Introduction

Suppose you wish to represent uncertainty about an empirical quantity by a probability distribution. If you have some empirical data directly relevant to the quantity, you may want to use statistical methods to help select a distribution and estimate its parameters. If you feel you know little or nothing about the quantity before seeing the observations, you may want to use standard classical statistical methods. If you feel you do have some prior opinions about the quantity, based on whatever knowledge and reasoning, you may want to combine these prior opinions with the observed evidence and use Rayesian updating methods to obtain posterior distributions. If you have no directly relevant observations of the quantity, then you may wish to express your opinion directly by a subjective probability distribution. We discuss methods for doing this Chapters 6 and 7, but before getting to them it will be useful to review some of the basic properties of probability distributions.

The methods presented in this chapter cover a range of useful procedures in probability and statistics. The discussion is provided as a review and a compact reference and is not intended to replace a full course or text on the subject, many of which are available (e.g., Benjamin and Cornell, 1970; Ang and Tang, 1975; DeGroot, 1975).