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Quasi-Monte Carlo submodule (:mod:`scipy.stats.qmc`)

Quasi-Monte Carlo



Introduction to Quasi-Monte Carlo


            <Unimplemented 'footnote' '.. [1] Owen, Art B. "Monte Carlo Book: the Quasi-Monte Carlo parts." 2019.'>
            <Unimplemented 'footnote' '.. [2] Niederreiter, Harald. "Random number generation and quasi-Monte Carlo\n   methods." Society for Industrial and Applied Mathematics, 1992.'>
            <Unimplemented 'footnote' '.. [3] Dick, Josef, Frances Y. Kuo, and Ian H. Sloan. "High-dimensional\n   integration: the quasi-Monte Carlo way." Acta Numerica no. 22: 133, 2013.'>
            <Unimplemented 'footnote' '.. [4] Aho, A. V., C. Aistleitner, T. Anderson, K. Appel, V. Arnol\'d, N.\n   Aronszajn, D. Asotsky et al. "W. Chen et al.(eds.), "A Panorama of\n   Discrepancy Theory", Sringer International Publishing,\n   Switzerland: 679, 2014.'>
            <Unimplemented 'footnote' '.. [5] Hickernell, Fred J. "Koksma-Hlawka Inequality." Wiley StatsRef:\n   Statistics Reference Online, 2014.'>
            <Unimplemented 'footnote' '.. [6] Owen, Art B. "On dropping the first Sobol\' point." :arxiv:`2008.08051`,\n   2020.'>
            <Unimplemented 'footnote' '.. [7] L\'Ecuyer, Pierre, and Christiane Lemieux. "Recent advances in randomized\n   quasi-Monte Carlo methods." In Modeling uncertainty, pp. 419-474. Springer,\n   New York, NY, 2002.'>
            <Unimplemented 'footnote' '.. [8] DiCiccio, Thomas J., and Bradley Efron. "Bootstrap confidence\n   intervals." Statistical science: 189-212, 1996.'>
            <Unimplemented 'footnote' '.. [9] Dimov, Ivan T. "Monte Carlo methods for applied scientists." World\n   Scientific, 2008.'>
            <Unimplemented 'footnote' '.. [10] Caflisch, Russel E., William J. Morokoff, and Art B. Owen. "Valuation\n   of mortgage backed securities using Brownian bridges to reduce effective\n   dimension." Journal of Computational Finance: no. 1 27-46, 1997.'>
            <Unimplemented 'footnote' '.. [11] Sloan, Ian H., and Henryk Wozniakowski. "When are quasi-Monte Carlo\n   algorithms efficient for high dimensional integrals?." Journal of Complexity\n   14, no. 1 (1998): 1-33.'>
            <Unimplemented 'footnote' '.. [12] Owen, Art B., and Daniel Rudolf, "A strong law of large numbers for\n   scrambled net integration." SIAM Review, to appear.'>
            <Unimplemented 'footnote' '.. [13] Loh, Wei-Liem. "On the asymptotic distribution of scrambled net\n   quadrature." The Annals of Statistics 31, no. 4: 1282-1324, 2003.'>
            <Unimplemented 'footnote' '.. [14] Sloan, Ian H. and S. Joe. "Lattice methods for multiple integration."\n   Oxford University Press, 1994.'>
            <Unimplemented 'footnote' '.. [15] Dick, Josef, and Friedrich Pillichshammer. "Digital nets and sequences:\n   discrepancy theory and quasi-Monte Carlo integration." Cambridge University\n   Press, 2010.'>
            <Unimplemented 'footnote' '.. [16] Dick, Josef, F. Kuo, Friedrich Pillichshammer, and I. Sloan.\n   "Construction algorithms for polynomial lattice rules for multivariate\n   integration." Mathematics of computation 74, no. 252: 1895-1921, 2005.'>
            <Unimplemented 'footnote' '.. [17] Sobol\', Il\'ya Meerovich. "On the distribution of points in a cube and\n   the approximate evaluation of integrals." Zhurnal Vychislitel\'noi Matematiki\n   i Matematicheskoi Fiziki 7, no. 4: 784-802, 1967.'>
            <Unimplemented 'footnote' '.. [18] Halton, John H. "On the efficiency of certain quasi-random sequences of\n   points in evaluating multi-dimensional integrals." Numerische Mathematik 2,\n   no. 1: 84-90, 1960.'>
            <Unimplemented 'footnote' '.. [19] Faure, Henri. "Discrepance de suites associees a un systeme de\n   numeration (en dimension s)." Acta arithmetica 41, no. 4: 337-351, 1982.'>
            <Unimplemented 'footnote' '.. [20] Niederreiter, Harold, and Chaoping Xing. "Low-discrepancy sequences and\n   global function fields with many rational places." Finite Fields and their\n   applications 2, no. 3: 241-273, 1996.'>
            <Unimplemented 'footnote' '.. [21] Hong, Hee Sun, and Fred J. Hickernell. "Algorithm 823: Implementing\n   scrambled digital sequences." ACM Transactions on Mathematical Software\n   (TOMS) 29, no. 2: 95-109, 2003.'>
            <Unimplemented 'footnote' '.. [22] Dick, Josef. "Higher order scrambled digital nets achieve the optimal\n   rate of the root mean square error for smooth integrands." The Annals of\n   Statistics 39, no. 3: 1372-1398, 2011.'>
            <Unimplemented 'footnote' '.. [23] Niederreiter, Harald. "Multidimensional numerical integration using\n   pseudorandom numbers." In Stochastic Programming 84 Part I, pp. 17-38.\n   Springer, Berlin, Heidelberg, 1986.'>
            <Unimplemented 'footnote' '.. [24] Hickernell, Fred J. "Obtaining O (N-2+e) Convergence for Lattice\n   Quadrature Rules." In Monte Carlo and Quasi-Monte Carlo Methods 2000,\n   pp. 274-289. Springer, Berlin, Heidelberg, 2002.'>
            <Unimplemented 'footnote' '.. [25] Owen, Art B., and Seth D. Tribble. "A quasi-Monte Carlo Metropolis\n   algorithm." Proceedings of the National Academy of Sciences 102,\n   no. 25: 8844-8849, 2005.'>
            <Unimplemented 'footnote' '.. [26] Chen, Su. "Consistency and convergence rate of Markov chain quasi Monte\n   Carlo with examples." PhD diss., Stanford University, 2011.'>
            <Unimplemented 'footnote' '.. [27] Joe, Stephen, and Frances Y. Kuo. "Constructing Sobol sequences with\n   better two-dimensional projections." SIAM Journal on Scientific Computing\n   30, no. 5: 2635-2654, 2008.'>


See :

Back References

The following pages refer to to this document either explicitly or contain code examples using this.

scipy.optimize._differentialevolution:DifferentialEvolutionSolver scipy.optimize._differentialevolution:differential_evolution scipy.optimize._shgo:shgo

Local connectivity graph

Hover to see nodes names; edges to Self not shown, Caped at 50 nodes.

Using a canvas is more power efficient and can get hundred of nodes ; but does not allow hyperlinks; , arrows or text (beyond on hover)

SVG is more flexible but power hungry; and does not scale well to 50 + nodes.

All aboves nodes referred to, (or are referred from) current nodes; Edges from Self to other have been omitted (or all nodes would be connected to the central node "self" which is not useful). Nodes are colored by the library they belong to, and scaled with the number of references pointing them

GitHub : /scipy/stats/
type: <class 'module'>