Importance sampling

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This research monograph focuses on fast stochastic simulation utilizing importance sampling (IS) principles and explores its applications, particularly an adaptive form of IS effective for estimating probabilities of rare events. Rare events, which can lead to significant consequences, are prevalent in scientific and engineering contexts. Their accurate characterization is crucial, as they can result in catastrophic outcomes, such as material fatigue in engineering structures, dangerous river flood levels, or false target declarations in radar systems. Fast simulation via IS acts as a forced Monte Carlo procedure to expedite the occurrence of these rare events. The development of this simulation method is often credited to mathematician von Neumann and others. Since its introduction, Monte Carlo simulation has been widely applied, from statistical thermodynamics in disordered systems to the analysis and design of complex engineering structures. When engineering problems are analytically intractable and numerical solutions are computationally expensive, simulation becomes a vital tool for determining the input-output characteristics or states within a system.