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Original Articles

Parallel Statistical Computing for Statistical Inference

Pages 536-565 | Published online: 10 Aug 2012

References

  • Adams , N. M. , Kirby , S. P. J. , Harris , P. and Clegg , D. B. 1996 . A review of parallel processing for statistical computation . Statist. Computing , 6 : 37 – 49 .
  • Arnal , J. , Migallon , V. , Penades , J. and Szyld , D. B. 2008 . Newton additive and multiplicative Schwarz iterative methods . IMA J. Numer. Anal , 28 : 143 – 161 .
  • Azzini , I. , Girardi , R. and Ratto , M. Parallelization of Matlab codes under Windows platform for Bayesian estimation: a dynare application . Working Paper 1, Euro-area Economy Modelling Centre . Available at: http://eemc.jrc.ec.europa.eu/
  • Björck , A. 1996 . Numerical methods for least squares problems , Philadelphia : SIAM .
  • Beddo , V. 2002 . Applications of parallel programming in statistics , Los Angeles : PhD dissertation, University of California .
  • Beliakov , G. 2011 . Parallel calculation of the median and order statistics on GPUs with application to robust regression . arXiv , 1104.2732v1
  • Benzi , M. and Dayar , T. 1995 . The arithmetic mean method for finding the stationary vector of Markov chains . Parallel Algorithms Appl , 6 : 25 – 37 .
  • Benzi , M. , Sgallari , F. and Spaletta , G. 1995 . “ A parallel block projection method of the Cimmino type for finite Markov chains ” . In Computations with Markov chains , Edited by: Stewart , W. J. 65 – 80 . Dordrecht : Kluwer Academic .
  • Benzi , M. and Tuma , M. 2002 . A parallel solver for large-scale Markov chains . Appl. Numer. Math , 41 : 135 – 153 .
  • Bouaricha , A. and Schnabel , R. B. 1993 . Parallel tensor methods for nonlinear equations and nonlinear least squares . PPSC , : 639 – 643 .
  • Bouyouli , R. , Jbilou , K. , Sadaka , R. and Sadok , H. 2006 . Convergence properties of some block Krylov subspace methods for multiple linear systems . J. Comput. Appl. Math , 196 : 498 – 511 .
  • Brockwell , A. 2006 . Parallel Markov chain Monte Carlo simulation by prefetching . J. Comput. Graphical Stati , 15 : 246 – 261 .
  • Bru , R. , Pedroche , F. and Szyld , D. B. 2005 . Additive Schwarz iterations for Markov chains . SIAM J. Matrix Anal. Appl , 27 : 445 – 458 .
  • Buckner , J. , Wilson , J. , Seligman , M. , Athey , B. , Watson , S. and Meng , F. 2010 . The gputools package enables GPU computing in R . Bioinformatics , 26 : 134 – 135 .
  • Burrage , K. , Burrage , P. M. and Tian , T. 2004 . Numerical methods for strong solutions of stochastic differential equations: An overview . Proc. R. Soc. Lond. A , 460 : 373 – 402 .
  • Bylina , J. A distributed approach to solve large Markov chains . Proceedings from EuroNGIWorkshop: New Trends in Modeling, Quantitative Methods and Measurements . pp. 145 – 154 . Gliwice : Jacek Skalmierski Computer Studio .
  • Chilson , J. , Ng , R. , Wagner , A. and Zamar , R. 2006 . Parallel computation of high-dimensional robust correlation and covariance matrices . Algorithmica , 45 : 403 – 431 .
  • Coleman , T. F. and Plassmann , P. E. 1992 . A parallel nonlinear least-squares solver: Theoretical analysis and numerical results . SIAM J. Sci. Stat. Comput , 13 : 771 – 793 .
  • Craiu , R. V. and Meng , X. L. 2005 . Multi-process parallel antithetic coupling for forward and backward Markov chain Monte Carlo . Ann. Stat , 33 : 661 – 697 .
