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

• Main Authors: Radu Herbei, L. Mark Berliner
• Format: Article in Journal/Newspaper
• Language: unknown
• Subjects: South Atlantic Ocean
• Online Access: http://hdl.handle.net/10.1080/01621459.2014.914439

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.