Bibliography for Monte Carlo Integration

unabridged

  1. Adaptive integration method for Monte Carlo simulations
    Fasnacht, Marc; Swendsen, Robert H.; Rosenberg, John M.  
    Physical Review E, v 69, n 5 1, May, 2004, p 056704-1-056704-15, Compendex.
  2. Adaptive radial-based direction sampling: Some flexible and robust Monte Carlo integration methods
    Bauwens, Luc; Bos, Charles S.; Van Dijk, Herman K.; Van Oest, Rutger D.  
    Journal of Econometrics, v 123, n 2, December, 2004, Recent Advances in Bayesian Econometrics, p 201-225, Compendex.
  3. On a Likelihood Approach for Monte Carlo Integration
    Zhiqiang Tan
    Journal of the American Statistical Association, December 2004, vol. 99, no. 468, pp. 1027-1036, Ingenta.  
  4. Error trends in Quasi-Monte Carlo integration
    Schlier, Ch.
    Computer Physics Communications, v 159, n 2, May 15, 2004, p 93-105, Compendex.
  5. Bidirectional Ray Tracing for the Integration of Illumination by the Quasi-Monte Carlo Method
    A. G. Voloboi; V. A. Galaktionov; K. A. Dmitriev; E. A. Kopylov
    Programming and Computer Software, September 2004, vol. 30, no. 5, pp. 258-265, Ingenta.  
  6. Error estimates in Monte Carlo and Quasi-Monte Carlo integration
    Lazopoulos, Achilleas
    Acta Physica Polonica, Series B, v 35, n 11, November, 2004, p 2617-2632, Compendex .
  7. Methods for the calculation of occupied volumes in glassy polymers: The lattice integration and the Monte Carlo methods
    Rozhkov E.M.; Schukin B.V.; Ronova I.A.
    Central European Journal of Chemistry, 1 July 2003, vol. 1, no. 4, pp. 402-426, Ingenta.  
  8. A theory of statistical models for Monte Carlo integration
    Kong A.; McCullagh P.; Meng X.-L.; Nicolae D.; Tan Z.
    Journal of the Royal Statistical Society: Series B (Statistical Methodology), August 2003, vol. 65, no. 3, pp. 585-604, Ingenta.  
  9. Dynamic random Weyl sampling for drastic reduction of randomness in Monte Carlo integration
    Sugita H.
    Mathematics and Computers in Simulation, 3 March 2003, vol. 62, no. 3, pp. 529-537, Ingenta.  
  10. A comparison between (quasi-)Monte Carlo and cubature rule based methods for solving high-dimensional integration problems
    Schurer R.
    Mathematics and Computers in Simulation, 3 March 2003, vol. 62, no. 3, pp. 509-517, Ingenta.  
  11. Strong tractability of multivariate integration using quasi-Monte Carlo algorithms.  
    Wang, Xiaoqun
    Math. Comp.  72  (2003),  no. 242, 823--838 (electronic), MathSciNet.  
  12. A new Monte Carlo method of the numerical integration "superposing method"
    Kaneko, T.; Tobimatsu, K.  
    Nuclear Instruments and Methods in Physics Research, Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, v 502, n 2-3, Apr 21, 2003, p 590-592, Compendex.
  13. Defects in parallel Monte Carlo and quasi-Monte Carlo integration using the leap-frog technique
    Entacher, Karl (RIST++); Schell, Thomas; Schmid, Wolfgang Ch.; Uhl, Andreas  
    Parallel Algorithms and Applications, v 18, n 1-2, May, 2003, p 13-26, Compendex.
  14. Monte-Carlo Integration Using Cryptographically Secure Pseudo-random Generator
    Sugita, H.
    Lecture Notes in Computer Science, 2003, no. 2542, pp. 140-148, Ingenta.
  15. Error bounds for quasi-Monte Carlo integration with uniform point sets
    Niederreiter, Harald
    Journal of Computational and Applied Mathematics, v 150, n 2, Jan 15, 2003, p 283-292, Compendex.
  16. Using Genetic Operators to Speed up Markov Chain Monte Carlo Integration
    Lukka, T. J.; Kujala, J. V.
    Monte Carlo Methods and Applications, 2002, vol. 8, no. 1, pp. 51-72, Ingenta.
  17. A constructive approach to strong tractability using quasi-Monte Carlo algorithms.  
    Wang, Xiaoqun
    J. Complexity  18  (2002),  no. 3, 683--701, MathSciNet.  
  18. A Quasi-Monte Carlo Method for Integration with Improved Covergence
    Karaivanova, A.; Dimov, I.; Ivanovska, S.
