Preprint
On the mixing properties of some preconditioned multiproposal Markov Chain Monte Carlo algorithms
ArXiv.org
05 Jul 2026
Abstract
We study two recently discovered "dimension-free" Monte Carlo sampling algorithms, the multiproposal and multiple-try preconditioned Crank-Nicolson methods (mpCN and MTpCN). These methods were designed to address certain non-parametric (i.e. infinite-dimensional) sampling problems, defined relative to a Gaussian reference measure, by combining proposal and acceptance mechanisms that take non-trivial advantage of parallel computing architectures. We provide the first rigorous analysis of both algorithms, establishing exponential convergence to the target measure through the weak Harris framework, both for a finite number of proposals and in the infinite-proposal limit. The resulting mixing rates are independent of the dimension and uniform in the number of proposals, and apply to targets with bounded, Lipschitz log-likelihoods, without requiring convexity. At the center of the analysis are two new coupling constructions, together with analytical tools of independent interest, yielding Wasserstein contraction estimates,L²spectral gaps, and associated statistical guarantees (laws of large numbers, central limit theorems, and non-asymptotic concentration bounds) for the corresponding Monte Carlo estimators. These theoretical results are complemented by a numerical study on benchmark problems with complex posterior geometries and high-dimensional structure, comparing mpCN and MTpCN against standard pCN and independent parallel-chain implementations. The experiments indicate that the multiproposal methods can offer a shorter warm-up phase and greater robustness to the choice of tuning parameters as the number of proposals grows.
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Details
- Title
- On the mixing properties of some preconditioned multiproposal Markov Chain Monte Carlo algorithms
- Creators
- Giulia Carigi - Indiana UniversityNathan E Glatt-Holtz - Indiana UniversityCecilia F Mondaini - Drexel UniversityGuillermina Senn - Norwegian University of Science and Technology
- Publication Details
- ArXiv.org
- Resource Type
- Preprint
- Language
- English
- Academic Unit
- Mathematics
- Other Identifier
- 991022195653304721