THE ROLES OF CONDITIONING IN INFERENCE

This paper reviews the use of sufficient and ancillary statistics in c onstructing conditional distributions for inference about a parameter. Special emphasis is given to recent developments in accurate approxim ation of densities, distribution functions and likelihood functions, a nd to the role of conditioning in these approximations. Exact conditio nal or marginal inference is available for essentially two classes of models, exponential family models and transformation family models. Th e approximations are very useful for practical implementation of these exact results. The form of the approximations suggests methods for in ference in more general families.