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Independent sampling for Bayesian normal conditional autoregressive models with OpenCL acceleration

Author

Listed:
  • Mary Kathryn Cowles

    () (The University of Iowa)

  • Stephen Bonett

    (University of Pennsylvania School of Nursing)

  • Michael Seedorff

    (The University of Iowa)

Abstract

Abstract A new computational strategy produces independent samples from the joint posterior distribution for a broad class of Bayesian spatial and spatiotemporal conditional autoregressive models. The method is based on reparameterization and marginalization of the posterior distribution and massive parallelization of rejection sampling using graphical processing units (GPUs) or other accelerators. It enables very fast sampling for small to moderate-sized datasets (up to approximately 10,000 observations) and feasible sampling for much larger datasets. Even using a mid-range GPU and a high-end CPU, the GPU-based implementation is up to 30 times faster than the same algorithm run serially on a single CPU, and the numbers of effective samples per second are orders of magnitude higher than those obtained with popular Markov chain Monte Carlo software. The method has been implemented in the R package CARrampsOcl. This work provides both a practical computing strategy for fitting a popular class of Bayesian models and a proof of concept that GPU acceleration can make independent sampling from Bayesian joint posterior densities feasible.

Suggested Citation

  • Mary Kathryn Cowles & Stephen Bonett & Michael Seedorff, 2018. "Independent sampling for Bayesian normal conditional autoregressive models with OpenCL acceleration," Computational Statistics, Springer, vol. 33(1), pages 159-177, March.
  • Handle: RePEc:spr:compst:v:33:y:2018:i:1:d:10.1007_s00180-017-0752-0
    DOI: 10.1007/s00180-017-0752-0
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    References listed on IDEAS

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    1. Lee, Duncan, 2013. "CARBayes: An R Package for Bayesian Spatial Modeling with Conditional Autoregressive Priors," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 55(i13).
    2. Reich, Brian J. & Hodges, James S. & Carlin, Bradley P., 2007. "Spatial Analyses of Periodontal Data Using Conditionally Autoregressive Priors Having Two Classes of Neighbor Relations," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 44-55, March.
    3. Hans K√ľnsch, 1994. "Robust priors for smoothing and image restoration," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 46(1), pages 1-19, March.
    4. J. Besag & D. Higdon, 1999. "Bayesian analysis of agricultural field experiments," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(4), pages 691-746.
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