The estimation of system failure probabilities may be a difficult task when the values involved are very small, so that sampling-based Monte Carlo methods may become computationally impractical, especially if the computer codes used to model the system response require large computational efforts, both in terms of time and memory. This paper proposes a modification of an algorithm proposed in l...

Proxel-based simulation is a state-space based method for the transient solution of discrete stochastic models with general distributions. The method is very promising for the simulation and evaluation of rare events, even in stiff models. It computes the probability of model states and events deterministically. Contrary to rare event simulation techniques like, e.g., Importance Sampling or Spl...

We first present a sampling algorithm for continuous time Bayesian networks based on importance sampling. We then extend it to continuous-time particle filtering and smoothing algorithms. The three algorithms can estimate the expectation of any function of a trajectory, conditioned on any evidence set constraining the values of subsets of the variables over subsets of the timeline. We present e...

| In this article, we generalize the input{domain based software reliability measures by Nelson and by Weiss and Weyuker, introducing expected failure costs under the operational distribution as a measure for software unreliability. This approach incorporates in the reliability concept a distinction between diierent degrees of failure severity. It is shown how to estimate the proposed quantity ...

Successful efficient rare-event simulation typically involves using importance sampling tailored to a specific rare event. However, in applications one may be interested in simultaneous estimation of many probabilities or even an entire distribution. In this paper, we address this issue in a simple but fundamental setting. Specifically, we consider the problem of efficient estimation of the pro...

In this article, we propose a nonparametric adaptive importance sampling (NAIS) algorithm to estimate rare event quantile. Indeed, Importance Sampling (IS) is a well-known adapted random simulation technique. It consists in generating random weighted samples from an auxiliary distribution rather than the distribution of interest. The optimization of this auxiliary distribution is often very dif...

This paper presents a method for estimating the probability μ of a union of J rare events. The method uses n samples, each of which picks one of the rare events at random, samples conditionally on that rare event happening and counts the total number of rare events that happen. We call it ALORE, for ‘at least one rare event’. The ALORE estimate is unbiased and has a coefficient of variation no ...

Improving Importance Sampling estimators for rare event probabilities requires sharp approximations of conditional densities. This is achieved for events En := (u(X1) + ...+ u(Xn)) ∈ An where the summands are i.i.d. and En is a large or moderate deviation event. The approximation of the conditional density of the vector (X1, ..., Xkn) with respect to En on long runs, when kn/n → 1, is handled. ...

A wide variety of conditional and stochastic variance models has been used to estimate latent volatility (or risk). In this paper, we propose a new long memory asymmetric volatility model which captures more flexible asymmetric patterns as compared with existing models. We extend the new specification to realized volatility by taking account of measurement errors, and use the Efficient Importan...

One of themain applications of probabilisticmodel 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...