Interacting Markov chains algorithms for Bayesian inversion

Thomas Romary (1)

1 GEOSCIENCES - Centre de Géosciences

Markov chains Monte - Carlo ( MCMC ) methods are popular to generate samples of virtually any distribution. They have been successfully applied in a wide range of problems over the years. However, they suffer from slow mixing when the target distribution is high dimensional and/or multimodal . This is often the case in Bayesian inversion in the field of geosciences : the phenomenon under stu dy ( resistivity , pressure, porosity,...) is generally modeled by a random field (Gaussian related or not) discretized over a large grid, and the forward problem may be highly nonlinear. Recently, the idea of making interact several Markov chains has been explored. This approach improves the mixing properties with respect to classical single MCMC . Furthermore, these algorithms can make efficient use of large CPU clusters, with a computational cost similar to standard MCMC . In this work, we expose the princ iples of interacting MCMC methods and show how to design algorithms for Bayesian inversion. These methods are illustrated on two examples from geosciences . The first is the history matching problem in reservoir engineering. This problem terms to conditio n a Gaussian random field, describing either the permeability field or, when thresholded , the lithofacies distribution in the reservoir, to fluid flow data. A preliminary step consists in parameterizing the Gaussian random field. A low rank representation is generally used where the components can be selected according to ad - hoc criteria. The second example is an application to first arrival travel time tomography which relies on an ad - hoc parameterization of the velocity field.

Domaines: Statistiques [math.ST]

Thomas Romary. Interacting Markov chains algorithms for Bayesian inversion. GRF - Sim workshop : Simulation of Gaussian and related Random Fields, Nov 2014, Bern, Switzerland. ⟨hal-01102344⟩