Information and Conditional Inference

Abstract

Consider non-Bayesian inference about a parameter of interest β in the presence of a nuisance parameter λ based on a statistic S = (T, A). If the conditional distribution of T given A does not depend on λ and if A contains no information about β in the presence of λ, then A is said to be ancillary for θ in the presence of λ, and inference about θ is to be based on the conditional distribution of T given A. This approach has been the basis for several definitions of ancillarity in the presence of a nuisance parameter; the definitions vary in how the phrase “no information about θ in the presence of λ” is interpreted. In this article a definition of ancillarity in the presence of a nuisance parameter is proposed using a definition of “no information about θ in the presence of λ” based on Bayesian inference.

Key Words:

• Ancillarity
• Bayesian inference
• Nuisance parameter