Similarity-Driven Proposals for MCMC Algorithms on Discrete Spaces
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866918515659767808 |
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| author | Aiello, Luca Argiento, Raffaele Beskos, Alexandros De Iorio, Maria |
| author_facet | Aiello, Luca Argiento, Raffaele Beskos, Alexandros De Iorio, Maria |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_21651 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Similarity-Driven Proposals for MCMC Algorithms on Discrete Spaces Aiello, Luca Argiento, Raffaele Beskos, Alexandros De Iorio, Maria Methodology Computation 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. |
| title | Similarity-Driven Proposals for MCMC Algorithms on Discrete Spaces |
| topic | Methodology Computation |
| url | https://arxiv.org/abs/2605.21651 |