Computing with Probability

  • Alexandre J. Chorin
  • Ole H. Hald
Part of the Texts in Applied Mathematics book series (TAM, volume 58)


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.


Posterior Distribution Probability Distribution Function Unbiased Estimate Importance Sampling Vector Variable 
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3.6. Bibliography

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    P. Bickel and K. Doksum, Mathematical Statistics: Basic Ideas and Selected Topics, Prentice Hall, Upper Saddle River, NJ, 2001.Google Scholar
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    A. Chorin, Hermite expansions in Monte-Carlo computation, J. Comput. Phys. 8 (1971), pp. 472–482.Google Scholar
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    A. Chorin, M. Morzfeld and X. Tu, Implicit Filters for Data Assimilation, Comm. Appl. Math. Comp. Sc. 5 (2009), pp. 221–240.Google Scholar
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    J. Hammersley and D. Handscomb, Monte Carlo Methods, Methuen, London, 1964.Google Scholar
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    J. Liu, Monte Carlo Strategies in Scientific Computing, Springer, New York, 2001.Google Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Alexandre J. Chorin
    • 1
  • Ole H. Hald
    • 2
  1. 1.Department of MathematicsUniversity of California, BerkeleyBerkeleyUSA
  2. 2.Department of MathematicsUniversity of California at BerkeleyBerkeleyUSA

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