arXiv subjects

Guillermina Senn

Publications and source records attributed to Guillermina Senn.

3 recordsLinked to original sources

arXiv2026

On the mixing properties of some preconditioned multiproposal Markov Chain Monte Carlo algorithms

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.

math.ST↗

arXiv2026

Multiproposal Elliptical Slice Sampling

We introduce Multiproposal Elliptical Slice Sampling, a self-tuning multiproposal Markov chain Monte Carlo method for Bayesian inference with Gaussian priors. Our method generalizes the Elliptical Slice Sampling algorithm by 1) allowing multiple candidate proposals to be sampled in parallel at each self-tuning step, and 2) basing the acceptance step on a distance-informed transition matrix that can favor proposals far from the current state. This allows larger moves in state space and faster self-tuning, at essentially no additional wall clock time for expensive likelihoods, and results in improved mixing. We additionally provide theoretical arguments and experimental results suggesting dimension-robust mixing behavior, making the algorithm particularly well suited for Bayesian PDE inverse problems.

stat.CO↗

arXiv2026

Bayesian Semi-Blind Deconvolution at Scale

Blind image deconvolution refers to the problem of simultaneously estimating the blur kernel and the true image from a set of observations when both the blur kernel and the true image are unknown. Sometimes, additional image and/or blur information is available and the term semi-blind deconvolution (SBD) is used. We consider a recently introduced Bayesian conjugate hierarchical model for SBD, formulated on an extended cyclic lattice to allow a computationally scalable Gibbs sampler. In this article, we extend this model to the general SBD problem, rewrite the previously proposed Gibbs sampler so that operations are performed in the Fourier domain whenever possible, and introduce a new marginal Hamiltonian Monte Carlo (HMC) blur update, obtained by analytically integrating the blur-image joint conditional over the image. The cyclic formulation combined with non-trivial linear algebra manipulations allows a Fourier-based, scalable HMC update, otherwise complicated by the rigid constraints of the SBD problem. Having determined the padding size in the cyclic embedding through a numerical experiment, we compare the mixing and exploration behaviour of the Gibbs and HMC blur updates on simulated data and on a real geophysical seismic imaging problem where we invert a grid with $300\times50$ nodes, corresponding to a posterior with approximately $80,000$ parameters.

stat.CO↗