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2022 | OriginalPaper | Buchkapitel

Quasi-Monte Carlo Software

verfasst von : Sou-Cheng T. Choi, Fred J. Hickernell, Rathinavel Jagadeeswaran, Michael J. McCourt, Aleksei G. Sorokin

Erschienen in: Monte Carlo and Quasi-Monte Carlo Methods

Verlag: Springer International Publishing

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Abstract

Practitioners wishing to experience the efficiency gains from using low discrepancy sequences need correct, robust, well-written software. This article, based on our MCQMC 2020 tutorial, describes some of the better quasi-Monte Carlo (QMC) software available. We highlight the key software components required by QMC to approximate multivariate integrals or expectations of functions of vector random variables. We have combined these components in QMCPy, a Python open-source library, which we hope will draw the support of the QMC community. Here we introduce QMCPy.

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Vorheriges Kapitel Density Estimation by Monte Carlo and Quasi-Monte Carlo

Nächstes Kapitel A Tool for Custom Construction of QMC and RQMC Point Sets

QMCPy is in active development. This article is based on version 1.2 on PyPI.

The operator \(\oplus \) is commonly used to denote exclusive-or, which is its meaning for digital sequences in base 2. However, we are using it here in a more general sense.

Abadi, M., Agarwal, A., Barham, P., Brevdo, E., Chen, Z., Citro, C., Corrado, G.S., Davis, A., Dean, J., Devin, M., Ghemawat, S., Goodfellow, I., Harp, A., Irving, G., Isard, M., Jia, Y., Jozefowicz, R., Kaiser, L., Kudlur, M., Levenberg, J., Mané, D., Monga, R., Moore, S., Murray, D., Olah, C., Schuster, M., Shlens, J., Steiner, B., Sutskever, I., Talwar, K., Tucker, P., Vanhoucke, V., Vasudevan, V., Viégas, F., Vinyals, O., Warden, P., Wattenberg, M., Wicke, M., Yu, Y., Zheng, X.: TensorFlow: Large-scale machine learning on heterogeneous systems (2015). https://www.tensorflow.org/. Software available from tensorflow.org

Asmussen, S., Glynn, P.: Stochastic simulation: algorithms and analysis. In: Stochastic Modelling and Applied Probability, vol. 57. Springer, New York (2007). https://doi.org/10.1007/978-0-387-69033-9

Bezanson, J., Karpinski, S., Shah, V.B., Edelman, A.: Julia: A fast dynamic language for technical computing (2012). arXiv:1209.5145

Burkhardt, J.: Various Software (2020). http://people.sc.fsu.edu/~jburkardt/

Choi, S.C.T., Ding, Y., Hickernell, F.J., Jiang, L., Jiménez Rugama, Ll.A., Li, D., Jagadeeswaran, R., Tong, X., Zhang, K., Zhang, Y., Zhou, X.: GAIL: Guaranteed Automatic Integration Library (versions 1.0–2.3.2). MATLAB software. http://gailgithub.github.io/GAIL_Dev/ (2021). https://doi.org/10.5281/zenodo.4018189

Choi, S.C.T., Hickernell, F.J., Jagadeeswaran, R., McCourt, M., Sorokin, A.: QMCPy: A quasi-Monte Carlo Python library (2020). https://doi.org/10.5281/zenodo.3964489, https://qmcsoftware.github.io/QMCSoftware/

Choi, S.C.T., Hickernell, F.J., Jagadeeswaran, R., McCourt, M.J., Sorokin, A.: QMCPy Documentation (2020). https://qmcpy.readthedocs.io/en/latest/

Cools, R., Kuo, F.Y., Nuyens, D.: Constructing embedded lattice rules for multivariate integration. SIAM J. Sci. Comput. 28(6), 2162–2188 (2006). https://doi.org/10.1137/06065074X

Darmon, Y., Godin, M., L’Ecuyer, P., Jemel, A., Marion, P., Munger, D.: LatNet Builder (2018). https://github.com/umontreal-simul/latnetbuilder

10.

Dick, J., Kuo, F., Sloan, I.H.: High dimensional integration—the Quasi-Monte Carlo way. Acta Numer. 22, 133–288 (2013). https://doi.org/10.1017/S0962492913000044

11.

Giles, M.: Multi-level (Quasi-)Monte Carlo software (2020). https://people.maths.ox.ac.uk/gilesm/mlmc/

12.

Google Inc.: TF Quant Finance: Tensorflow Based Quant Finance Library (2021). https://github.com/google/tf-quant-finance

13.

