Quasi Importance Sampling

Wolfgang Hörmann and Josef Leydold


There arise two problems when the expectation of some function with respect to a nonuniform multivariate distribution has to be computed by (quasi-) Monte Carlo integration: the integrand can have singularities when the domain of the distribution is unbounded and it can be very expensive or even impossible to sample points from a general multivariate distribution. We show that importance sampling is a simple method to overcome both problems.

Mathematics Subject Classification: 65C05 (Monte Carlo Methods), 65C10, 65D32 (Quadrature formulas - numerical methods)

General Terms: Algorithms

Key Words: quasi-Monte Carlo method, nonuniform random variate generation, inversion method, importance sampling, Markov chain Monte Carlo

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