Abstract
While Chapter 2 focussed on developing techniques to produce random variables by computer, this chapter introduces the central concept of Monte Carlo methods, that is, taking advantage of the availability of computer generated random variables to approximate univariate and multidimensional integrals. In Section 3.2, we introduce the basic notion of Monte Carlo approximations as a byproduct of the Law of Large Numbers, while Section 3.3 highlights the universality of the approach by stressing the versatility of the representation of an integral as an expectation.
Cadfael had heard the words without hearing them and enlightenment fell on him so dazzlingly that he stumbled on the threshold.
—Ellis Peter, The Heretic’s Apprentice
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Notes
Bucklew, J. (1990). Large Deviation Techniques in Decision, Simulation and Estimation. John Wiley, New York.
Lugannani, R. and Rice, S. (1980). Saddlepoint approximation for the distribution of the sum of independent random variables. Adv. Appl. Probab., 12: 475–490.
DiCiccio, T. J. and Martin, M. A. (1993). Simple modifications for signed roots of likelihood ratio statistics. J. Royal Statist. Soc. Series B, 55: 305–316.
Wood, A., Booth, J., and Butler, R. (1993). Saddlepoint approximations to the CDF of some statistics with nonnormal limit distributions. J. American Statist. Assoc., 88: 680–686.
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© 2004 Springer Science+Business Media New York
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Robert, C.P., Casella, G. (2004). Monte Carlo Integration. In: Monte Carlo Statistical Methods. Springer Texts in Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-4145-2_3
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DOI: https://doi.org/10.1007/978-1-4757-4145-2_3
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-1939-7
Online ISBN: 978-1-4757-4145-2
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