The maximum likelihood estimator (MLE) is generally asymptotically consistent but is susceptible to overfitting. To combat this problem, regularization methods which reduce the variance at the cost of (slightly) increasing the bias are often employed in practice. In this paper, we present an alternative variance reduction (regularization) technique that quantizes the MLE estimates as a post pro...

Asymptotic approximations and importance sampling methods are presented for evaluating a class of probability integrals with multiple design points that may arise in the calculation of the reliability of uncertain dynamical systems. An approximation based on asymptotics is used as a ®rst step to provide a computationally ecient estimate of the probability integral. The importance sampling meth...

I give a quick summary of my proposal for simulating an improvement on quenched QCD with dynamical fermions which interact with the gluon configuration only via the topological index of the latter. It amounts to include only the topological part of the functional determinant into the measure, thereby absorbing a correction factor into the observable. I discuss the prospects of this concept from...

This abstract presents the basic idea of a new adaptive methodology for reliability assessment using probabilistic classification vector machines (PCVMs) [1], a variant of support vector machines (SVMs) [2, 3]. The proposed method is pivoted around two principal concepts definition of an explicit failure boundary and its variability using PCVMs, and importance sampling (IS) [4–6]. The proposed ...

We revisit the multiple importance sampling (MIS) estimator and investigate the bound on the efficiency improvement over balance heuristic estimator with equal count of samples established in Veach’s thesis. We revise the proof for this and come to the conclusion that there is no such bound and henceforth it makes sense to look for new estimators that improve on balance heuristic estimator with...

We present two improvements on the technique of importance sampling. First we show that importance sampling from a mixture of densities, using those densities as control variates, results in a useful upper bound on the asymptotic variance. That bound is a small multiple of the asymptotic variance of importance sampling from the best single component density. This allows one to beneet from the g...

We consider the problem of calculating tail probabilities of the returns of linear asset portfolios. As a flexible and accurate model for the logarithmic returns we use the t-copula dependence structure and marginals following the generalized hyperbolic distribution. Exact calculation of the tail-loss probabilities is not possible and even simulation leads to challenging numerical problems. App...

We consider the problem of estimating via simulation the tails of the performability of a system. Traditional simulation is ine cient in this case because the number of samples required to obtain an adequate characterization of the tails is very large. The system we consider is the M/M/1/K system subject to server breakdowns and repairs. This system is simple, but has the characteristics shared...

Adaptive importance sampling involves successively estimating the function of interest and then constructing an importance sampling scheme built on the estimate. Here, we investigate such a scheme used in simulations of Markov chains derived from particle transport problems. Previous work had shown that for nite state spaces the convergence was exponential, which veri ed computational experienc...

In this paper we demonstrate how to use the importance sampling method to simulate rare events in a germ-grain model. We analyze conditions under which two germ-grain models are mutually absolutely continuous. We also find the likelihood set process. We apply these results in simulating the probability that the radius of the occupied component of the origin in continuous percolation is greater ...