Parallel computations for Metropolis Markov chains with Picard maps
Authors
Research Topics
Paper Information
-
Journal:
Biometrika -
DOI:
10.1093/biomet/asag022 -
Published:
March 31, 2026 -
Added to Tracker:
Apr 02, 2026
Abstract
Abstract We develop parallel algorithms for simulating zeroth-order (also known as gradient-free) Metropolis Markov chains based on the Picard map. For random-walk Metropolis Markov chains targeting log-concave distributions π on ℝd, our algorithm generates samples close to π in O(d) parallel iterations using O(d) processors, thereby speeding up the convergence of the corresponding sequential implementation by a factor (d). Furthermore, a modification of our algorithm generates samples from an approximate measure πr in O(1) parallel iterations and O(d) processors. We empirically assess the performance of the proposed algorithms in high-dimensional regression problems, an epidemic model where the gradient is unavailable and a real-word application in precision medicine. Our algorithms are straightforward to implement and may constitute a useful tool for practitioners seeking to sample from a prescribed distribution π using only pointwise evaluations of π and parallel computing.
Author Details
G Zanella
AuthorS Grazzi
AuthorResearch Topics & Keywords
Machine Learning
Research AreaBayesian Statistics
Research AreaCitation Information
APA Format
G Zanella
&
S Grazzi
(2026)
.
Parallel computations for Metropolis Markov chains with Picard maps.
Biometrika
, 10.1093/biomet/asag022.
BibTeX Format
@article{paper1102,
title = { Parallel computations for Metropolis Markov chains with Picard maps },
author = {
G Zanella
and S Grazzi
},
journal = { Biometrika },
year = { 2026 },
doi = { 10.1093/biomet/asag022 },
url = { https://doi.org/10.1093/biomet/asag022 }
}