    Lecture Notes in Computer Science, 2001, no. 2179, pp. 158-165, Ingenta.
  19. Tractability of multivariate integration for periodic functions.
    Hickernell, Fred J.; Wozniakowski, Henryk
    Complexity of multivariate problems (Kowloon, 1999).  J. Complexity  17  (2001),  no. 4, 660--682, MathSciNet.  
  20. Path integral Monte Carlo applications to quantum fluids in confined geometries
    Ceperley, David M.; Manousakis, Efstratios  
    Journal of Chemical Physics, v 115, n 22, Dec 8, 2001, p 10111-10118, Compendex.
  21. On Variance Reducing Multipliers for Monte Carlo Integration
    Gorbacheva, N. B.; Sobol, I. M.; Trikuzov, A. I.
    Computational Mathematics and Mathematical Physics, 2001, vol. 41, no. 9, pp. 1246-1250, Ingenta.
  22. Choice of integrator in the hybrid Monte Carlo algorithm
    Takaishi, Tetsuya   
    Computer Physics Communications, v 133, n 1, Dec, 2000, p 6-17, Compendex.
  23. Monte-Carlo and quasi-Monte-Carlo methods for numerical integration.
    Faure, Henri
    Combinatorial & computational mathematics (Pohang, 2000), 1--12, World Sci. Publishing, River Edge, NJ, 2001, MathSciNet.  
  24. Geometrical Monte Carlo method and its modifications.
    Voytishek, A. V.; Dyatlova, E. G.; Mezentseva, T. E.
    Monte Carlo Methods Appl. 6 (2000), no. 2, 131--139, MathSciNet.  
  25. High dimensional integration
    Edited by E. Novak.
    Adv. Comput. Math. 12 (2000), no. 1. Baltzer Science Publishers BV, Bussum, 2000. pp. i--vi and 1--93, MathSciNet.  
  26. A Classroom Note on Monte Carlo Integration.
    Kolpas, Sid
    Mathematics and computer education, 1998, vol. 32, no. 1, pp. 6, Ingenta.  
  27. The Randomness of Remainders (in Notes)  
    D. A. Moran; B. M. Stewart  
    Mathematics Magazine, Vol. 71, No. 2. (Apr., 1998), pp. 139-141, Jstor.  
  28. A Quasi-Monte Carlo Scheme using Nets for a Linear Boltzmann Equation  
    Christian Lecot; Ibrahim Coulibaly  
    SIAM Journal on Numerical Analysis, Vol. 35, No. 1. (Feb., 1998), pp. 51-70, Jstor.  
  29. Variance reduction order using good lattice points in Monte Carlo methods.
    Tuffin, B.
    Computing 61 (1998), no. 4, 371--378, MathSciNet.  
  30. Improved Monte Carlo from factor integration.
    Pianykh, O.S.; Tyler, J.M.; Waggenspack Jr., W.N.
    Computers & Graphics (Pergamon), 1998, vol. 22, no. 6, pp. 723-734, Ingenta.
  31. Path integral Monte Carlo calculation of electronic forces
    Zong, Fenghua; Ceperley, D.M.  
    Physical Review E. Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, v 58, n 4, Oct, 1998, p 5123, Compendex.
  32. Applications to risk theory of a Monte Carlo multiple integration method.
    Usabel, M.A.
    Insurance, mathematics & economics, 1998, vol. 23, no. 1, pp. 71, Ingenta.
  33. Error analysis of an adaptive Monte Carlo method for numerical integration
    Karaivanova, Aneta; Dimov, Ivan  
    Mathematics and Computers in Simulation, v 47, n 2-5, Aug 1, 1998, p 201-213, Compendex.
  34. A Use of Monte Carlo Integration for Population Pharmacokinetics with Multivariate Population Distribution.
    Yafume, Akifumi; Takebe, Masato; Ogata, Hiroyasu
    Journal of pharmacokinetics and biopharmaceutics, 1998, vol. 26, no. 1, pp. 103, Ingenta.
  35. On Quasi-Monte Carlo Simulation of Stochastic Differential Equations  
    Norbert Hofmann; Peter Mathe  
    Mathematics of Computation, Vol. 66, No. 218. (Apr., 1997), pp. 573-589, Jstor.  
  36. On quasi-Monte Carlo integrations.
    Sobol, I. M.
    IMACS Seminar on Monte Carlo Methods (Brussels, 1997). Math. Comput. Simulation 47 (1998), no. 2-5, 103--112, Math. Sci. Net.   
