Distance-reducing Markov bases for sampling from a discrete sample space

Abstract

We study Markov bases for sampling from a discrete sample space equipped with a convenient metric. Starting from any two states in the sample space, we ask whether we can always move closer by an element of a Markov basis. We call a Markov basis distance-reducing if this is the case. The particular metric we consider in this paper is the L₁-norm on the sample space. Some characterizations of L₁-norm-reducing Markov bases are derived.