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In the simulation-on-demand paradigm, we invest computational effort by running a simulation experiment before a question is asked, and then we quickly provide an answer by making use of the results of the earlier simulation experiment. This can be done by building a metamodel, but standard metamodeling methods used in stochastic simulation have the disadvantage that they require validation. We show...
Consider a system that is subjected to a random load and having a corresponding random capacity to withstand the load. The system fails when the load exceeds capacity, and we consider efficient simulation methods for estimating the failure probability. Our approaches employ various combinations of stratified sampling, Latin hypercube sampling, and conditional Monte Carlo. We construct asymptotically...
Many Monte Carlo computations involve computing quantities that can be expressed as g(EX), where g is nonlinear and smooth, and X is an easily simulatable random variable. The nonlinearity of g makes the conventional Monte Carlo estimator for such quantities biased. In this paper, we show how such quantities can be estimated without bias. However, our approach typically increases the variance. Thus,...
We present general principles for the design and analysis of unbiased Monte Carlo estimators for quantities such as α = g(E (X)), where E (X) denotes the expectation of a (possibly multidimensional) random variable X, and g(·) is a given deterministic function. Our estimators possess finite work-normalized variance under mild regularity conditions such as local twice differentiability of g(·) and...
Since the 1950s, nonoverlapping batch means (NBM) has been a basis for confidence-interval procedures (CIPs) for the mean of a steady-state time series. In 1985, overlapping batch means (OBM) was introduced as an alternative to NBM for estimating the standard error of the sample mean. Despite OBM's inherent efficiency, because the OBM statistic does not approach normality via the chi-squared distribution,...
Static network unreliability computation is an NP-hard problem, leading to the use of Monte Carlo techniques to estimate it. The latter, in turn, suffer from the rare event problem, in the frequent situation where the system's unreliability is a very small value. As a consequence, specific rare event event simulation techniques are relevant tools to provide this estimation. We focus here on a method...
In the analysis of input and output models used in computer simulation, parametric bootstrapping provides an attractive alternative to asymptotic theory for constructing confidence intervals for unknown parameter values and functions involving such parameter values, and also for calculating critical values of EDF statistics used in goodness-of-fit tests, such as the Anderson-Darling A2 statistic....
This paper provides an efficient algorithm using Newton's method under sample average approximation (SAA) to solve the parametric optimization problem associated with the optimal importance sampling change of measure in simulating Lévy processes. Numerical experiments on variance gamma (VG), geometric Brownian motion (GBM), and normal inverse Gaussian (NIG) examples illustrate the computational advantages...
We consider the multi-objective simulation optimization problem on finite sets, where we seek the Pareto set corresponding to systems evaluated on multiple performance measures, using only Monte Carlo simulation observations from each system. We ask how a given simulation budget should be allocated across the systems, and a Pareto surface retrieved, so that the estimated Pareto set minimally deviates...
Power transformer is one of the most expensive equipments in the electrical power grid. Transformer outages may lead to substantial economical losses. One of the most important parameters governing a transformer's life expectancy and reliability is transformer aging condition and loading condition. At the same time, it is found that electric consumption is highly correlated with weather condition,...
We consider the multi-objective simulation optimization problem on finite sets, where we seek the Pareto set corresponding to systems evaluated on multiple performance measures, using only Monte Carlo simulation observations from each system. We ask how a given simulation budget should be allocated across the systems, and a Pareto surface retrieved, so that the estimated Pareto set minimally deviates...
A variable annuity is an insurance contract that contains financial guarantees. Due to the complexity of guarantees, there are no closed-form formulas to calculate the value of these guarantees. Insurance companies rely heavily on Monte Carlo simulation to calculate the value of the guarantees. However, almost all simulation software for variable annuity is proprietary, posing a substantial barrier...
When simulating a complex stochastic system, the behavior of the output response depends on the input parameters estimated from finite real-world data, and the finiteness of data brings input uncertainty to the output response. The quantification of the impact of input uncertainty on output response has been extensively studied. However, most of the existing literature focuses on providing inferences...
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 estimator of the true variance. We propose a simple remedy: to still use this estimator, but to rely on...
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