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.
Publié le : 2005-10-14
Classification:
contingency tables,
Graver bases,
Gröbner bases,
L_1-norm,
Markov chain Monte Carlo,
toric ideals
@article{1130077594,
author = {Takemura, Akimichi and Aoki, Satoshi},
title = {Distance-reducing Markov bases for sampling from a discrete sample space},
journal = {Bernoulli},
volume = {11},
number = {1},
year = {2005},
pages = { 793-813},
language = {en},
url = {http://dml.mathdoc.fr/item/1130077594}
}
Takemura, Akimichi; Aoki, Satoshi. Distance-reducing Markov bases for sampling from a discrete sample space. Bernoulli, Tome 11 (2005) no. 1, pp. 793-813. http://gdmltest.u-ga.fr/item/1130077594/