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Permutation tests are commonly used for estimating p-values from statistical hypothesis testing when the sampling distribution of the test statistic under the null hypothesis is not available or unreliable for finite sample sizes. One critical challenge for permutation tests in genomic studies is that an enormous number of permutations is needed for obtaining reliable estimations of small p-values, which requires intensive computational efforts. In this paper, we develop a computationally efficient algorithm for evaluating small p-values from permutation tests based on an adaptive importance sampling approach, which uses the cross-entropy method for finding the optimal proposal density. Simulation studies and analysis of a real microarray dataset demonstrate that our approach achieves considerable gains in computational efficiency comparing with existing methods.
Small $p$-values are often required to be accurately estimated in large scale genomic studies for the adjustment of multiple hypothesis tests and the ranking of genomic features based on their statistical significance. For those complicated test stat
Importance sampling (IS) is a Monte Carlo technique for the approximation of intractable distributions and integrals with respect to them. The origin of IS dates from the early 1950s. In the last decades, the rise of the Bayesian paradigm and the inc
This paper deals with the estimation of rare event probabilities using importance sampling (IS), where an optimal proposal distribution is computed with the cross-entropy (CE) method. Although, IS optimized with the CE method leads to an efficient re
The Adaptive Multiple Importance Sampling (AMIS) algorithm is aimed at an optimal recycling of past simulations in an iterated importance sampling scheme. The difference with earlier adaptive importance sampling implementations like Population Monte
Monte Carlo methods represent the de facto standard for approximating complicated integrals involving multidimensional target distributions. In order to generate random realizations from the target distribution, Monte Carlo techniques use simpler pro