Conditional inference of Poisson models and information geometry: an ancillary review

Abstract

The Poisson distribution is a fundamental tool in categorical data analysis. This paper reviews conditional inference for the independent Poisson model. It is noted that the conditioning variable is not an ancillary statistic in the exact sense except in the case of the product multinomial sampling scheme, whereas two versions of the ancillary property hold in general. The ancillary properties justify the use of conditional inference, as first proposed by R. A. Fisher and subsequently discussed by many researchers. The mixed coordinate system developed in information geometry is emphasized as effective for the description of facts.