Efficient Discretization‐Independent Bayesian Inversion of High‐Dimensional Multi‐Gaussian Priors Using a Hybrid MCMC

Discretization-invariant Bayesian Inversion and Besov Space Priors

Bayesian solution of an inverse problem for indirect measurement M = AU + E is considered, where U is a function on a domain of R. Here A is a smoothing linear operator and E is Gaussian white noise. The data is a realization mk of the random variable Mk = PkAU + PkE, where Pk is a linear, finite dimensional operator related to measurement device. To allow computerized inversion, the unknown is...

Efficient Sampling of Transpositions and Inverted Transpositions for Bayesian MCMC

The evolutionary distance between two organisms can be determined by comparing the order of appearance of orthologous genes in their genomes. Above the numerous parsimony approaches that try to obtain the shortest sequence of rearrangement operations sorting one genome into the other, Bayesian Markov chain Monte Carlo methods have been introduced a few years ago. The computational time for conv...

Inferring sound changes using Bayesian MCMC

In this paper we analyze dialect phonetic data using Bayesian Monte Carlo Markov Chain inference (MCMC), in recent years one of the most powerful and the most successful methods in molecular phylogeny for inferring the relationships between species. This method enables us to infer the historic relationships between the language varieties, but also to explore historical accounts of the sound cor...

Bayesian Tomographic Reconstruction Using Riemannian MCMC

This paper describes the use of Monte Carlo sampling for tomographic image reconstruction. We describe an efficient sampling strategy, based on the Riemannian Manifold Markov Chain Monte Carlo algorithm, that exploits the peculiar structure of tomographic data, enabling efficient sampling of the high-dimensional probability densities that arise in tomographic imaging. Experiments with positron ...

A Bayesian Estimation of Building Shape Using MCMC