  37. Quasi-Monte Carlo integration of digitally smooth functions by digital nets.
    Larcher, Gerhard; Pirsic, Gottlieb; Wolf, Reinhard
    Monte Carlo and quasi-Monte Carlo methods 1996 (Salzburg), 321--329, Lecture Notes in Statist., 127, Springer, New York, 1998, MathSciNet.  
  38. Monte Carlo integration with quasi-random numbers: experience with discontinuous integrands
    Berblinger, M.; Schlier, Ch.; Weiss, T.
    Computer Physics Communications, v 99, n 2-3, Jan, 1997, p 151-162, Compendex.  
  39. Error Bounds for Quasi-Monte Carlo Integration with Nets  
    Christian Lecot  
    Mathematics of Computation, Vol. 65, No. 213. (Jan., 1996), pp. 179-187, Jstor.  
  40. A Variance Reducing Multiplier for Monte Carlo Integrations
    Sobol', I. M.; Tutunnikov, A. V.  
    Mathematical and Computer Modelling (Oxford), v 23, n 8-9, 1996, p 87, Compendex.
  41. Quasi-Monte Carlo Methods for the Numerical Integration of Multivariate Walsh Series
    Larcher, G.; Schmid, W. C.; Wolf, R.
    Mathematical and Computer Modelling (Oxford), v 23, n 8-9, 1996, p 55, Compendex.
  42. The optimal error of Monte Carlo integration.
    Mathé, Peter
    J. Complexity 11 (1995), no. 4, 394--415, Math. Sci. Net.   
  43. On the numerical integration of high-dimensional Walsh-series by Quasi-Monte Carlo methods
    Larcher, G.; Schmid, W. Ch.  
    Mathematics and Computers in Simulation, v 38, n 1-3, May, 1995, p 127, Compendex.
  44. Quasi-Monte Carlo Integration.
    Morokoff, William J.; Caflisch, Russel E.
    Journal of computational physics, 1995, vol. 122, no. 2, pp. 218-230, Ingenta.  
  45. Monte Carlo integration, quadratic resampling, and asset pricing
    Barraquand, J.  
    Mathematics and Computers in Simulation, v 38, n 1-3, May, 1995, p 173, Compendex.
  46. Monte Carlo integration of dissipative quantum systems
    Naraschewski, M.; Schenzle, A.  
    Zeitschrift fuer Physik D: Atoms, Molecules and Clusters, v 33, n 2, 1995, p 79, Compendex.
  47. Semi-classical Monte Carlo path integration without root searches
    Kinugawa, T.  
    Chemical Physics Letters, v 235, n 5-6, 1995, p 395, Compendex.
  48. Using the weighted Monte Carlo method for solving nonlinear integral equations
    Plotnikov, M. Yu.  
    Russian Journal of Numerical Analysis and Mathematical Modelling, v 9, n 2, 1994, p 121-145, Compendex.
  49. Integration and approximation of multivariate functions: average case complexity with isotropic Wiener measure.  
    Wasilkowski, G. W.
    J. Approx. Theory  77  (1994),  no. 2, 212--227, MathSciNet.  
  50. Determining Sample Sizes for Monte Carlo Integration (in Classroom Computer Capsules)  
    David Neal  
    The College Mathematics Journal, Vol. 24, No. 3. (May, 1993), pp. 254-259, Jstor.  
  51. Estimation of multidimensional integrals: is Monte Carlo the best method?  
    Janse van Rensburg, E. J.; Torrie, G. M.
    J. Phys. A  26  (1993),  no. 4, 943--953, MathSciNet.  
  52. Good Parameters for a Class of Node Sets in Quasi-Monte Carlo Integration  
    Tom Hansen, Gary L. Mullen, Harald Niederreiter  
    Mathematics of Computation, Vol. 61, No. 203, Special Issue Dedicated to Derrick Henry Lehmer. (Jul., 1993), pp. 225-234, Jstor.  
  53. Integration of Multimodal Functions by Monte Carlo Importance Sampling (in Theory and Methods)  
    Man-Suk Oh; James O. Berger  
    Journal of the American Statistical Association, Vol. 88, No. 422. (Jun., 1993), pp. 450-456, Jstor.  
  54. A quasi-Monte Carlo approach to particle simulation of the heat equation.
    Morokoff, William J.; Caflisch, Russel E.
    SIAM J. Numer. Anal. 30 (1993), no. 6, 1558--1573, MathSciNet.  
