For rare-event simulations, importance sampling (IS) estimators are considered efficient when the relative error, that is, the ratio of standard deviation and mean, is well controlled. If the set of rare events contains multiple “significant regions” encoded by so-called dominant points, IS may need to account for them all by mixing to achieve efficiency. Widely known. In a typical experiment, missing dominant points of low importance does not necessarily cause inefficiency, and traditional analytical recipes tend to use relative error or estimated variance as efficiency criteria. argue that it may suffer from intrinsic slackness due to To fill this gap, we propose a new efficiency concept called stochastic efficiency. In particular, under the standard Gartner-Ellis large deviation regime, we show that IS using only the most significant dominant points is sufficient to achieve this notion of efficiency. Our findings are particularly relevant for high-dimensional settings where the computational effort to find all dominant points is enormous.
