Adaptive Sequential Posterior Simulators for Massively Parallel Computing Environments

Adaptive Sequential Posterior Simulators for Massively Parallel Computing Environments. Advances in Econometrics (Ivan Jeliazkov  and Dale J. Poirier, eds.). Bayesian Model Comparison (Advances in Econometrics, Volume 34) Emerald Group Publishing Limited. Chapter 1, 1-44. 

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. Sequential
Monte Carlo comes very close to this ideal whereas other approaches like Markov
chain Monte Carlo do not. This paper presents a sequential posterior simulator well
suited to this computing environment. 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 byproduct, 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.

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