  55. Monte Carlo simulation of the integrating sphere
    Research Reports: Helsinki University of Technology Department of Mechanical Engineering, n 891, Sept, 1993, p 42, Compendex.
  56. The Monte Carlo complexity of Fredholm integral equations.
    Heinrich, Stefan; Mathé, Peter
    Math. Comp. 60 (1993), no. 201, 257--278, MathSciNet.  
  57. Estimation of multidimensional integrals: is Monte Carlo the best method?  
    Janse van Rensburg, E. J.; Torrie, G. M.
    J. Phys. A  26  (1993),  no. 4, 943--953, MathSciNet.  
  58. Trapezoidal Stratified Monte Carlo Integration  
    Stamatis Cambanis, Elias Masry  
    SIAM Journal on Numerical Analysis, Vol. 29, No. 1. (Feb., 1992), pp. 284-301, Jstor.  
  59. A Monte Carlo Application to Approximate [Graphics:../Images/MonteCarloBib_gr_2.gif]   
    Kenneth Easterday and Tommy Smith   
    School Science and Mathematics, Vol. 92, No. 1, (1992), pp. 23-25.   
  60. Average-case complexity distributions: a generalization of the Wozniakowski lemma for multidimensional numerical integration
    Kleiss, Ronald
    Comput. Phys. Comm.  71  (1992),  no. 1-2, 39--46., MathSciNet.  
  61. Adaptive Importance Sampling in Monte Carlo Integration.
    Oh, Man-Suk; Berger, James O.
    Journal of statistical computation and simulation, 1992, vol. 41, no. 3/4, pp. 143-168, Ingenta.  
  62. Quasi-Monte Carlo methods for numerical integration
    CBMS-NSF Regional Conference Series in Applied Mathematics, n 63, 1992, p 13, Compendex.
  63. Monte carlo integration packages BASES and DICE
    Kawarata, S.  
    Proceedings of the International Workshop on Software Engineering, Artificial Intelligence and Expert Systems in High Energy and Nuclear Physics, New Computing Techniques in Physics Research II, 1992, p 745, Compendex.
  64. Monte Carlo Simulation of Infinite Series (in Notes)  
    Frederick Solomon  
    Mathematics Magazine, Vol. 64, No. 3. (Jun., 1991), pp. 188-196, Jstor.  
  65. Monte Carlo integration with quasi-random numbers: some experience.
    Berblinger, Michael; Schlier, Christoph
    Comput. Phys. Comm. 66 (1991), no. 2-3, 157--166, Math. Sci. Net.   
  66. Average Case Complexity of Multivariate Integration
    Wozniakowski, H.
    Bull. Amer. Math. Soc. 24, 185-194, 1991.
  67. Trapezoidal Monte Carlo Integration  
    Elias Masry, Stamatis Cambanis  
    SIAM Journal on Numerical Analysis, Vol. 27, No. 1. (Feb., 1990), pp. 225-246, Jstor.  
  68. Monte Carlo modeling of the tracking signal for forecast errors in computer integrated manufacture
    Ristroph, John H.   
    Computers & Industrial Engineering, v 19, n 1-4, 1990, p 67-71, Compendex.
  69. Bayesian Inference in Econometric Models Using Monte Carlo Integration  
    John Geweke  
    Econometrica, Vol. 57, No. 6. (Nov., 1989), pp. 1317-1339, Jstor.  
  70. Reducing of variance by spline functions in Monte Carlo integration.
    Blaga, Petru
    Studia Univ. Babe\c s-Bolyai Math. 34 (1989), no. 4, 69--78, MathSciNet.  
  71. Volume estimation by Monte Carlo methods.
    Fok, D. S. K.; Crevier, D.
    J. Statist. Comput. Simulation 31 (1989), no. 4, 223--235, MathSciNet.  
  72. A Monte Carlo method for high-dimensional integration.  
    Ogata, Yosihiko
    Numer. Math.  55  (1989),  no. 2, 137--157, MathSciNet.  
  73. Quasi-Monte Carlo methods for multidimensional numerical integration.
    Niederreiter, Harald
    Numerical integration, III (Oberwolfach, 1987), 157--171, Internat. Schriftenreihe Numer. Math., 85, Birkhäuser, Basel, 1988, MathSciNet.  
  74. Hierarchical Bayesian Analysis Using Monte Carlo Integration: Computing Posterior Distributions When There are Many Possible Models  
    Leland Stewart  
    The Statistician, Vol. 36, No. 2/3, Special Issue: Practical Bayesian Statistics. (1987), pp. 211-219, Jstor.  
