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Abstract:
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The standard importance sampling (IS) method uses samples from a single proposal distribution and assigns weights to them, according to the ratio of the target and proposal pdfs. This naive IS estimator, generally does not work well in multiple target examples as the weights can take arbitrarily large values making the estimator highly unstable. In such situations, alternative generalized IS estimators involving samples from multiple proposal distributions are preferred. Just like the standard IS, the success of these multiple IS estimators crucially depends on the choice of the proposal distributions. For selecting these proposal distributions, we propose three methods based on a nonparametric coverage criterion, the maximum entropy approach and a sequential approach, respectively. The proposed methods for selecting proposal densities are illustrated using several detailed examples.
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