Abstract
Massively parallel computing is a computing environment with thousands of subprocessors. It requires some special programming methods, but is well suited to certain imaging problems. One such statistical example is discussed in this paper. In addition there are other natural statistical problems for which this technology is well suited. This paper describes our experience, as statisticians, with a massively parallel computer in a problem of image correlation spectroscopy. Even with this computing environment some direct computations would still take in the order of a year to finish. It is shown that some of the algorithms of interest can be made parallel.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Abdelguerfi, M. and Lavington, S. eds (1995) Emerging Trends in Database and Knowledge-Base Machines: an application of parallel architectures to smart information systems. IEEE Computer Society Press, Los Alamitos, California.
Adams, N. M., Kirby, S. P. J., Harris, P. and Clegg, D. B. (1996) A review of parallel processing for statistical computation. Statistics and Computing, 6, 37–49.
Avila, J. and Tomlin, J. (1979) Solution of very large least squares problems by nested dissection on a parallel processor, in Proceedings of the 12th Symposium on the Interface, pp. 9–14.
Benn, A. (1996) Ph.D. thesis. University of Western Ontario.
Benn, A. and Kulperger, R. (1997) Integrated marked Poisson processes with application to image correlation spectroscopy. Canadian Journal of Statistics, 25, 215–31.
Bradford, R. and Thomas, A. (1996) Markov chain Monte Carlo methods for family trees using a parallel processor. Statistics and Computing, 6, 67–75.
Brillinger, D. R. (1975) Statistical inference for stationary point processes, in Stochastic Processes and Related Topics, Puri, M. L. (ed.) Vol. 1, pp. 55–99. Academic Press, New York.
Brillinger, D. R. (1981) Time Series: Data Analysis and Theory, (expanded edition). Holden-Day, San Francisco.
Carlstein, E. (1986) The use of subseries values for estimating the variance of a general statistic from a stationary sequence. Annals of Statistics, 14, 1171–1179.
Efron, B. and Tibshirani, R. (1993) An Introduction to the Bootstrap. Chapman and Hall.
Grenander, U. and Miller, M. (1994) Representations of knowledge in complex systems. Journal of the Royal Statistical Society, Series B, 56, 549–603.
Hall, P. (1992) Bootstrap and Edgeworth Expansion. Springer-Verlag, New York.
Hwang, K. (1993) Advanced Computer Architecture. McGraw-Hill.
Hwang, K. and Briggs, F. A. (1984) Computer Architecture and Parallel Processing. McGraw-Hill.
Keenan, D. M. (1987) Limiting behaviour of functionals of higher-order sample cumulant spectra. Annals of Statistics, 15, 134–151.
Kuck, D. J. (1996) High Performance Computing: Challenges for Future Systems. Oxford University Press, New York.
Lewis, T. G. and El-Rewini, H. (1992) Introduction to Parallel Programming. Prentice-Hall.
Ostrouchov, G. (1987) Parallel computing on a Hypercube: an overview of the architecture and some applications. Computer Science and Statistics: Proceedings of the 19th Symposium on the Interface, pp. 27–32.
Petersen, N. O. (1993) Quantitation of membrane receptor distributions by image correlation spectroscopy: concept and application. Biophysics Journal, 65, 1135–1146.
Raphalen, M. (1982) Applying parallel processing to data analysis: computing a distance's matrix on a SIMD machine. Compstat, Proceeding in Computational Statistics, pp. 382–386.
Schervish, M. J. (1988) Applications of parallel computation to statistical inference. Journal of the American Statistical Association, 83, 976–83.
Taniguchi, M. (1980) On estimation of the integrals of certain functions of spectral density. Journal of Applied Probability, 17, 73–83.
Taniguchi, M. (1982) On estimation of the integrals of the fourth-order cumulant spectral density. Biometrika, 69, 117–122.
Wang, Ouhon (1994) Applications of Numerical Interval Analysis to Obtain Self-validating Results in a Massively Parallel Computing Environment. ASA Proc. Statist. Comput. Sect., pp. 21–28.
Whichmann, W. A. and Hill, I. D. (1982) Algorithm AS 183. Applied Statistics, 31, 188–190.
Wilson, A., Malley, J., Pfiefer, J. and Petelin, A. (1992) The Gibbs sample and its implementation of a parallel machine. ASA Proceedigs of Statistical Computing Section, pp. 68–73.
Wollan, P. (1988) All-subsets regression on a hypercube multi-processor. Computer Science and Statistics: Proceedings of the 20th Sympoisium on the Interface, pp. 224–7.
Xu, Mingxian, Miller, J. J. and Wegman, E. (1991) Parallelzing multiple linear regression for speed and redundancy. Journal of Statistics Computing and Simulation, 39, 205–214.
Xu, Chong-wei and Wei-Kei Shiue (1990) Parallel bootstrap and inference for means. Computer Science and Statistics: Proceedings of the 22nd Symposium on the Interface, pp. 576–79.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
BENN, A., KULPERGER, R. Massively parallel computing: a statistical application. Statistics and Computing 8, 309–318 (1998). https://doi.org/10.1023/A:1008868404442
Issue Date:
DOI: https://doi.org/10.1023/A:1008868404442