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2 results on '"Calderhead, Ben"'

1. Population MCMC methods for history matching and uncertainty quantification.

Author

Mohamed, Linah, Calderhead, Ben, Filippone, Maurizio, Christie, Mike, and Girolami, Mark

Subjects
*MONTE Carlo method, *MARKOV processes, *OIL reservoir engineering, *DISTRIBUTION (Probability theory), *COMPUTATIONAL biology
Abstract

This paper presents the application of a population Markov Chain Monte Carlo (MCMC) technique to generate history-matched models. The technique has been developed and successfully adopted in challenging domains such as computational biology but has not yet seen application in reservoir modelling. In population MCMC, multiple Markov chains are run on a set of response surfaces that form a bridge from the prior to posterior. These response surfaces are formed from the product of the prior with the likelihood raised to a varying power less than one. The chains exchange positions, with the probability of a swap being governed by a standard Metropolis accept/reject step, which allows for large steps to be taken with high probability. We show results of Population MCMC on the IC Fault Model-a simple three-parameter model that is known to have a highly irregular misfit surface and hence be difficult to match. Our results show that population MCMC is able to generate samples from the complex, multi-modal posterior probability distribution of the IC Fault model very effectively. By comparison, previous results from stochastic sampling algorithms often focus on only part of the region of high posterior probability depending on algorithm settings and starting points. [ABSTRACT FROM AUTHOR]

Published
2012
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2. Estimating Bayes factors via thermodynamic integration and population MCMC

Author

Calderhead, Ben and Girolami, Mark

Subjects
*ESTIMATION theory, *BAYESIAN analysis, *THERMODYNAMICS, *MARKOV processes, *MONTE Carlo method, *MAXIMUM likelihood statistics, *NONLINEAR differential equations, *COMPARATIVE studies
Abstract

Abstract: A Bayesian approach to model comparison based on the integrated or marginal likelihood is considered, and applications to linear regression models and nonlinear ordinary differential equation (ODE) models are used as the setting in which to elucidate and further develop existing statistical methodology. The focus is on two methods of marginal likelihood estimation. First, a statistical failure of the widely employed Posterior Harmonic Mean estimator is highlighted. It is demonstrated that there is a systematic bias capable of significantly skewing Bayes factor estimates, which has not previously been highlighted in the literature. Second, a detailed study of the recently proposed Thermodynamic Integral estimator is presented, which characterises the error associated with its discrete form. An experimental study using analytically tractable linear regression models highlights substantial differences with recently published results regarding optimal discretisation. Finally, with the insights gained, it is demonstrated how Population MCMC and thermodynamic integration methods may be elegantly combined to estimate Bayes factors accurately enough to discriminate between nonlinear models based on systems of ODEs, which has important application in describing the behaviour of complex processes arising in a wide variety of research areas, such as Systems Biology, Computational Ecology and Chemical Engineering. [Copyright &y& Elsevier]

Published
2009
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