  75. Bayesian Posterior Distributions Over Sets of Possible Models with Inferences Computed by Monte Carlo Integration  
    Leland Stewart; William W. Davis  
    The Statistician, Vol. 35, No. 2, Special Issue: Statistical Modelling. (1986), pp. 175-182, Jstor.  
  76. A Monte Carlo Simulation Related to the St. Petersburg Paradox (in Computer Corner)  
    Allan J. Ceasar  
    The College Mathematics Journal, Vol. 15, No. 4. (Sep., 1984), pp. 339-342, Jstor.  
  77. Bayesian Analysis Using Monte Carlo Integration-a Powerful Methodology for Handling Some Difficult Problems  
    Leland Stewart  
    The Statistician, Vol. 32, No. 1/2, Proceedings of the 1982 I.O.S. Annual Conference on Practical Bayesian Statistics. (Mar. - Jun., 1983), pp. 195-200, Jstor.  
  78. Markov Chains in Monte Carlo  
    Hans Sagan  
    Mathematics Magazine, Vol. 54, No. 1. (Jan., 1981), pp. 3-10, Jstor.  
  79. Binomial Baseball (in Computers and Calculators)  
    Eugene M. Levin  
    The Two-Year College Mathematics Journal, Vol. 12, No. 4. (Sep., 1981), pp. 260-266, Jstor.  
  80. Weighted Monte Carlo Integration  
    S. Yakowitz, J. E. Krimmel, F. Szidarovszky  
    SIAM Journal on Numerical Analysis, Vol. 15, No. 6. (Dec., 1978), pp. 1289-1300, Jstor.  
  81. Multidimensional Monte Carlo Integration Based on Factorized Approximation Functions  
    Tateaki Sasaki  
    SIAM Journal on Numerical Analysis, Vol. 15, No. 5. (Oct., 1978), pp. 938-952, Jstor.  
  82. Bayesian Estimates of Equation System Parameters: An Application of Integration by Monte Carlo  
    T. Kloek; H. K. van Dijk  
    Econometrica, Vol. 46, No. 1. (Jan., 1978), pp. 1-19, Jstor.  
  83. Bisection method for Monte Carlo integration.
    Okamoto, Masashi; Takahashi, Rinya
    Math. Japon. 22 (1977), no. 3, 403--411, Math. Sci. Net.   
  84. Asymptotic Normality in Monte Carlo Integration  
    Masashi Okamot  
    Mathematics of Computation, Vol. 30, No. 136. (Oct., 1976), pp. 831-837, Jstor.  
  85. Calcul d'une intégrale sur un triangle par la méthode de Monte-Carlo.
    Hillion, Pierre
    C. R. Acad. Sci. Paris Sér. A-B 282 (1976), no. 1, Aiii, A59--A61, MathSciNet.  
  86. A Precalculus Unit on Area under Curves (in Computer Corner)  
    Samuel Goldberg
    The Two-Year College Mathematics Journal, Vol. 6, No. 4. (Dec., 1975), pp. 29-35, Jstor.  
  87. Fast Monte Carlo integration of PDF estimators.
    Batchelor, B. G.; Hand, D. J.
    J. Cybernet. 5 (1975), no. 3, 111--124 (1976), MathSciNet.  
  88. The Mathematical Basis of Monte Carlo and Quasi-Monte Carlo Methods  
    S. K. Zaremba  
    SIAM Review, Vol. 10, No. 3. (Jul., 1968), pp. 303-314, Jstor.  
  89. Bernstein Polynomials and Monte Carlo Integration  
    Lloyd Rosenberg  
    SIAM Journal on Numerical Analysis, Vol. 4, No. 4. (Dec., 1967), pp. 566-574, Jstor.  
  90. A Modified Monte-Carlo Quadrature  
    Seymour Haber  
    Mathematics of Computation, Vol. 20, No. 95. (Jul., 1966), pp. 361-368, Jstor.  
  91. Monte Carlo Methods for Solving Multivariable Problems  
    Hammersley, J. M.
    Ann. New York Acad. Sci. 86, 844-874, 1960.
  92. The Monte Carlo Method  
    W. F. Bauer  
    Journal of the Society for Industrial and Applied Mathematics, Vol. 6, No. 4. (Dec., 1958), pp. 438-451, Jstor.  
  93. Some Monte Carlo Experiments in Computing Multiple Integrals  
    P. Davis; P. Rabinowitz  
    Mathematical Tables and Other Aids to Computation, Vol. 10, No. 53. (Jan., 1956), pp. 1-8, Jstor.  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2005