Hypothesis Testing for Rare-Event Simulation: Limitations and Possibilities

Abstract

One of the main applications of probabilistic model checking is to decide whether the probability of a property of interest is above or below a threshold. Using statistical model checking (SMC), this is done using a combination of stochastic simulation and statistical hypothesis testing. When the probability of interest is very small, one may need to resort to rare-event simulation techniques, in particular importance sampling (IS). However, IS simulation does not yield 0/1-outcomes, as assumed by the hypothesis tests commonly used in SMC, but likelihood ratios that are typically close to zero, but which may also take large values. In this paper we consider two possible ways of combining IS and SMC. One involves a classical IS-scheme from the rare-event simulation literature that yields likelihood ratios with bounded support when applied to a certain (nontrivial) class of models. The other involves a particular hypothesis testing scheme that does not require a-priori knowledge about the samples, only that their variance is estimated well.