Logic of Inferential Separation. Ancillarity and Sufficiency
Ole Eiler Barndorff-Nielsen · Wiley series in probability and statistics · 2014
The operations of margining to a sufficient statistic and conditioning on an ancillary statistic are the primary procedures leading to separate interference, interference on a parameter of interest based on only a part of the original model and data. This chapter discusses the logic relating to inferential separation and in particular to the general, intuitive notions of ancillarity and sufficiency. It presents mathematically defined concepts of ancillarity and sufficiency. A key problem in this connection is that of giving precise meaning to the notion that a certain part of the model and data does not contain any information with respect to the parameter of interest are also presented in the chapter. The chapter also states the principle of nonformation. It provides some results on the relations between conditional and unconditional plausibility functions.