Harris, C.R., Millman, K.J., van der Walt, S.J., Gommers, R., Virtanen, P., Cournapeau, D., Wieser, E., Taylor, J., Berg, S., Smith, N.J., Kern, R., Picus, M., Hoyer, S., van Kerkwijk, M.H., Brett, M., Haldane, A., del Río, J.F., Wiebe, M., Peterson, P., Gérard-Marchant, P., Sheppard, K., Reddy, T., Weckesser, W., Abbasi, H., Gohlke, C., Oliphant, T.E.: Array programming with NumPy. Nature 585(7825), 357–362 (2020). https://doi.org/10.1038/s41586-020-2649-2, https://doi.org/10.1038/s41586-020-2649-2

14.

Hickernell, F.J., Choi, S.C.T., Jiang, L., Jiménez Rugama, L.A.: Monte Carlo Simulation, Automatic Stopping Criteria for Wiley StatsRef: Statistics Reference Online, pp. 1–7 (2014)

15.

Hickernell, F.J., Sorokin, A.: Quasi-Monte Carlo (QMC) software in QMCPy Google Colaboratory Notebook (2020). http://tinyurl.com/QMCPyTutorial

16.

Hickernell, F.J., Sorokin, A.: Quasi-Monte Carlo (QMC) software in QMCPy Google Colaboratory Notebook for MCQMC2020 Article (2020). https://tinyurl.com/QMCPyArticle2021

17.

Hickernell, F.J.: A generalized discrepancy and quadrature error bound. Math. Comput. 67, 299–322 (1998). https://doi.org/10.1090/S0025-5718-98-00894-1

18.

Hickernell, F.J.: Goodness-of-fit statistics, discrepancies and robust designs. Statist. Prob. Lett. 44, 73–78 (1999). https://doi.org/10.1016/S0167-7152(98)00293-4

19.

Hickernell, F.J., Jiang, L., Liu, Y., Owen, A.B.: Guaranteed conservative fixed width confidence intervals via Monte Carlo sampling. In: Dick, J., Kuo, F.Y., Peters, G.W., Sloan, I.H. (eds.) Monte Carlo and Quasi-Monte Carlo Methods 2012, Springer Proceedings in Mathematics and Statistics, vol. 65, pp. 105–128. Springer, Berlin (2013). https://doi.org/10.1007/978-3-642-41095-6

20.

Hickernell, F.J., Jiménez Rugama, Ll.A.: Reliable adaptive cubature using digital sequences. In: Cools, R., Nuyens, D. (eds.) Monte Carlo and Quasi-Monte Carlo Methods: MCQMC, Leuven, Belgium, April 2014, Springer Proceedings in Mathematics and Statistics, vol. 163, pp. 367–383. Springer, Berlin (2016). ArXiv:1410.8615 [math.NA]

21.

Hickernell, F.J., Jiménez Rugama, Ll.A., Li, D.: Adaptive quasi-Monte Carlo methods for cubature. In: Dick, J., Kuo, F.Y., Woźniakowski, H. (eds.) Contemporary Computational Mathematics—A Celebration of the 80th Birthday of Ian Sloan, pp. 597–619. Springer, Berlin (2018). https://doi.org/10.1007/978-3-319-72456-0

22.

Hickernell, F.J., Lemieux, C., Owen, A.B.: Control variates for quasi-Monte Carlo. Stat. Sci. 20, 1–31 (2005). https://doi.org/10.1214/088342304000000468

23.

Hofert, M., Lemieux, C.: qrng R package (2017). https://cran.r-project.org/web/packages/qrng/qrng.pdf

24.

Jagadeeswaran, R., Hickernell, F.J.: Fast automatic Bayesian cubature using lattice sampling. Stat. Comput. 29, 1215–1229 (2019). https://doi.org/10.1007/s11222-019-09895-9

25.

Jagadeeswaran, R., Hickernell, F.J.: Fast automatic Bayesian cubature using Sobol’ sampling (2021+). In preparation for submission for publication

26.

Jiménez Rugama, Ll.A., Hickernell, F.J.: Adaptive multidimensional integration based on rank-1 lattices. In: Cools, R., Nuyens, D. (eds.) Monte Carlo and Quasi-Monte Carlo Methods: MCQMC, Leuven, Belgium, April 2014, Springer Proceedings in Mathematics and Statistics, vol. 163, pp. 407–422. Springer, Berlin (2016). ArXiv:1411.1966

27.

Keister, B.D.: Multidimensional quadrature algorithms. Comput. Phys. 10, 119–122 (1996). https://doi.org/10.1063/1.168565

28.

Kucherenko, S.: BRODA (2020). https://www.broda.co.uk/index.html

29.

Kumaraswamy, P.: A generalized probability density function for double-bounded random processes. J. Hydrol. 46(1), 79–88 (1980). https://doi.org/10.1016/0022-1694(80)90036-0

30.

