Module Identifier MA36010  
Academic Year 2000/2001  
Co-ordinator Mr D A Jones  
Semester Semester 1  
Pre-Requisite MA26010  
Course delivery Lecture   19 x 1hour lectures  
  Seminars / Tutorials   3 x 1hour example classes  
Assessment Exam   2 Hours (written examination)   100%  
  Resit assessment   2 Hours (written examination)   100%  

General description
This module re-examines the ideas of confidence intervals and hypothesis testing in Classical Inference and considers their interpretation more deeply. An alternative approach known as Bayesian Inference is introduced and developed, and consideration given to the formal description of prior information along with the way this information is modified in the presence of data. The concepts prior, posterior, predictive and preposterior are introduced. Applications to inferences about a (Normal) population mean and a (Binomial) probability parameter are discussed in detail, and extensions to other distributional families indicated. [The meanings and interpretations of the two approaches are discussed at length, along with the philosophical bases of other forms of statistical inference, such as the fiducial and likelihood approaches.]

To introduce the statistical ideas involved in designing efficient experiements and in the analysis of results.

Learning outcomes
On completion of this module, a student should be able to:

1. CLASSICAL INFERENCE: Basic aims and concepts. Point estimation. Interval estimation and hypothesis testing. Uniformly most powerful tests.
2. BAYESIAN INFERENCE: Thomas Bayes. Prior and posterior distributions. Odds ratios. Prior ignorance and prior knowledge. Quantification of knowledge. Bayesian confidence intervals. Predictive distributions. Predictive intervals. Preposterior distributions.
3. OTHER APPROACHES: Decision Theory. Fiducial Inference. Likelihood Inference. Information.

Reading Lists
** Essential Reading
V D Barnett. Comparative Staistical Inference. Wiley