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When lattice bases are Markov bases

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  • Hazelton, Martin L.
  • Karimi, Masoud

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.

Suggested Citation

  • Hazelton, Martin L. & Karimi, Masoud, 2024. "When lattice bases are Markov bases," Statistics & Probability Letters, Elsevier, vol. 209(C).
    • Handle: RePEc:eee:stapro:v:209:y:2024:i:c:s0167715224000750
    DOI: 10.1016/j.spl.2024.110106
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    References listed on IDEAS

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    1. Martin L. Hazelton, 2001. "Estimation of origin–destination trip rates in Leicester," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 50(4), pages 423-433.
    2. Jason Sutherland & Carl James Schwarz, 2005. "Multi-List Methods Using Incomplete Lists in Closed Populations," Biometrics, The International Biometric Society, vol. 61(1), pages 134-140, March.
    3. repec:bla:biomet:v:71:y:2015:i:4:p:1070-1080 is not listed on IDEAS
    4. Robert L. Smith, 1984. "Efficient Monte Carlo Procedures for Generating Points Uniformly Distributed over Bounded Regions," Operations Research, INFORMS, vol. 32(6), pages 1296-1308, December.
    Full references (including those not matched with items on IDEAS)

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