  • Craiu , R. V. , Rosenthal , J. S. and Yang , C. 2009 . Learn from thy neighbor: Parallel-chain and regional adaptive MCMC . J. Am. Stat. Associ , 104 : 1454 – 1466 .
  • Creel , M. 2005 . User-friendly parallel computations with econometric examples . Comput. Econ , 26 ( 2 ) : 107 – 128 .
  • Creel , M. and Goffe , W. L. 2008 . Multi-core CPUs, clusters, and grid computing: A tutorial . Comput. Econom , 32 ( 4 ) : 353 – 382 .
  • Dai , B. , Peng , Y. and Gong , B. Parallel option pricing with BSDE method on GPU . Ninth International Conference on Grid and Cloud Computing . pp. 191 – 195 . IEEE .
  • Dennis , J. E. and Steihaug , T. A Ferris–Mangasarian technique applied to linear least squares problems . Tech. Rep. CRPC-TR 98740 . 1998 . Rice University
  • Dhillon , I. S. and Modha , D. S. 2000 . “ A parallel data-clustering algorithm for distributed memory multiprocessors ” . In Large-scale parallel data mining, Lecture notes in artificial intelligence , Edited by: Zaki , M. J. and Ho , C. T. Vol. 1759 , 245 – 260 . New York : Springer-Verlag .
  • Fischer , M. and Kemper , P. Distributed numerical Markov chain analysis . Proc. 8th Euro PVM/MPI . Santorini , Greece. Edited by: Cotronis , Y. and Dongarra , J. pp. 272 – 279 . vol. 2131 of LNCS
  • Flegal , J. M. and Jones , G. L. 2010 . “ Implementing Markov chain Monte Carlo: Estimating with confidence ” . In Handbook of Markov chain Monte Carlo , Edited by: Brooks , S. , Gelman , A. , Jones , G. and Meng , X. Boca Raton , FL : Chapman and Hall/CRC Press . p. 175–197
  • Flynn , M. J. 1966 . Very high-speed computing systems . Proc. IEEE , 54 : 1901 – 1909 .
  • Flynn , M. J. 1972 . Some computer organizations and their effectiveness . IEEE Trans. Computers , C-21 : 948 – 960 .
  • Gelman , A. and Rubin , D. B. 1992 . Inference from iterative simulation using multiple sequences (with discussion) . Statis. Sci , 7 : 457 – 511 .
  • Gentle , J. E. , ärdle , W. H and Mori , Y. , eds. 2004 . Handbook of computational statistics , New York : Springer .
  • Geyer , C. J. 1991 . “ Markov chain Monte Carlo maximum likelihood ” . In Computing science and statistics: Proceedings of the 23rd Symposium on the Interface , Edited by: Keramidas , E. M. 156 – 163 . Fairfax Station , VA : Interface Foundation .
  • Guo , G. 2008 . Schwarz methods for quasi-likelihood in generalized linear models . Commun. Stat. Simul Comput , 37 : 2027 – 2036 .
  • Guo , G. and Lin , S. 2010 . Schwarz method for penalized quasi-likelihood in generalized additive models . Commun. Statist. Theory Methods , 39 : 1847 – 1854 .
  • Guo , G. and Zhao , W. 2012 . Schwarz methods for quasi stationary distributions of Markov chains . Calcolo , 49 : 21 – 39 .
  • Gursoy , A. 2003 . “ Data decomposition for parallel k-means clustering ” . In PPAM, Lecture Notes in Computer Science , Edited by: Wyrzykowski , R. , Dongarra , J. , Paprzycki , M. and Wasniewski , J. Vol. 319 , 241 – 248 . New York : Springer .
  • Havranek , T. and Stratkos , Z. 1989 . On practical experience with parallel processing of linear models . Bull. Inter. Statis. Inst , 53 : 105 – 117 .
  • Hayfield , T. and Racine , J. 2008 . Nonparametric econometrics: The np package . J. Stat. Software , 27 : 1 – 32 .
