Mathematical Sciences 804

# Statistical Inference

## Course Objective

Statistics is a very broad subject, with applications in a vast number of different fields. At heart it is an applied subject, but it would be unsatisfactory if each application had to be tackled separately, devising fresh techniques for each new problem. For this reason, a body of common statistical theory has been developed so that most problems can be tackled within the same framework.

There are three main subdivisions within statistics: efficient summarization, tabulation and graphical display of data; design of experiments; and statistical inference. Data summarization was historically the first major statistical activity. Experimental design is of crucial importance before data are collected. However, it is statistical inference which has seen most research and practical application in recent years, and it is inference which forms the direction of this course. There are three main types of inference, namely point estimation, interval estimation and hypothesis testing. In point estimation, for each unknown parameter of interest a single value is computed from the data, and used as an estimate of that parameter. Instead of producing a single estimate of a parameter, interval estimation provides a range of values which have a predetermined high probability of including the true, but unknown, value of the parameter. Hypothesis testing sets up specific hypotheses regarding the parameters of interest and assesses the plausibility of any specified hypothesis by seeing whether the observed data support or refute that hypothesis. Although hypothesis testing can often be artificial in the sense that none of the proposed hypotheses will be exactly correct (for example, exact equality of p for two species of birds is unlikely), it is often a convenient way to proceed and underlies a substantial part of scientific research.

The statistical community has during the last 10 years experienced a significant transformation stimulated by the technological developments in statistical computing environments, theoretical developments in stochastic based inference and simulation.

Students will learn how to use statistical software to facilitate the understanding of the foundations of multivariate analysis. Statistical packages will include SAS, S-Plus, and MatLab.

• Enrollees

## First Day's Handouts Syllabus & Review Notes

• Course Syllabus
• Probability Distributions
• Moment Generating Functions

## Class Notes....Updated and Corrected Frequently

• Binomial Expectation
• Geometric Expectation

## Assignments, Due Dates and Solutions to Previous Assignments (in Adobe Acrobat pdfs)

• MthSc804 Students Assignments:
• Problems I
• Problems II