Kuo, F.Y., Nuyens, D.: Application of quasi-Monte Carlo methods to elliptic PDEs with random diffusion coefficients—a survey of analysis and implementation. Found. Comput. Math. 16, 1631–1696 (2016). https://people.cs.kuleuven.be/~dirk.nuyens/qmc4pde/

31.

Lataniotis, C., Marelli, S., Sudret, B.: Uncertainty quantification in the cloud with UQCloud. In: 4th International Conference on Uncertainty Quantification in Computational Sciences and Engineering (UNCECOMP 2021), pp. 209–217 (2021)

32.

L’Ecuyer, P.: SSJ: Stochastic Simulation in Java (2020). https://github.com/umontreal-simul/ssj

33.

L’Ecuyer, P., Marion, P., Godin, M., Puchhammer, F.: A tool for custom construction of QMC and RQMC point sets. In: Arnaud, E., Giles, M., Keller, A. (eds.) Monte Carlo and Quasi-Monte Carlo Methods: MCQMC, Oxford 2020 (2021+)

34.

L’Ecuyer, P., Munger, D.: Algorithm 958: Lattice Builder: a general software tool for constructing rank-1 latice rules. ACM Trans. Math. Softw. 42, 1–30 (2016)

35.

L’Ecuyer, P., Tuffin, B.: Approximate zero-variance simulation. In: Proceedings of the 40th Conference on Winter Simulation, WSC ’08, pp. 170–181. Winter Simulation Conference (2008)

36.

Marelli, S., Sudret, B.: UQLab: A framework for uncertainty quantification in MATLAB. In: The 2nd International Conference on Vulnerability and Risk Analysis and Management (ICVRAM 2014), pp. 2554–2563. ASCE Library (2014). https://www.uqlab.com

37.

Matoušek, J.: On the \(L_2\)-discrepancy for anchored boxes. J. Complex. 14, 527–556 (1998)

38.

Niederreiter, H.: Random Number Generation and Quasi-Monte Carlo Methods. CBMS-NSF Regional Conference Series in Applied Mathematics. SIAM, Philadelphia (1992)

39.

Nuyens, D.: Magic Point Shop (2017). https://people.cs.kuleuven.be/~dirk.nuyens/qmc-generators/

40.

OpenTURNS Developers: An Open Source Initiative for the Treatment of Uncertainties, Risks ’N Statistics (2020). http://www.openturns.org

41.

Owen, A.B.: Scrambling Sobol’ and Niederreiter-Xing points. J. Complex. 14(4), 466–489 (1998)

42.

Owen, A.B.: On dropping the first Sobol’ point. In: Keller, A. (ed.) Monte Carlo and Quasi-Monte Carlo Methods. Springer Proceedings in Mathematics & Statistics, vol. 387, pp. xx–yy. Springer, Cham (this volume). https://doi.org/10.1007/978-3-030-98319-2_4

43.

Owen, A.B.: Randomized Halton Sequences in R (2020). http://statweb.stanford.edu/~owen/code/

44.

Owen, A.B.: About the R function: rsobol (2021). https://statweb.stanford.edu/~owen/reports/seis.pdf

45.

Owen, A.B., Zhou, Y.: Safe and effective importance sampling. J. Am. Stat. Assoc. 95, 135–143 (2000)

46.

Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An imperative style, high-performance deep learning library. In: Wallach, H., Larochelle, H., Beygelzimer, A., d’Alché-Buc, F., Fox, E., Garnett, R. (eds.) Advances in Neural Information Processing Systems 32, pp. 8024–8035. Curran Associates, Inc. (2019). http://papers.neurips.cc/paper/9015-pytorch-an-imperative-style-high-performance-deep-learning-library.pdf

47.

PyTorch Developers: PyTorch (2020). https://pytorch.org

48.

Robbe, P.: Low Discrepancy Sequences in Julia (2020). https://github.com/PieterjanRobbe/QMC.jl

49.

Robbe, P.: Multilevel Monte Carlo simulations in Julia (2021). https://github.com/PieterjanRobbe/MultilevelEstimators.jl

50.

SciPy Developers: SciPy Ecosystem (2018). www.scipy.org

51.

The MathWorks Inc: MATLAB R2021a. Natick, MA (2020)

52.

Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nat. Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2

Titel: Quasi-Monte Carlo Software
verfasst von: Sou-Cheng T. Choi
Fred J. Hickernell
Rathinavel Jagadeeswaran
Michael J. McCourt
Aleksei G. Sorokin
Verlag: Springer International Publishing
Buch: Monte Carlo and Quasi-Monte Carlo Methods
Print ISBN: 978-3-030-98318-5

Electronic ISBN: 978-3-030-98319-2

Copyright-Jahr: 2022
DOI: https://doi.org/10.1007/978-3-030-98319-2_2

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