AS2A-Statistical Theory and Methods
Module Provider: Applied Statistics
Number of credits: 20 [10ECTS credits]
Level:
5
Terms in which taught: Autumn, Spring and Summer
Module Convenor: Dr
HJ
Kimber
Pre-requisites: AS1A AS1B
Co-requisites:
Modules excluded:
Module version for: 2009/0
Email: h.j.kimber@reading.ac.uk
Aims:
This module develops the theoretical foundations of methods used in statistical practice. Many of these methods assume or are motivated by statistical models. The first part of this module will introduce the basic ideas of probability and probabilistic models, and will show how these models can be used to answer statistical questions. The following topics will be discussed: probability, joint and conditional distributions of random variables; properties of the normal, lognormal, chi-squared, t and F distributions, and the relationships between these distributions and with other distributions.
In the second part of this module, some fundamental methods of statistical analysis are introduced. The method of moments and the method of maximum likelihood are considered for point estimation of parameters, and properties of estimators, such as bias and consistency, are described. Interval estimation and hypothesis testing are also developed.
Assessable learning outcomes:
On completion of this module students will have acquired:
Additional outcomes:
Outline content:
Introduction: basic probability; case study; random variables.
Moments: definition, moment generating functions, manipulation of distributions.
Bivariate Distributions: introduction, marginal distributions; conditional distribution; independence; bivariate normal distribution and its properties.
Transformations of Variables: univariate and bivariate case.
Standard Distributions: review of common discrete distributions, normal, lognormal, gamma, chi-square, t- and F-distributions.
Introduction to inference.
Point estimators: bias, mean square error, sufficiency, minimum variance unbiased estimators.
Estimation methods: method of moments, maximum likelihood.
Confidence intervals: likelihood technique, central limit theorem.
Hypothesis testing: basic principles; likelihood ratio test.
Recommended reading:
Beaumont, G P (1980). Intermediate Mathematical Statistics, Chapman & Hall.
Bulmer, M G (1979). Principles of Statistics, 2nd edition, Dover.
Hoel, P.G. (1984). Introduction to Mathematical Statistics, 5th edition, Wiley.
Hogg, R V and Tanis, E A (1993). Probability and Statistical Inference.
4th edition, Macmillan.
Hogg, R V and Tanis, E A (2008). A Brief Course in Mathematical Statistics, Prentice Hall.
Brief description of teaching and learning methods:
Lectures supported by tutorials.
Contact hours:
| Autumn | Spring | Summer | |
| Lectures | 16 | 16 | |
| Tutorials/seminars | 2 | 2 | 4 |
| Practicals | |||
| Other contact (eg study visits) | 2 | 2 | |
| Total hours | 20 | 20 | 4 |
| Number of essays or assignments | 2 | 2 | |
| Other (eg major seminar paper) | 2 class tests | 2 class tests |
Assessment:
Coursework
Four assignments and four class tests
Relative percentage of coursework: 40%
Penalties for late submission:
Penalties for late submission of course work will be in accordance with University policy.
Examination:
One paper of three hours duration
Relative percentage of examination: 60%
Requirement for a Pass
An overall mark of at least 40%
Reassessment arrangements
One examination paper of 3 hours duration
Last updated: 23 November 2009