When lattice bases are Markov bases

Sampling the fibre comprising the solutions of a linear inverse problem for count data is an important practical problem. Connectivity of the sampler is guaranteed only if a Markov basis, defining a sufficiently rich variety of sampling directions, is available. Computation of a Markov basis is typi...

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Bibliographic Details
Published inStatistics & probability letters Vol. 209; p. 110106
Main Authors Hazelton, Martin L., Karimi, Masoud
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.06.2024
Subjects
Hit-and-run algorithm
Linear inverse problem
Markov chain mixing
MCMC
Mixed matrix
MCMC
Hit-and-run algorithm
Markov chain mixing
Linear inverse problem
Mixed matrix
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ISSN0167-7152
1879-2103
1879-2103
DOI10.1016/j.spl.2024.110106

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Summary:Sampling the fibre comprising the solutions of a linear inverse problem for count data is an important practical problem. Connectivity of the sampler is guaranteed only if a Markov basis, defining a sufficiently rich variety of sampling directions, is available. Computation of a Markov basis is typically challenging, and the mixing properties of the resulting sampler can be poor. However, for some problems a suitably chosen lattice basis will be a Markov basis. We provide an easily checkable condition for the existence of such a lattice Markov basis, and demonstrate that associated hit-and-run samplers will mix rapidly for uniform target distributions.
ISSN:0167-7152
1879-2103
1879-2103
DOI:10.1016/j.spl.2024.110106