Weighted Average Importance Sampling and Defensive Mixture Distributions

Importance sampling uses observations from one distribution to estimate for another distribution by weighting the observations. Including the target distribution as one component of a mixture distribution bounds the weights and makes importance sampling more reliable. The usual importance-sampling estimate is a weighted average with weights that do not sum to 1. We discuss simple normalization and other, more efficient normalization methods. These innovations make importance sampling useful in a wider variety of problems. We demonstrate with a case study of oil-inventory reliability at a large utility.