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Importance sampling is a variance reduction technique that can be used in the Monte Carlo method.The idea behind importance sampling is that certain values of the input random variables in a simulation have more impact on the parameter being estimated than others.
Subset simulation [1] is a method used in reliability engineering to compute small (i.e., rare event) failure probabilities encountered in engineering systems. The basic idea is to express a small failure probability as a product of larger conditional probabilities by introducing intermediate failure events.
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The GHK algorithm (Geweke, Hajivassiliou and Keane) [1] is an importance sampling method for simulating choice probabilities in the multivariate probit model.These simulated probabilities can be used to recover parameter estimates from the maximized likelihood equation using any one of the usual well known maximization methods (Newton's method, BFGS, etc.).
The sequential importance resampling technique provides another interpretation of the filtering transitions coupling importance sampling with the bootstrap resampling step. Last, but not least, particle filters can be seen as an acceptance-rejection methodology equipped with a recycling mechanism.
It is an alternative to methods from the Bayesian literature [3] such as bridge sampling and defensive importance sampling. Here is a simple version of the nested sampling algorithm, followed by a description of how it computes the marginal probability density Z = P ( D ∣ M ) {\displaystyle Z=P(D\mid M)} where M {\displaystyle M} is M 1 ...
Let the unknown parameter of interest be , and assume we have a statistic such that the expected value of m is μ: [] =, i.e. m is an unbiased estimator for μ. Suppose we calculate another statistic such that [] = is a known value.
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