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Approximating Integrals via Monte Carlo and Deterministic Methods


  • Evans, Michael

    (University of Toronto)

  • Swartz, Timothy

    (Simon Fraser University)


This book is designed to introduce graduate students and researchers to the primary methods useful for approximating integrals. The emphasis is on those methods that have been found to be of practical use, and although the focus is on approximating higher- dimensional integrals the lower-dimensional case is also covered. Included in the book are asymptotic techniques, multiple quadrature and quasi-random techniques as well as a complete development of Monte Carlo algorithms. For the Monte Carlo section importance sampling methods, variance reduction techniques and the primary Markov Chain Monte Carlo algorithms are covered. This book brings these various techniques together for the first time, and hence provides an accessible textbook and reference for researchers in a wide variety of disciplines.

Suggested Citation

  • Evans, Michael & Swartz, Timothy, 2000. "Approximating Integrals via Monte Carlo and Deterministic Methods," OUP Catalogue, Oxford University Press, number 9780198502784.
  • Handle: RePEc:oxp:obooks:9780198502784

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    6. Berridge, S.J. & Schumacher, J.M., 2004. "Pricing High-Dimensional American Options Using Local Consistency Conditions," Discussion Paper 2004-19, Tilburg University, Center for Economic Research.
    7. Peter J. Diggle & Irene Kaimi & Rosa Abellana, 2010. "Partial-Likelihood Analysis of Spatio-Temporal Point-Process Data," Biometrics, The International Biometric Society, vol. 66(2), pages 347-354, June.
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    9. Hankin, Robin K. S., 2010. "A Generalization of the Dirichlet Distribution," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 33(i11).
    10. Berridge, S.J. & Schumacher, J.M., 2002. "An Irregular Grid Approach for Pricing High Dimensional American Options," Discussion Paper 2002-99, Tilburg University, Center for Economic Research.
    11. L'Ecuyer, Pierre, 2004. "Random number generation," Papers 2004,21, Humboldt University of Berlin, Center for Applied Statistics and Economics (CASE).
    12. A. N. Pettitt & N. Friel & R. Reeves, 2003. "Efficient calculation of the normalizing constant of the autologistic and related models on the cylinder and lattice," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(1), pages 235-246.
    13. Kuonen, Diego, 2003. "Numerical Integration in S-PLUS or R: A Survey," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 8(i13).
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    17. A. Kong & P. McCullagh & X.-L. Meng & D. Nicolae & Z. Tan, 2003. "A theory of statistical models for Monte Carlo integration," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(3), pages 585-604.
    18. Lucio Barabesi, 2003. "A Monte Carlo integration approach to Horvitz-Thompson estimation in replicated environmental designs," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 355-374.
    19. Nott, David J. & Fielding, Mark & Leonte, Daniela, 2009. "On a generalization of the Laplace approximation," Statistics & Probability Letters, Elsevier, vol. 79(11), pages 1397-1403, June.
    20. Qian, Zhiguang & Shapiro, Alexander, 2006. "Simulation-based approach to estimation of latent variable models," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 1243-1259, November.
    21. Djennad, Abdelmajid & Rigby, Robert & Stasinopoulos, Dimitrios & Voudouris, Vlasios & Eilers, Paul, 2015. "Beyond location and dispersion models: The Generalized Structural Time Series Model with Applications," MPRA Paper 62807, University Library of Munich, Germany.
    22. Sartori, N. & Severini, T.A. & Marras, E., 2010. "An alternative specification of generalized linear mixed models," Computational Statistics & Data Analysis, Elsevier, vol. 54(2), pages 575-584, February.
    23. P. Gareth Ridall & Anthony N. Pettitt & Robert D. Henderson & Pamela A. McCombe, 2006. "Motor Unit Number Estimation—A Bayesian Approach," Biometrics, The International Biometric Society, vol. 62(4), pages 1235-1250, December.
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    25. Fakhereddine, Rana & Haddad, Rami El & Lécot, Christian & Maalouf, Joseph El, 2017. "Stratified Monte Carlo simulation of Markov chains," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 135(C), pages 51-62.

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