling A, Generalised Linear Models, and Theory of Inference, and desirable for Linear Models.

Teaching Methods

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

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.

Assessment Methods

The final assessment mark will be made up as follows:

  • 20% from two practical assignments
  • 80% from a 2½-hour examination in ***April*** (details below).

Practical Assignments

Three computer practicals are set (in roughly the fourth, seventh and tenth weeks), and the second and third count 10% each to the final assessed mark.

Deadlines: Late submission of practicals will be penalised in line with the Faculty of Science policy at http://www.bristol.ac.uk/science/undergraduates/penalties.html

Examination

The examination in April consists of one 2 ½-hour paper consisting of FIVE questions; you should attempt FOUR. If you attempt more than four, your best four answers will be used for assessment. Candidates may bring one A4 double-sided sheet of notes into the exam. Calculators of an approved type (non-programmable, no text facility) are allowed. From 2012-13 ONLY calculators carrying a 'Faculty of Science approved' sticker will be allowed in the examination room. Statistical tables will be provided.

Award of Credit Points

To be awarded the credit points for this unit you must normally pass the unit, i.e. you must achieve an assessment mark of at least 40.

Transferable Skills

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

Texts

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).

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.