Similarity-Driven Proposals for MCMC Algorithms on Discrete Spaces
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.
Cite
@article{arxiv.2605.21651,
title = {Similarity-Driven Proposals for MCMC Algorithms on Discrete Spaces},
author = {Luca Aiello and Raffaele Argiento and Alexandros Beskos and Maria De Iorio},
journal= {arXiv preprint arXiv:2605.21651},
year = {2026}
}