Estimating Ocean Circulation: An MCMC Approach With Approximated Likelihoods via the Bernoulli Factory

Radu Herbei and L. Mark Berliner

Journal of the American Statistical Association, 2014, vol. 109, issue 507, 944-954

Abstract: We provide a Bayesian analysis of ocean circulation based on data collected in the South Atlantic Ocean. The analysis incorporates a reaction-diffusion partial differential equation that is not solvable in closed form. This leads to an intractable likelihood function. We describe a novel Markov chain Monte Carlo approach that does not require a likelihood evaluation. Rather, we use unbiased estimates of the likelihood and a Bernoulli factory to decide whether or not proposed states are accepted. The variates required to estimate the likelihood function are obtained via a Feynman-Kac representation. This lifts the common restriction of selecting a regular grid for the physical model and eliminates the need for data preprocessing. We implement our approach using the parallel graphic processing unit (GPU) computing environment.

Date: 2014
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DOI: 10.1080/01621459.2014.914439

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