https://hal-mines-paristech.archives-ouvertes.fr/hal-01102344Romary, ThomasThomasRomaryGEOSCIENCES - Centre de Géosciences - MINES ParisTech - École nationale supérieure des mines de Paris - PSL - Université Paris sciences et lettresInteracting Markov chains algorithms for Bayesian inversionHAL CCSD2014[MATH.MATH-ST] Mathematics [math]/Statistics [math.ST]Romary, Thomas2015-01-12 15:36:402021-11-17 12:31:202015-01-12 15:36:40enConference papers1Markov chains Monte-Carlo (MCMC) methods are popular togeneratesamples of virtually any distribution. They have been successfullyapplied in a wide range of problems over the years. However, theysuffer fromslow mixing when the target distribution is highdimensional and/ormultimodal. This is often the case in Bayesianinversion in the field ofgeosciences: the phenomenon under study(resistivity, pressure, porosity,...) isgenerally modeled by a randomfield (Gaussian related or not)discretizedovera large grid, and theforward problem may be highly nonlinear.Recently, the idea of making interact several Markov chains has beenexplored.This approach improves the mixing properties with respect toclassical singleMCMC. Furthermore, these algorithms can makeefficient use of large CPUclusters, with a computational cost similarto standardMCMC. In this work,we expose the principles ofinteractingMCMCmethods and show how todesign algorithms forBayesian inversion.These methods are illustrated on two examples fromgeosciences. Thefirst isthe history matching problem in reservoir engineering. Thisproblem terms tocondition a Gaussian random field, describing eitherthe permeability field or,whenthresholded, thelithofaciesdistribution in the reservoir, to fluid flowdata. A preliminary stepconsists inparameterizingthe Gaussian random field.A low rankrepresentationis generally used where the components can beselectedaccording to ad-hoccriteria. The second example is an application to first arrival travel time tomography which relies on an ad-hocparameterizationof the velocity field.