Basic Principles: Rejection, Weighting, and Others

  • Jun S. Liu
Part of the Springer Series in Statistics book series (SSS)


To generate random variables that follow a general probability distribution function π, we need first to generate random variables uniformly distributed in [0,1]. These random variables are often called random numbers for simplicity. However, this “simple-sounding” task is not easily achievable on a computer. But even if it were possible, it might not be desirable to use authentic random numbers because of the need to debug computer programs. In debugging a program, we often have to repeat the same computation many times; this require us to reproduce the same sequence of random numbers repeatedly. What becomes an accepted alternative in the community of scientific computing is to generate pseudo-random numbers.


Mean Square Error Importance Sampling Monte Carlo Computation Importance Weight Effective Sample Size 


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Copyright information

© Springer Science+Business Media New York 2004

Authors and Affiliations

  • Jun S. Liu
    • 1
  1. 1.Department of StatisticsHarvard UniversityCambridgeUSA

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