There is a lack of methodological results to design efficient Markov chain Monte Carlo (MCMC) algorithms for statistical models with discrete-valued high-dimensional parameters. Motivated by this consideration, we propose a simple framework for the design of informedMCMCproposals (i.e., Metropolis–Hastings proposal distributions that appropriately incorporate local information about the target) which is naturally applicable to discrete spaces. Using Peskun-type comparisons of Markov kernels, we explicitly characterize the class of asymptotically optimal proposal distributions under this framework, which we refer to as locally balanced proposals. The resulting algorithms are straightforward to implement in discrete spaces and provide orders of magnitude improvements in efficiency compared to alternativeMCMCschemes, including discrete versions of Hamiltonian Monte Carlo. Simulations are performed with both simulated and real datasets, including a detailed application to Bayesian record linkage. A direct connection with gradient-basedMCMCsuggests that locally balanced proposals can be seen as a natural way to extend the latter to discrete spaces. Supplementary materials for this article are available online.

Informed proposals for local MCMC in discrete spaces

Zanella Giacomo
2020

Abstract

There is a lack of methodological results to design efficient Markov chain Monte Carlo (MCMC) algorithms for statistical models with discrete-valued high-dimensional parameters. Motivated by this consideration, we propose a simple framework for the design of informedMCMCproposals (i.e., Metropolis–Hastings proposal distributions that appropriately incorporate local information about the target) which is naturally applicable to discrete spaces. Using Peskun-type comparisons of Markov kernels, we explicitly characterize the class of asymptotically optimal proposal distributions under this framework, which we refer to as locally balanced proposals. The resulting algorithms are straightforward to implement in discrete spaces and provide orders of magnitude improvements in efficiency compared to alternativeMCMCschemes, including discrete versions of Hamiltonian Monte Carlo. Simulations are performed with both simulated and real datasets, including a detailed application to Bayesian record linkage. A direct connection with gradient-basedMCMCsuggests that locally balanced proposals can be seen as a natural way to extend the latter to discrete spaces. Supplementary materials for this article are available online.
2020
2019
Zanella, Giacomo
File in questo prodotto:
File Dimensione Formato  
Informed Proposals for Local MCMC in Discrete Spaces.pdf

non disponibili

Tipologia: Pdf editoriale (Publisher's layout)
Licenza: NON PUBBLICO - Accesso privato/ristretto
Dimensione 2.67 MB
Formato Adobe PDF
2.67 MB Adobe PDF   Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11565/4028550
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 68
  • ???jsp.display-item.citation.isi??? 58
social impact