On the theory of importance sampling applied to the analysis of detection systems

Detection systems are designed to operate with optimal or nearly optimal probability of a wrong decision. Analytical solutions of the performance of these systems have been very difficult to obtain. Monte Carlo simulations are often the most tractable method of estimating performance. However, in systems with small probability of error, this technique requires very large amounts of computer time. A technique known as importance sampling substantially reduces the number of simulation trials needed, for a given accuracy, over the standard Monte Carlo method. The theory and application of the importance sampling method in Monte Carlo simulation is considered in a signal detection context. A general method of applying this technique to the optimal detection problem is given. Results show that in cases examined, the gain is approximately proportional to the inverse of the error probability. Applications of the proposed method are not limited to optimum detection systems; analysis, leading to a measure of the gain in using this biasing scheme, shows that in all optimal systems considered, less than 100 trials is needed to achieve estimates with 45% confidence, even for extremely small error probabilities.<
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