  • Kontoghiorghes , E. 1999 . Special issue on parallel processing and statistics . Comput. Statist. Data Anal , 31 : 373 – 516 .
  • Keese , A. 2003 . “ A review of recent developments in the numerical solution of stochastic PDEs (stochastic finite elements) ” . In Informatikbericht , Braunschweig , , Germany : Technische Universitat Braunschweig . 2003-6
  • Keese , A. and Matthies , H. G. 2003 . “ Hierarchical parallel solution of stochastic systems ” . In Computational fluid and solid mechanics , Edited by: Bathe , K.-J. Vol. 2 , 2023 – 2025 . Amsterdam : Elsevier .
  • Keese , A. and Matthies , H. G. 2004 . Parallel computation of stochastic groundwater flow . Proc. NIC Symposium. , : 399 – 408 . Germany
  • Kontoghiorghes , E. 2000 . Parallel algorithms for linear models: Numerical methods and estimation problems, Advances in computational economics , Vol. 15 , Boston , MA : Kluwer Academic Publishers .
  • Kontoghiorghes , E. 2006 . Handbook of parallel computing and statistics , Boca Raton , FL : CRC Press .
  • Kwiatkowska , M. , Parker , D. , Zhang , Y. and Mehmood , R. 2004 . Dual-processor parallelization of symbolic probabilistic model checking . MASCOTS'04 , : 123 – 130 . IEEE Computer Society, Volendam, The Netherlands.
  • Lee , A. , Yau , C. , Giles , M. , Doucet , A. and Holmes , C. 2010 . On the utility of graphics cards to perform massively parallel simulation with advanced Monte Carlo methods . J. Comp. Graph. Stat , 19 ( 4 ) : 769 – 789 .
  • Liu , H. , Peng , Y. , Wei , D. and Dai , B. 2011 . X10 implementation of parallel option pricing with BSDE method . ACM SIGPLAN X10 Workshop. , In Proceedings of the ACM SIGPLAN X10'11 Workshop, California, USA, June 2011.
  • Lozano , E. and Acuña , E. Parallel computation of kernel density estimates classifiers and their ensembles . Proc. International Conference on Computer, Communication and Control Technologies . Orlando , FL .
  • Lukasik , S. 2007 . Parallel computing of kernel density estimates with MPI . Lecture Notes Computer Sci , 4489 : 726 – 734 .
  • Lubinsky , B. and Nicolls , F. 2011 . “ Fast implementation of the FRAME algorithm using a GPU Gibbs sampler ” . In PRASA2011 Johannesburg , South Africa
  • Marek , I. and Szyld , D. B. 2004 . Algebraic Schwarz methods for the numerical solution of Markov chains . Linear Algebra Appl , 386 : 67 – 81 .
  • Mehmood , R. and Crowcroft , J. Parallel iterative solution method for large sparse linear equation systems . Tech. Rep. UCAM-CL-TR-650 . 2005 . Computer Laboratory, University of Cambridge, UK
  • Murray , L. 2012 . GPU acceleration of the particle filter: The Metropolis resampler . arXiv , 1202 : 6163
  • Hasenbusch , M. and Schaefer , S. 2010 . Speeding up parallel tempering simulations . Phys. Rev , E82 : 046707
  • Heeswijk , M. , Miche , Y. , Oja , E. and Lendasse , A. 2011 . GPU-accelerated and parallelized ELM ensembles for large-scale regression . Neurocomputing , 74 ( 16 ) : 2430 – 2437 .
  • Hegland , M. , McIntosh , I. and Turlach , B. A. 1999 . A parallel solver for generalized additive models . Comput. Stat. Data Anal , 31 ( 4 ) : 377 – 396 .
  • Hussain , H. M. , Benkrid , K. , Erdogan , A. T. and Seker , H. Highly parameterized k-means clustering on FPGAs: Comparative results with GPPs and GPUs . Proc. ReConFig (2011) . Cancun , Mexico .
