COMPUTING TAIL AREAS FOR A HIGH-DIMENSIONAL GAUSSIAN MIXTURE

We consider the problem of computing tail probabilities - that is, probabilities of regions with low density - for high-dimensional Gaussian mixtures. We consider three approaches: the first is a bound based on the central and non-central chi(2) distributions; the second uses Pearson curves with the first three moments of the criterion random variable U; the third embeds the distribution of U in an exponential family, and uses exponential tilting, which in turn suggests an importance sampling distribution. We illustrate each method with examples and assess their relative merits.