https://hal-mines-paristech.archives-ouvertes.fr/hal-00505406Romary, ThomasThomasRomaryGEOSCIENCES - Centre de Géosciences - Mines Paris - PSL (École nationale supérieure des mines de Paris) - PSL - Université Paris sciences et lettresBayesian inversion by parallel interacting Markov chainsHAL CCSD2010Inverse problemBayesian inversionMCMCInteracting Markov chainsTemperingHistory matching[MATH.MATH-ST] Mathematics [math]/Statistics [math.ST][STAT.TH] Statistics [stat]/Statistics Theory [stat.TH]Nalon, Pascale2010-07-23 15:39:212022-10-22 05:09:562010-07-24 16:03:47enJournal articleshttps://hal-mines-paristech.archives-ouvertes.fr/hal-00505406/document10.1080/17415970903234620application/pdf1Markov chains Monte-Carlo (MCMC) methods are known to produce samples of virtually any distribution. They have already been widely used in the resolution of non-linear inverse problems where no analytical expression for the forward relation between data and model parameters is available, and where linearization is unsuccessful. However, in Bayesian inversion, the total number of simulations we can afford is highly related to the computational cost of the forward model. Hence, the complete browsing of the support of the posterior distribution is hardly performed at final time, especially when the posterior is high dimensional and/or multimodal. In the latter case, the chain may stay stuck in one of the modes. Recently, the idea of making interact several Markov chains at different temperatures has been explored. These methods improve the mixing properties of classical single MCMC. Furthermore, these methods can make efficient use of large CPU clusters, without increasing the global computational cost with respect to classical MCMC.