Weighted average importance sampling and defensive mixture distributions. (English) Zbl 0822.62002

Hesterberg, Tim

Technometrics 37, No. 2, 185-194 (1995).

Summary: 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.

MSC:

62D05	Sampling theory, sample surveys
90B05	Inventory, storage, reservoirs
62P99	Applications of statistics

Keywords:

Monte Carlo; variance reduction; integration estimate; ratio estimate; regression estimate; exponential estimates; maximum likelihood; mixture distribution; importance sampling; normalization methods; oil-inventory reliability