  • Nagel , K. and Rickert , M. 2001 . Parallel implementation of the TRANSIMS microsimulation . Parallel Comput , 27 : 1611 – 1639 .
  • Nakano , J. 2004 . “ Parallel computing techniques ” . In Handbook of computational statistics , Edited by: Gentle , J. E. , Hadle , W. and Mori , Y. 237 – 266 . Berlin , , Germany : Springer .
  • Niemi , J. and Wheeler , M. 2011 . Efficient Bayesian inference in stochastic chemical kinetic models using graphical processing units . arXiv , 1101.4242v1
  • Owens , J. , Houston , M. , Luebke , D. , Green , S. , Stone , J. and Phillips , J. 2008 . GPU computing . Proc. IEEE , 96 ( 5 ) : 879 – 899 .
  • Pagan , A. and Ullah , A. 1999 . Nonparametric econometrics , New York : Cambridge University Press .
  • Pan , J. and Manocha , D. 2011 . Fast GPU-based locality sensitive hashing for k-nearest neighbor computation . GISACM (2011) , : 211 – 220 .
  • Peng , Y. , Gong , B. , Liu , H. and Zhang , Y. 2010 . “ Parallel computing for option pricing based on the backward stochastic diffierential equation ” . In High performance computing and applications (Lecture Notes in Computer Science) , Vol. 5938 , 325 – 330 . Berlin : Springer .
  • Peng , Y. , Gong , B. , Liu , H. and Dai , B. 2011 . “ Option pricing on the GPU with backward stochastic differential equation ” . In PAAP , 19 – 23 . Fourth International Symposium on Parallel Architectures, Algorithms and Programming .
  • Platen , E. and Bruti-Liberati , N. 2010 . Numerical solution of SDEs with jumps in finance. Applications of mathematics , Berlin : Springer .
  • Preis , T. 2011 . GPU-computing in econophysics and statistical physics . EPJ-Special Topics , 194 : 87 – 119 .
  • Racine , J. 1995 . Parallel distributed kernel estimation . Comput. Stat. Data Anal , 40 : 293 – 302 .
  • Racine , J. , Hart , J. and Li , Q. 2006 . Testing the significance of categorical predictor variables in nonparametric regression models . Econometric Rev , 25 : 523 – 544 .
  • Renaut , R. A. 1998 . A parallel multisplitting solution of the least squares problem . Numer. Linear Algebra Appl , 5 : 11 – 31 .
  • Rossini , A. J. , Tierney , L. and Li , N. 2007 . Simple parallel statistical computing in R . J. Comput. Graph. Stat , 16 : 399 – 420 .
  • Rue , H. 2001 . Fast sampling of Gaussian Markov random fields . J. R. Stat. Soc. B , 63 : 325 – 338 .
  • Ruoming , J. and Agrawal , G. A Middleware for developing parallel data mining applications . Proc. First SIAM Conference on Data Mining . Chicago , IL 2001.
  • Sarkar , A. , Benabbou , N. and Ghanem , R. 2006 . Domain decomposition of stochastic PDEs and its parallel . HPCS , 2006 : 14 – 17 .
  • Schmidberger , M. 2009 . Parallel computing for biological data , Munich , , Germany : Dissertation, LMU Munchen, Fakultat fur Mathematik, Informatik und Statistik .
  • Silverman , B. W. 1985 . Density estimation for statistics and data analysis , London : Chapman and Hall .
  • Steinsland , I. 2007 . Parallel exact sampling and evaluation of Gaussian Markov random fields . Comput. Stat. Data Anal , 51 : 2969 – 2981 .
  • Stewart , W. J. 2007 . “ Performance modeling and Markov chains ” . In Formal methods for performance evaluation , Edited by: Bernardo , M. and Hillston , J. 1 – 33 . New York : Springer . SFM 2007, LNCS 4486
  • Strid , I. 2010 . Efficient parallelisation of Metropolis–Hastings algorithms using a prefetching approach . Comput. Stat. Data Anal , 54 : 2814 – 2835 .
