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Approximating Integrals via Monte Carlo and Deterministic Methods

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  • Evans, Michael

    (University of Toronto)

  • Swartz, Timothy

    (Simon Fraser University)

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    Abstract

    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.

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    Bibliographic Info

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    This book is provided by Oxford University Press in its series OUP Catalogue with number 9780198502784 and published in 2000.

    ISBN: 9780198502784
    Order: http://ukcatalogue.oup.com/product/9780198502784.do
    Handle: RePEc:oxp:obooks:9780198502784

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    Cited by:
    1. 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.
    2. Berridge, S.J. & Schumacher, J.M., 2004. "An Irregular Grid Approach for Pricing High-Dimensional American Options," Discussion Paper 2004-18, Tilburg University, Center for Economic Research.
    3. Tian, Guo-Liang & Ng, Kai Wang & Li, Kai-Can & Tan, Ming, 2009. "Non-iterative sampling-based Bayesian methods for identifying changepoints in the sequence of cases of Haemolytic uraemic syndrome," Computational Statistics & Data Analysis, Elsevier, vol. 53(9), pages 3314-3323, July.
    4. 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.
    5. L'Ecuyer, Pierre, 2004. "Random number generation," Papers 2004,21, Humboldt-Universität Berlin, Center for Applied Statistics and Economics (CASE).
    6. 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.
    7. Robin K. S. Hankin, . "A Generalization of the Dirichlet Distribution," Journal of Statistical Software, American Statistical Association, vol. 33(i11).
    8. Diego Kuonen, . "Numerical Integration in S-PLUS or R: A Survey," Journal of Statistical Software, American Statistical Association, vol. 8(i13).
    9. 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.
    10. 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.
    11. Sugita, Katsuhiro, 2002. "Testing For Cointegration Rank Using Bayes Factors," The Warwick Economics Research Paper Series (TWERPS) 654, University of Warwick, Department of Economics.
    12. Episcopos, Athanasios, 2004. "The implied reserves of the Bank Insurance Fund," Journal of Banking & Finance, Elsevier, vol. 28(7), pages 1617-1635, July.

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