Estimating ocean circulation: : an MCMC approach with approximated likelihoods via the bernoulli factory
JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION(2014)
摘要
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.
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关键词
Parallel computing,Feynman-Kac formula,Inverse problem,Bayesian modeling
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