Sampling informative/complex a priori probability distributions using Gibbs sampling assisted by sequential simulation

Thomas Mejer Hansen, Klaus Mosegaard, Knud Skou Cordua

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Abstract

Markov chain Monte Carlo methods such as the Gibbs sampler and the Metropolis algorithm can be used to sample the solutions to non-linear inverse problems. In principle these methods allow incorporation of arbitrarily complex a priori information, but current methods allow only relatively simple priors to be used. We demonstrate how sequential simulation can be seen as an application of the Gibbs sampler, and how such a Gibbs sampler assisted by sequential simulation can be used to perform a random walk generating realizations of a relatively complex random function. We propose to combine this algorithm with the Metropolis algorithm to obtain an efficient method for sampling posterior probability densities for nonlinear inverse problems.
Original languageEnglish
Title of host publicationIAMG Extended Abstracts
Number of pages8
Publication date2010
Publication statusPublished - 2010
Event14th Annual Conference of the International Association for Mathematical Geosciences - Budapest, Hungary
Duration: 29 Aug 20102 Sep 2010
Conference number: 14
http://www.iamg2010-budapest.hu/

Conference

Conference14th Annual Conference of the International Association for Mathematical Geosciences
Number14
CountryHungary
CityBudapest
Period29/08/201002/09/2010
Internet address

Keywords

  • Monte Carlo
  • Prior
  • Sequential simulation
  • Inverse problem

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