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Tools and Techniques for Importance Sampling

  • James Antonio Bucklew
Part of the Springer Series in Statistics book series (SSS)

Abstract

All of the simulation distribution families that we have seen and worked with in this book are some sort of parametric family parameterized by some vector parameter θ. The mean shift method can be thought of as a family of distributions parameterized by the mean shift. The same is true for the variance scaling method. Of course the exponential shifts have the exponential shift parameter. A mixture of m exponential shifts can be thought of as a parametric class where we have the parameters θ 1, θ 2,..., θ m, p 1, p 2,..., p m, where the {θ i } are the (vector) exponential shifts for each element of the mixture and the {p i } are the scalar mixture weights (they must sum to one which implies there are really only m — 1 free mixture weight parameters). The universal simulation distributions (once we select the “covering measure” 7) are characterized by a single scalar parameter. In fact this is their major selling point.

Keywords

Importance Sampling Simulation Distribution Noise Sample Empirical Variance Standard Normal Random Variable 
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.

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Copyright information

© Springer Science+Business Media New York 2004

Authors and Affiliations

  • James Antonio Bucklew
    • 1
  1. 1.Department of Electrical and Computer EngineeringUniversity of Wisconsin-MadisonMadisonUSA

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