When lattice bases are Markov bases

Martin L. Hazelton and Masoud Karimi

Statistics & Probability Letters, 2024, vol. 209, issue C

Abstract: 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.

Keywords: Hit-and-run algorithm; MCMC; Linear inverse problem; Markov chain mixing; Mixed matrix (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1016/j.spl.2024.110106

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