  • Subber , W. and Sarkar , A. 2010 . “ Domain decomposition of stochastic PDEs: A novel preconditioner and its parallel performance ” . In High performance computing systems and applications , Edited by: Mewhort , D. , Cann , N. , Slater , G. and Naughton , T. 251 – 268 . New York : Springer .
  • Suchard , M. A. , Wang , Q. , Chan , C. , Frelinger , J. , Cron , A. and West , M. 2010 . Understanding GPU programming for statistical computation: Studies in massively parallel massive mixtures . J. Comput. Graph. Stat , 19 ( 2 ) : 419 – 438 .
  • Suri , R. , Deodhare , D. and Nagabhushan , P. Parallel Levenberg–Marquardt-based neural network training on linux clusters—A case study . ICVGIP, Ahmadabad, India .
  • Temple Lang , D. 1997 . A multi-threaded extension to a high level interactive statistical computing environment , Berkeley : PhD dissertation, University of California .
  • Tibbits , M. M. , Haran , M. and Liechty , J. C. 2010 . Parallel multivariate slice sampling . Stat. Comput , 20 : 1 – 16 .
  • Trebst , S. , Troyer , M. and Hansmann , U. 2006 . Optimized parallel tempering simulations of proteins . J. Chem. Phys , 124 : 174903
  • Tran , M. 2010 . A parallel four step domain decomposition scheme for coupled forward backward stochastic differential equation . arXiv , 1008.0353v1
  • Weare , J. 2007 . Efficient conditional path sampling of stochastic differential equations by parallel marginalization . Proc. Natl. Acad. Sci. USA , 104 : 12657 – 12662 .
  • Whiley , M. and Wilson , S. P. 2004 . Parallel algorithms for Markov chain Monte Carlo in latent spatial Gaussian models . Stat. Comput , 14 : 171 – 179 .
  • Wilkinson , D. 2006 . “ Parallel Bayesian computation ” . In Handbook of parallel computing and statistics , Edited by: Kontoghiorghes , E. J. 477 – 508 . Boca Raton , FL : Chapman and Hall .
  • Xiu , D. and Karniadakis , G. E. 2003 . Modeling uncertainty in flow simulations via generalized polynomial chaos . J. Comput. Phys , 187 : 137 – 167 .
  • Xu , M. , Wegman , E. and Miller , J. 1991 . Parallelizing multiple linear regression for speed and redundancy: An empirical study . J. Stat Comput. Simulation , 39 : 205 – 214 .
  • Yan , J. , Cowles , M. K. , Wang , S. and Armstrong , M. P. 2007 . Parallelizing MCMC for Bayesian spatiotemporal geostatistical models . Stat. Comput , 17 : 323 – 335 .
  • Yang , T. Execution time analysis for least squares problems on massively parallel distributed memory computers . Proc. International Conference on Computational Modeling and Computing (CMCP-96) . Dubna , Russia.
  • Zareski , D. , Wade , B. , Hubbard , P. and Shirley , P. 1995 . Efficient parallel global illumination using density-estimation . Proc. ACM Parallel Rendering Symposium , : 47 – 54 . Atlanta, GA, 1995.
  • Zhang , Y. , Parker , D. and Kwiatkowska , M. 2005 . “ A wavefront parallelisation of CTMC solution using MTBDDs ” . In DSN'05 , 732 – 742 . IEEE Computer Society Press . Yokohama, Japan.
  • Zhou , H. , Lange , K. and Suchard , M. A. 2010 . Graphics processing units and high-dimensional optimization . Stat. Sci , 25 ( 3 ) : 311 – 324 .
  • Zhu , W. and Li , Y. GPU-accelerated differential evolutionary Markov chain Monte Carlo method for multi-objective optimization over continuous space . Proc. 7th IEEE ICAC-BADS . Washington , DC .

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