Abstract:
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I present a simple and generally applicable method for building an approximating distribution given samples from a multivariate target. This can be used to sample the distribution more efficiently or approximate its normalizing constant. The method involves estimating each marginal distribution separately and combining these marginals with a Gaussian copula. Because this distribution may then be used as the instrumental distribution in an importance sampler, we call our method copula importance sampling. It is especially effective (compared to Gaussian-based methods) when the target is skewed, but performs well on symmetric targets as well. While developed for use on unimodal targets, the method can be adapted to deal with multimodal distributions. I illustrate performance on a wide variety of problems including highly skewed distributions in more than 100 dimensions.
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