Abstract
This paper presents the parallel computing implementation of the MitISEM algorithm, labeled Parallel MitISEM. The basic MitISEM algorithm provides an automatic and flexible method to approximate a non-elliptical target density using adaptive mixtures of Student-t densities, where only a kernel of the target density is required. The approximation can be used as a candidate density in Importance Sampling or Metropolis Hastings methods for Bayesian inference on model parameters and probabilities. We present and discuss four canonical econometric models using a Graphics Processing Unit and a multi-core Central Processing Unit version of the MitISEM algorithm. The results show that the parallelization of the MitISEM algorithm on Graphics Processing Units and multi-core Central Processing Units is straightforward and fast to program using MATLAB. Moreover the speed performance of the Graphics Processing Unit version is much higher than the Central Processing Unit one.
Highlights
In several statistical and econometric models, the joint and marginal posterior distributions of the parameters have unknown analytical properties and non-elliptical Bayesian Highest Posterior Density (HPD) credible sets, see e.g. Berger (1985), Hoogerheide et al (2007b) and De Pooter et al (2008)
MitISEM is a general and automatic algorithm based on Importance Sampling (IS) for the approximation of a possibly non-elliptical target density using an adaptive mixture of Student-t densities as approximating or candidate density
The parallelization strategy is based on IS steps of the MitISEM algorithm, where we exploit the parallelization of the IS draws and functions of IS draws
Summary
In several statistical and econometric models, the joint and marginal posterior distributions of the parameters have unknown analytical properties and non-elliptical Bayesian Highest Posterior Density (HPD) credible sets, see e.g. Berger (1985), Hoogerheide et al (2007b) and De Pooter et al (2008). Hoogerheide et al (2012) proposed the Mixture of Student-t Distributions using Importance Sampling weighted Expectation Maximization (MitISEM) algorithm which is an automatic and flexible method to approximate a target posterior or predictive density which possibly has non-elliptical shapes that are not known a priori. Numerical efficiency in sampling methods is related to the efficient sample size or relative numerical efficiency, and to the possibility to perform the simulation process in a parallel fashion Unlike alternative methods such as the random walk MH or the Gibbs sampler, IS makes use of independent draws from the candidate density, which can be obtained from multiple-core processors or computer clusters. In all four cases considered, it is shown that parallel implementation of the MitISEM algorithm on GPUs provides substantial speed gains, inference is more accurate given the same amount of computation time.
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