Multiple independent streams of random numbers are often required in simulation studies, for instance, to facilitate synchronization for variance-reduction purposes, and for making independent replications. A portable set of software utilities is described for uniform randomnumber generation. It provides for multiple generators (streams) running simultaneously, and each generator (stream) has i...

Subsampling the output of a Gibbs sampler in a non-systematic fashion can improve the e ciency of marginal estimators if the subsampling strategy is tied to the actual updates made. We illustrate this point by example, approximation, and asymptotics. The results hold both for random scan and xed scan Gibbs samplers.

This tutorial gives a concise overview of existing PAC-Bayesian theory focusing on three generalization bounds. The first is an Occam bound which handles rules with finite precision parameters and which states that generalization loss is near training loss when the number of bits needed to write the rule is small compared to the sample size. The second is a PAC-Bayesian bound providing a genera...

Countable-state, continuous-time Markov chains are often analyzed through simulation when simple analytical expressions are unavailable. Simulation is typically used to estimate costs or performance measures associated with the chain and also characteristics like state probabilities and mean passage times. Here we consider the problem of estimating derivatives of these types of quantities with ...

We introduce the concept of an extremely negatively dependent (END) sequence of random variables with a given common marginal distribution. An END sequence has a partial sum which, subtracted by its mean, does not diverge as the number of random variables goes to infinity. We show that an END sequence always exists for any given marginal distributions with a finite mean and we provide a probabi...

In this paper, we examine a joint lot-sizing and process investment problem with random yield and backorders. We allow for inspection and develop stochastic models which provide the optimal inspection and lot-sizing policy as well as the optimal process investment for variance reduction. The process quality loss profile around the target is captured via a modification of the Reflected Normal lo...

In a linear regression model with homoscedastic Normal noise, I consider James–Stein type shrinkage in the estimation of nuisance parameters associated with control variables. For at least three control variables and exogenous treatment, I show that the standard leastsquares estimator is dominated with respect to squared-error loss in the treatment effect even among unbiased estimators and even...

FALL 1999 This article develops a variance-reduction technique for pricing derivatives by simulation in highdimensional multifactor models. A premise of this work is that the greatest gains in simulation efficiency come from taking advantage of the structure of both the cash flows of a security and the model in which it is priced. For this to be feasible in practice requires automating the iden...

respectively. In either case, choosing α̂(ω) = δ(ω) results in a variance proportional to that of the integrand. These equations provide different insight into the choice of importance function for variance reduction. Eq. 2 suggests that ideally, g(x) = 1/α(x) should be chosen so that α̂(ω) contains all its energy at frequencies where the square of the integrand has no energy. Eq. 3, on the other...

Rare properties remain a challenge for statistical model checking (SMC) due to the quadratic scaling of variance with rarity. We address this with a variance reduction framework based on lightweight importance splitting observers. These expose the model-property automaton to allow the construction of score functions for high performance algorithms. The confidence intervals defined for importanc...