Introduction and Examples

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


An essential part of many scientific problems is the computation of integral
$$I = \int_D {g\left( x \right)} {\kern 1pt} dx$$
, where D is often a region in a high-dimensional space and g(x) is the target function of interest. If we can draw independent and identically distributed (i.i.d.) random samples x(1) ... , x(m) uniformly from D (by a computer), an approximation to I can be obtained as
$$ {\hat I_m} = \frac{1}{m}\left\{ {g\left( {{x^{\left( 1 \right)}}} \right) + \cdots + g\left( {{x^{\left( m \right)}}} \right)} \right\}. $$


Markov Chain Partition Function Markov Chain Monte Carlo Ising Model Umbrella Sampling 
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

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

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