Unbiased Monte Carlo Estimation of the Reciprocal of an Integral

A method to provide an unbiased Monte Carlo estimate of the reciprocal of an integral is described. In Monte Carlo transport calculations, one often uses a single sample as an estimate of an integral. This paper shows that a similar situation exists with respect to a single sample for an unbiased estimate of the reciprocal of an integral. If an appropriate approximation to the integrand is known, then obtaining a single unbiased estimate of the reciprocal of an integral will not be much more time consuming than obtaining a single unbiased estimate of the integral itself.