Conditional Inference

Abstract

The present chapter has a somewhat different character from the preceding ones. It is concerned with problems regarding the proper choice and interpretation of tests and confidence procedures, problems which—despite a large literature—have not found a definitive solution. The discussion will thus be more tentative than in earlier chapters, and will focus on conceptual aspects more than on technical ones. Consider the situation in which either the experiment ${\mathcal {E}}$ of observing a random quantity X with density $p_{\theta }$ (with respect to $\mu$) or the experiment ${\mathcal {F}}$ of observing an X with density $q_{\theta }$ (with respect to $\nu$) is performed with probability p and $q=1-p$ respectively.