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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.
The cross-entropy (CE) method is a Monte Carlo method for importance sampling and optimization. It is applicable to both combinatorial and continuous problems, with either a static or noisy objective. The method approximates the optimal importance sampling estimator by repeating two phases: [1] Draw a sample from a probability distribution.
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.
Exponential Tilting is used in Monte Carlo Estimation for rare-event simulation, and rejection and importance sampling in particular. In mathematical finance [ 1 ] Exponential Tilting is also known as Esscher tilting (or the Esscher transform ), and often combined with indirect Edgeworth approximation and is used in such contexts as insurance ...
The best-known importance sampling method, the Metropolis algorithm, can be generalized, and this gives a method that allows analysis of (possibly highly nonlinear) inverse problems with complex a priori information and data with an arbitrary noise distribution.
A variety of data re-sampling techniques are implemented in the imbalanced-learn package [1] compatible with the scikit-learn Python library. The re-sampling techniques are implemented in four different categories: undersampling the majority class, oversampling the minority class, combining over and under sampling, and ensembling sampling.
The nested sampling algorithm is a computational approach to the Bayesian statistics problems of comparing models and generating samples from posterior distributions. It was developed in 2004 by physicist John Skilling.
In 2000, Liu and Aragon proposed a decomposition of unequal selection probabilities design effect for different strata in stratified sampling. [39] In 2002, Liu et al. extended that work to account for stratified samples, where within each stratum is a set of unequal selection probability weights.