Bayesian Statistics: An Introduction, 4th Edition

4.1 Hypothesis testing

4.1.1 Introduction

If preferred, the reader may begin with the example at the end of this section, then return to the general theory at the beginning.

4.1.2 Classical hypothesis testing

Most simple problems in which tests of hypotheses arise are of the following general form. There is one unknown parameter θ which is known to be from a set Θ, and you want to know whether or where

Usually, you are able to make use of a set of observations whose density depends on θ. It is convenient to denote the set of all possible observations by .

In the language of classical statistics, it is usual to refer to

and to

and to say that if you decide to reject H0 when it is true then ...