A lattice path method for exact conditional inference.

摘要

This thesis outlines a methodology for completely enumerating the outcome space of a discrete exponential family conditional on linear sufficient statistics. We start by constructing a rectangular lattice that contains all of the points in the conditional outcome space. We then extend the idea of Gray code paths to obtain an efficient method for searching the lattice and generating a list of possible outcomes in the conditional outcome space. To conclude, we discuss proposals for integrating the methodology into other existing algorithms. Examples will include contingency tables, the conditional bootstrap, and conditional logistic regression.