20,689 research outputs found
Semiparametric Cross Entropy for rare-event simulation
The Cross Entropy method is a well-known adaptive importance sampling method
for rare-event probability estimation, which requires estimating an optimal
importance sampling density within a parametric class. In this article we
estimate an optimal importance sampling density within a wider semiparametric
class of distributions. We show that this semiparametric version of the Cross
Entropy method frequently yields efficient estimators. We illustrate the
excellent practical performance of the method with numerical experiments and
show that for the problems we consider it typically outperforms alternative
schemes by orders of magnitude
Variance Reduction Techniques in Monte Carlo Methods
Monte Carlo methods are simulation algorithms to estimate a numerical quantity in a statistical model of a real system. These algorithms are executed by computer programs. Variance reduction techniques (VRT) are needed, even though computer speed has been increasing dramatically, ever since the introduction of computers. This increased computer power has stimulated simulation analysts to develop ever more realistic models, so that the net result has not been faster execution of simulation experiments; e.g., some modern simulation models need hours or days for a single ’run’ (one replication of one scenario or combination of simulation input values). Moreover there are some simulation models that represent rare events which have extremely small probabilities of occurrence), so even modern computer would take ’for ever’ (centuries) to execute a single run - were it not that special VRT can reduce theses excessively long runtimes to practical magnitudes.common random numbers;antithetic random numbers;importance sampling;control variates;conditioning;stratied sampling;splitting;quasi Monte Carlo
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