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

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  • Radu Herbei
  • L. Mark Berliner

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.

Suggested Citation

  • Radu Herbei & L. Mark Berliner, 2014. "Estimating Ocean Circulation: An MCMC Approach With Approximated Likelihoods via the Bernoulli Factory," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(507), pages 944-954, September.
    • Handle: RePEc:taf:jnlasa:v:109:y:2014:i:507:p:944-954
    DOI: 10.1080/01621459.2014.914439
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    References listed on IDEAS

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    2. Marc C. Kennedy & Anthony O'Hagan, 2001. "Bayesian calibration of computer models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(3), pages 425-464.
    3. Paul Fearnhead & Dennis Prangle, 2012. "Constructing summary statistics for approximate Bayesian computation: semi-automatic approximate Bayesian computation," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 74(3), pages 419-474, June.
    4. Christophe Andrieu & Arnaud Doucet & Roman Holenstein, 2010. "Particle Markov chain Monte Carlo methods," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(3), pages 269-342, June.
    5. RADU HERBEI & IAN W. McKEAGUE, 2009. "Hybrid Samplers for Ill‐Posed Inverse Problems," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(4), pages 839-853, December.
    6. Cron, Andrew J. & West, Mike, 2011. "Efficient Classification-Based Relabeling in Mixture Models," The American Statistician, American Statistical Association, vol. 65(1), pages 16-20.
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    Cited by:

    1. Cole, D. Austin & Gramacy, Robert B. & Ludkovski, Mike, 2022. "Large-scale local surrogate modeling of stochastic simulation experiments," Computational Statistics & Data Analysis, Elsevier, vol. 174(C).

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