Hybrid nested sampling algorithm for Bayesian model selection applied to inverse subsurface flow problems

Ahmed H Elsheikh, Mary F Wheeler, Ibrahim Hoteit

Research output: Contribution to journalArticle

16 Citations (Scopus)

Abstract

A Hybrid Nested Sampling (HNS) algorithm is proposed for efficient Bayesian model calibration and prior model selection. The proposed algorithm combines, Nested Sampling (NS) algorithm, Hybrid Monte Carlo (HMC) sampling and gradient estimation using Stochastic Ensemble Method (SEM). NS is an efficient sampling algorithm that can be used for Bayesian calibration and estimating the Bayesian evidence for prior model selection. Nested sampling has the advantage of computational feasibility. Within the nested sampling algorithm, a constrained sampling step is performed. For this step, we utilize HMC to reduce the correlation between successive sampled states. HMC relies on the gradient of the logarithm of the posterior distribution, which we estimate using a stochastic ensemble method based on an ensemble of directional derivatives. SEM only requires forward model runs and the simulator is then used as a black box and no adjoint code is needed. The developed HNS algorithm is successfully applied for Bayesian calibration and prior model selection of several nonlinear subsurface flow problems.

Original languageEnglish
Pages (from-to)319-337
Number of pages19
JournalJournal of Computational Physics
Volume258
Early online date10 Oct 2013
DOIs
Publication statusPublished - Feb 2014

Keywords

  • Bayesian model comparison
  • Hybrid Monte Carlo
  • Nested sampling
  • Stochastic ensemble method
  • Subsurface flow models
  • Uncertainty quantification

ASJC Scopus subject areas

  • Computer Science Applications
  • Physics and Astronomy (miscellaneous)

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