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Approximating Integrals via Monte Carlo and Deterministic Methods

Author

Listed:
  • Evans, Michael

    (University of Toronto)

  • Swartz, Timothy

    (Simon Fraser University)

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.

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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    References listed on IDEAS

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    1. Gordon,Robert J., 2004. "Productivity Growth, Inflation, and Unemployment," Cambridge Books, Cambridge University Press, number 9780521531429, March.
    2. Dale W. Jorgenson, 2001. "Information Technology and the U.S. Economy," American Economic Review, American Economic Association, vol. 91(1), pages 1-32, March.
    3. Gordon,Robert J., 2004. "Productivity Growth, Inflation, and Unemployment," Cambridge Books, Cambridge University Press, number 9780521800082, March.
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    Cited by:

    1. repec:eee:reensy:v:92:y:2007:i:10:p:1374-1387 is not listed on IDEAS
    2. Sugita, Katsuhiro, 2002. "Testing For Cointegration Rank Using Bayes Factors," The Warwick Economics Research Paper Series (TWERPS) 654, University of Warwick, Department of Economics.
    3. repec:eee:reensy:v:91:y:2006:i:3:p:320-348 is not listed on IDEAS
    4. repec:eee:reensy:v:124:y:2014:i:c:p:171-200 is not listed on IDEAS
    5. 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.
    6. 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.
    7. Hankin, Robin K. S., 2010. "A Generalization of the Dirichlet Distribution," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 33(i11).
    8. 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.
    9. L'Ecuyer, Pierre, 2004. "Random number generation," Papers 2004,21, Humboldt University of Berlin, Center for Applied Statistics and Economics (CASE).
    10. 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.
    11. Kuonen, Diego, 2003. "Numerical Integration in S-PLUS or R: A Survey," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 8(i13).
    12. repec:eee:reensy:v:94:y:2009:i:3:p:699-721 is not listed on IDEAS
    13. repec:eee:reensy:v:91:y:2006:i:10:p:1175-1209 is not listed on IDEAS
    14. Episcopos, Athanasios, 2004. "The implied reserves of the Bank Insurance Fund," Journal of Banking & Finance, Elsevier, vol. 28(7), pages 1617-1635, July.
    15. 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.
    16. Lucio Barabesi, 2003. "A Monte Carlo integration approach to Horvitz-Thompson estimation in replicated environmental designs," Metron - International Journal of Statistics, Dipartimento di Statistica, ProbabilitĂ  e Statistiche Applicate - University of Rome, vol. 0(3), pages 355-374.
    17. 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.
    18. 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.
    19. 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.
    20. 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.
    21. Fakhereddine, Rana & Haddad, Rami El & LĂ©cot, 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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