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Computing the probability of evidence even with known error bounds isNP-hard. In this paper we address this hard problem by settling on an easierproblem. We propose an approximation which provides high confidence lowerbounds on probability of evidence but does not have any guarantees in terms ofrelative or absolute error. Our proposed approximation is a randomizedimportance sampling scheme that uses the Markov inequality. However, astraight-forward application of the Markov inequality may lead to poor lowerbounds. We therefore propose several heuristic measures to improve itsperformance in practice. Empirical evaluation of our scheme with state-of-the-art lower bounding schemes reveals the promise of our approach.

Studies in Lower Bounding Probabilities of Evidence using the Markov Inequality