The estimation of rare event probabilities using importance sampling (IS) is studied in this paper. A new method is suggested in the context of iid sums which makes full use of the form of the component density function of the sum. It is proved that this results in an estimation technique that enhances the power of IS biasing methods which do not explicitly use this knowledge. The method is suitable for finite sums. Optimization of the scheme and its performance are illustrated through example and asymptotic analysis and new asymptotic expansions for tail probability are given. This technique facilitates solution of the inverse IS problem. The inverse problem is one of finding a number or threshold that is exceeded by a random variable or sum with a given probability. It turns out that with a suitably decreasing threshold the simulation gain becomes asymptotically constant. These methods are then applied to CFAR detection algorithms. New results for a censored ordered statistic cell averaging CFAR detector are obtained.
|Number of pages||15|
|Publication status||Published - 1998|
- Importance sampling
- CFAR detection
- Inverse IS