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

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 chai...

Full description

Saved in:
Bibliographic Details
Published in:Journal of the American Statistical Association 2014-07, Vol.109 (507), p.944-954
Main Authors: Herbei, Radu, Berliner, L. Mark
Format: Article
Language:English
Subjects:
Algorithms
Applications and Case Studies
Approximation
Bayesian analysis
Bayesian modeling
Bayesian theory
Bernoulli Hypothesis
Diffusion coefficient
Dirichlet problem
equations
Estimating techniques
Feynman-Kac formula
Fortran
Inverse problem
Inverse problems
Markov analysis
Markov chain
Markov chains
Ocean circulation
Oceans
Parallel computing
Partial differential equations
Random variables
Simulations
Statistics
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:1537-274X
0162-1459
1537-274X
DOI:10.1080/01621459.2014.914439