Computing with Probability
In this chapter we present some of the ways in which probability can be put to use in scientific computation. We begin with a class of Monte Carlo methods (so named in honor of that town’s gambling casinos) where one evaluates a nonrandom quantity, for example a definite integral, as the expected value of a random variable.
- .T. Amemiya, Introduction to Statistics and Econometrics, Harvard University Press, Cambridge, MA, 1994.Google Scholar
- .P. Bickel and K. Doksum, Mathematical Statistics: Basic Ideas and Selected Topics, Prentice Hall, Upper Saddle River, NJ, 2001.Google Scholar
- .A. Chorin, Hermite expansions in Monte-Carlo computation, J. Comput. Phys. 8 (1971), pp. 472–482.Google Scholar
- .A. Chorin, M. Morzfeld and X. Tu, Implicit Filters for Data Assimilation, Comm. Appl. Math. Comp. Sc. 5 (2009), pp. 221–240.Google Scholar
- .J. Hammersley and D. Handscomb, Monte Carlo Methods, Methuen, London, 1964.Google Scholar
- .J. Liu, Monte Carlo Strategies in Scientific Computing, Springer, New York, 2001.Google Scholar