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arXiv · 2605.21651

Similarity-Driven Proposals for MCMC Algorithms on Discrete Spaces

Luca Aiello·Raffaele Argiento·Alexandros Beskos·Maria De Iorio
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Abstract

Recent research has led to the development of MCMC algorithms with likelihood-informed proposals when targeting posterior distributions supported on discrete state spaces. Our work is placed within this field and puts forward a new MCMC methodology based upon similarity-driven proposals. Such proposals sway transitions towards states favored by the posterior via use of a data-driven measure of discrepancy between observations and the proposed model. Our approach can naturally cover classes of hierarchical models that involve both discrete variables and additional latent ones, without a requirement of integrating our the latter, in contrast to previous works in this field. The new algorithms are illustrated in simulation settings and in a involved real data scenario with a Dirichlet-Multinomial regression model.

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Luca Aiello, Raffaele Argiento, Alexandros Beskos, Maria De Iorio. 2026-05-20. Similarity-Driven Proposals for MCMC Algorithms on Discrete Spaces. https://arxiv.org/abs/2605.21651

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