Abstract
This article reports on the contents of a tutorial session at MCQMC 2008. The tutorial explored various places in statistics where Monte Carlo methods can be used. There was a special emphasis on areas where Quasi-Monte Carlo ideas have been or could be applied, as well as areas that look like they need more research.
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References
Brown, B.W., Hollander, M.: Statistics, A Biomedical Introduction. John Wiley & Sons, New York (1977)
Caflisch, R.E., Morokoff, W., Owen, A.B.: Valuation of mortgage backed securities using Brownian bridges to reduce effective dimension. Journal of Computational Finance 1, 27–46 (1997)
Chentsov, N.: Pseudorandom numbers for modelling Markov chains. Computational Mathematics and Mathematical Physics 7, 218–2332 (1967)
Davison, A.C., Hinkley, D.V., Schechtman, E.: Efficient bootstrap simulation. Biometrika 73(3), 555–566 (1986)
Efron, B.: Bootstrap methods: Another look at the jackknife. The Annals of Statistics 7, 1–26 (1979)
Efron, B., Tibshirani, R., Storey, J.D., Tusher, V.: Empirical Bayes analysis of a microarray experiment. Journal of the American Statistical Association 96, 1151–1160 (2001)
Efron, B.M., Tibshirani, R.J.: An Introduction to the Bootstrap. Chapman and Hall (1993)
Fernholz, L.T.: von Mises calculus for statistical functionals. Springer-Verlag, New York (1983)
Finney, D.J.: The estimation from individual records of the relationship between dose and quantal response. Biometrika 34, 320–334 (1947)
Gelman, A., Carlin, J.B., Stern, H.S., Rubin, D.B.: Bayesian Data Analysis. Chapman & Hall, Boca Raton, FL (2003)
Genz, A., Bretz, F., Hochberg, Y.: Approximations to multivariate t integrals with application to multiple comparison procedures. In: Recent Developments in Multiple Comparison Procedures, vol. 47, pp. 24–32. Institute of Mathematical Statistics (2004)
Graham, R.L., Hinkley, D.V., John, P.W.M., Shi, S.: Balanced design of bootstrap simulations. Journal of the Royal Statistical Society, Series B 52, 185–202 (1990)
Hall, P.G.: The Bootstrap and Edgeworth Expansion. Springer, New York (1992)
Huber, P.J.: Robust Statistics. Wiley, New York (1981)
Lécot, C.: Low discrepancy sequences for solving the Boltzmann equation. Journal of Computational and Applied Mathematics 25, 237–249 (1989)
L’Ecuyer, P., Lécot, C., Tuffin, B.: A randomized Quasi-Monte Carlo simulation method for Markov chains. Operations Research 56(4), 958–975 (2008)
Lehmann, E.L., Romano, J.P.: Testing Statistical Hypotheses, third edn. Springer, New York (2005)
Levin, M.B.: Discrepancy estimates of completely uniformly distributed and pseudo-random number sequences. International Mathematics Research Notices pp. 1231–1251 (1999)
Liao, L.G.: Variance reduction in Gibbs sampler using quasi random numbers. Journal of Computational and Graphical Statistics 7, 253–266 (1998)
Liu, J.S.: Monte Carlo strategies in scientific computing. Springer, New York (2001)
Liu, R.: New findings of functional ANOVA with applications to computational finance and statistics. Ph.D. thesis, Stanford University (2005)
McKay, M.D., Beckman, R.J., Conover, W.J.: A comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics 21(2), 239–45 (1979)
Newman, M.E.J., Barkema, G.T.: Monte Carlo Methods in Statistical Physics. Oxford University Press, New York (1999)
Newton, M.A., Raftery, A.E.: Approximate Bayesian inference with the weighted likelihood bootstrap (disc: P26-48). Journal of the Royal Statistical Society, Series B, Methodological 56, 3–26 (1994)
Niederreiter, H.: Multidimensional integration using pseudo-random numbers. Mathematical Programming Study 27, 17–38 (1986)
Niederreiter, H.: Random Number Generation and Quasi-Monte Carlo Methods. S.I.A.M., Philadelphia, PA (1992)
Niederreiter, H., Peart, P.: Quasi-Monte Carlo optimization in general domains. Caribbean Journal of Mathematics 4(2), 67–85 (1985)
Owen, A.B.: Discussion of the paper by Newton and Raftery. Journal of the Royal Statistical Society, Series B 56(1), 42–43 (1994)
Owen, A.B.: Lattice sampling revisited: Monte Carlo variance of means over randomized orthogonal arrays. The Annals of Statistics 22, 930–945 (1994)
Owen, A.B.: Randomly permuted (t,m,s)-nets and (t,s)-sequences. In: H. Niederreiter, P.J.S. Shiue (eds.) Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing, pp. 299–317. Springer-Verlag New York (1995)
Owen, A.B., Tribble, S.D.: A quasi-Monte Carlo Metropolis algorithm. Proceedings of the National Academy of Sciences 102(25), 8844–8849 (2005)
Politis, D.N., Romano, J.P., Wolf, M.: Subsampling. Springer, New York (1999)
Robert, C., Casella, G.: Monte Carlo Statistical Methods, 2nd edn. Springer, New York (2004)
Rodwell, G., Sonu, R., Zahn, J.M., Lund, J., Wilhelmy, J., Wang, L., Xiao, W., Mindrinos, M., Crane, E., Segal, E., Myers, B., Davis, R., Higgins, J., Owen, A.B., Kim, S.K.: A transcriptional profile of aging in the human kidney. PLOS Biology 2(12), 2191–2201 (2004)
Rosenthal, J.S.: Minorization conditions and convergence rates for Markov chain Monte Carlo. Journal of the American Statistical Association 90, 558–566 (1995)
Rousseeuw, P.J., Driessen, van K.: Computing LTS regression for large data sets. Data Mining and Knowledge Discovery 12, 29–45 (2006)
Rousseeuw, P.J., Leroy, A.M.: Robust Regression and Outlier Detection. Wiley, New York (1987)
Rubin, D.B.: The Bayesian bootstrap. The Annals of Statistics 9, 130–134 (1981)
Sloan, I.H., Kuo, F.Y., Dunsmuir, W.T., Wand, M., Womersley, R.S.: Quasi-Monte Carlo for highly structured generalised response models. Tech. rep., University of Wollongong Faculty of Informatics (2007)
Southworth, L.K., Kim, S.K., Owen, A.B.: Properties of balanced permutations. Journal of Computational Biology 16 (2009). In press.
Tang, B.: Orthogonal array-based Latin hypercubes. Journal of the American Statistical Association 88, 1392–1397 (1993)
Tribble, S.D.: Markov chain Monte Carlo algorithms using completely uniformly distributed driving sequences. Ph.D. thesis, Stanford University (2007)
Tribble, S.D., Owen, A.B.: Construction of weakly CUD sequences for MCMC sampling. Electronic Journal of Statistics 2, 634–660 (2008)
Zelazo, P.R., Zelazo, N.A., Kolb, S.: Walking in the newborn. Science 176, 314–315 (1972)
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Owen, A.B. (2009). Monte Carlo and Quasi-Monte Carlo for Statistics. In: L' Ecuyer, P., Owen, A. (eds) Monte Carlo and Quasi-Monte Carlo Methods 2008. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04107-5_1
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DOI: https://doi.org/10.1007/978-3-642-04107-5_1
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