In this note, we propose a general method to find cuts for a contingency table. Useful cuts are, in many cases, statistics S-sufficient for the nuisance parameter and S-ancillary for the parameter of interest. In general, cuts facilitate a strong form of parameter separation known to be useful...

This note provides some equivalence results across the partition lattice, the monotypic lattice, and the subset lattice, for decomposing a multivariate density.

Most work on conditionally specified distributions has focused on approaches that operate on the probability space, and the constraints on the probability space often make the study of their properties challenging. We propose decomposing both the joint and conditional discrete distributions into...

We provide lattice decompositions for multivariate distributions. The lattice decompositions reveal the structural relationship between the Lancaster/Bahadur model and the model of Streitberg (Ann. Statist. 18 (1990) 1878). For multivariate categorical data, the decompositions allows modeling...