Parallel Statistical Computing for Statistical Inference

Abstract

Parallel statistical computing is an interesting and topical problem, driven by recent growth in the size of statistical data sets and the availability of network computing. This article reviews parallel statistical computing in regression analysis, nonparametric inference, and stochastic processes. In particular, we describe a range of methods including parallel multisplitting and the parallel QR method for least squares estimation in linear regression, parallel computing methods for nonlinear regression, the theoretical framework of the parallel bootstrap in nonparametric inference, preconditioner methods for Markov chains, and parallel Markov-chain Monte Carlo methods. We conclude that there is a need for further research in parallel statistical computing, and describe some of the important unsolved problems.

Parallel Bootstrap and Optimal Subsample Lengths in Smooth Function Models

“…(2.2) E i and R i is introduced by Guo (2008Guo ( , 2012 and Guo and Lin (2010). For each i, we construct matrices E i , associated with R i , as follows:…”

“…Several common block bootstrap methods have been introduced, such as the moving block bootstrap (Künsch, 1989;Lahiri, 1999), non-overlapping block bootstrap (Carlstein, 1986), stationary bootstrap (Nordman, 2009;Politis and Romano, 1994), circular block bootstrap , etc. The parallel bootstrap method discussed in the present study, has a special relationship with the block bootstrap methods, see Guo (2012). Some literature of the related bootstrap including Amaral, et al (2007), Andrews (2002), Buhlmann (2002) , Chernick (2007), Cheung, et al (2005), Davidson, et al (2008), Gentle, et al (2004), Kaufman, et al (1988), Hardle, et al (2003, Horowitz (2003), Lele (2003), Li (2008), Liu (1992), MacKinnon (2002), Nishiyama (2005), Paparodities (2009), Park (2003), and so on.…”

“…Tierney et al (2009) used parallel bootstrap to compute the prediction interval for the cost of a nuclear power plant. Guo (2012) gave the matrix form of parallel bootstrap by a projection matrix, and a graphical illumination by a figure.…”

Harnessing graphics processing units for improved neuroimaging statistics

“…(Zhu et al, 2007). GPUs can of course also be used to speedup these other non-parametric algorithms, see for example the review by Guo (2012).…”

“…See the work by Guo (2012) for a review on parallel statistical computing in regression analysis, nonparametric inference and stochastic processes. Suchard et al (2010) focused on how to use a GPU to accelerate Bayesian mixture models.…”