There are various importance sampling schemes to estimate rare event probabilities in Markovian systems such as Markovian reliability models and Jackson networks. In this work, we present a general state dependent importance sampling method which partitions the state space and applies the...

A sequence of real numbers (xn) is Benford if the significands, i.e. the fractionparts in the floating-point representation of (xn), are distributed logarithmically.Similarly, a discrete-time irreducible and aperiodic finite-state Markov chain withprobability transition matrix P and limiting...

We apply the splitting method to three well-known counting problems, namely 3-SAT, random graphs with prescribed degrees, and binary contingency tables. We present an enhanced version of the splitting method based on the capture-recapture technique, and show by experiments the superiority of...

In this paper we describe a Sequential Importance Sampling (SIS) procedure for counting the number of vertex covers in general graphs. The performance of SIS depends heavily on how close the SIS proposal distribution is to a uniform one over a suitably restricted set. The proposed algorithm...

In rare event simulation, we look for estimators such that the relative accuracy of the output is ''controlled'' when the rarity is getting more and more critical. Different robustness properties have been defined in the literature, that an estimator is expected to satisfy. Though, those...

The Cross Entropy method is a well-known adaptive importance sampling method for rare-event probability estimation, which requires estimating an optimal importance sampling density within a parametric class. In this article we estimate an optimal importance sampling density within a wider...

In this article we consider the efficient estimation of the tail distribution of the maximum of correlated normal random variables. We show that the currently recommended Monte Carlo estimator has difficulties in quantifying its precision, because its sample variance estimator is an inefficient...

Monte Carlo methods are simulation algorithms to estimate a numerical quantity in a statistical model of a real system. These algorithms are executed by computer programs. Variance reduction techniques (VRT) are needed, even though computer speed has been increasing dramatically, ever since the...

A version of the classical secretary problem is studied, in which one is interested in selecting one of the <I>b</I> best out of a group of <I>n</I> differently ranked persons who are presented one by one in a random order. It is assumed that <I>b</I> is bigger than or equal to 1 is a preassigned number. It is...</i></i></i>