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.
Importance Sampling Tail Probability Finite Variance Laplace Approximation Monte Carlo Integration
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in to check access
Bucklew, J. (1990). Large Deviation Techniques in Decision, Simulation and Estimation. John Wiley, New York.Google Scholar
Lugannani, R. and Rice, S. (1980). Saddlepoint approximation for the distribution of the sum of independent random variables. Adv. Appl. Probab., 12: 475–490.MathSciNetMATHCrossRefGoogle Scholar
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.MathSciNetMATHGoogle Scholar
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.MathSciNetMATHCrossRefGoogle Scholar