Massively parallel desktop computing capabilities now well within the reach of individual academics modify the environment for posterior simulation in fundamental and potentially quite advantageous ways. But to fully exploit these benefits algorithms that conform to parallel computing environments are needed. This paper presents a sequential posterior simulator designed to operate efficiently in this context. The simulator makes fewer analytical and programming demands on investigators, and is faster, more reliable, and more complete than conventional posterior simulators. The paper extends existing sequential Monte Carlo methods and theory to provide a thorough and practical foundation for sequential posterior simulation that is well suited to massively parallel computing environments. It provides detailed recommendations on implementation, yielding an algorithm that requires only code for simulation from the prior and evaluation of prior and data densities and works well in a variety of applications representative of serious empirical work in economics and finance. The algorithm facilitates Bayesian model comparison by producing marginal likelihood approximations of unprecedented accuracy as an incidental by-product, is robust to pathological posterior distributions, and provides estimates of numerical standard error and relative numerical efficiency intrinsically. The paper concludes with an application that illustrates the potential of these simulators for applied Bayesian inference.
We acknowledge useful comments from Nicolas Chopin, discussions with Ron Gallant, and tutorials in CUDA programming from Rob Richmond. We bear sole responsibility for the content of the paper. An earlier version of this work was posted with the title “Massively Parallel Sequential Monte Carlo for Bayesian Inference.” Geweke acknowledges partial financial support from Australian Research Council grants DP110104372 and DP130103356.
Durham, G. and Geweke, J. (2014), "Adaptive Sequential Posterior Simulators for Massively Parallel Computing Environments", Bayesian Model Comparison (Advances in Econometrics, Vol. 34), Emerald Group Publishing Limited, Bingley, pp. 1-44. https://doi.org/10.1108/S0731-905320140000034003
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