When lattice bases are Markov bases - Hazelton, Martin L.; Karimi, Masoud (Statistics & probability letters, 2024)
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.