{"ID":5937782,"CreatedAt":"2026-07-07T03:14:33.014478982Z","UpdatedAt":"2026-07-08T19:06:43.087480983Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2607.04466","arxiv_id":"2607.04466","title":"On the mixing properties of some preconditioned multiproposal Markov Chain Monte Carlo algorithms","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, $L^2$ spectral 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.","short_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 refere...","url_abs":"https://arxiv.org/abs/2607.04466","url_pdf":"https://arxiv.org/pdf/2607.04466v1","authors":"[\"Giulia Carigi\",\"Nathan E. Glatt-Holtz\",\"Cecilia F. Mondaini\",\"Guillermina Senn\"]","published":"2026-07-05T19:20:44Z","proceeding":"math.ST","tasks":"[\"math.ST\",\"math.PR\",\"stat.CO\"]","methods":"[]","has_code":false}