1,720,990 research outputs found
Fast Simulation of Multifactor Portfolio Credit Risk in the t-Copula Model
No full textWe present an importance sampling procedure for the estimation of multifactor portfolio credit risk for the t-copula model, i.e, the case where the risk factors have the multivariate t distribution. We use a version of the multivariate t that can be expressed as a ratio of a multivariate normal and a scaled chi-square random variable. The procedure consists of two steps. First, using the large deviations result for the Gaussian model in Glasserman, Kang, and Shahabuddin (2005a), we devise and apply a change of measure to the chi-square random variable. Then, conditional on the chi-square random variable, we apply the importance sampling procedure developed for the Gaussian copula model in Glasserman, Kang, Shahabuddin (2005b). We support our importance sampling procedure by numerical examples
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No full textPerwez Shahabuddin was an accomplished researcher, teacher, and participant in the simulation community. This article provides an overview of his career and a summary of some of his many professional accomplishments. Categories and Subject Descriptors: A.0 [General Literature]: General—Biographies/autobiographies; G.3 [Mathematics of Computing]: Probability and Statistics—Probabilistic algorithm
Importance Sampling for the Simulation of Highly Reliable Markovian Systems
No full textIn this paper we investigate importance sampling techniques for the simulation of Markovian systems with highly reliable components. The need for simulation arises because the state space of such systems is typically huge, making numerical computation inefficient. Naive simulation is inefficient due to the rarity of the system failure events. Failure biasing is a useful importance sampling technique for the simulation of such systems. However, until now, this technique has been largely heuristic. We present a mathematical framework for the study of failure biasing. Using this framework we derive variance reduction results which explain the orders of magnitude of variance reduction obtained in practice. We show that in many cases the magnitude of the variance reduction is such that the relative errors of the estimates remain bounded as the failure rates of components tend to zero. We also prove that the failure biasing heuristic in its original form may not give bounded relative error for a large class of systems and that a modification of the heuristic works for the general case. The theoretical results in this paper agree with experiments on the subject which have been reported in a previous paper.stochastic simulation, importance sampling, failure biasing, Markov chains, reliability, availability, mean time to failure
Rare event simulation techniques for models of computer and communication systems
No full textThis talk reviews some of the fast simulation techniques used for estimating probabilities of rare events and related quantities in stochastic models of computer and communication systems. It is by no means a complete survey of these rare event simulation techniques. However, an attempt will be made to give some of the basic concepts, intuitions, and algorithms used for different types of stochastic models. The reader is referred to Heidelberger (1995) and Shahabuddin (1995) for recent comprehensive surveys in this area, and the reference list of Boots and Shahabuddin (2000) for some of the later papers in this area. Estimations of the small probabilities of rare events are required in the design and operation of many engineering systems. Consider the case of a telecommunication network. It is customary to model such systems as network of queues, with each queue having a buffer of finite capacity. Information packets that arrive to a queue when its buffer is full are lost. The rare event of interest may be the event of a packet being lost. Current regulations stipulate that the probability of packet loss should not exceed 10 to the power-9. Or in a reliability model of a space craft computer, we may be interested in estimating the probability of the event that th
Fast Simulation of Markov Chains with Small Transition Probabilities
No full textConsider a finite-state Markov chain where the transition probabilities differ by orders of magnitude. This Markov chain has an "attractor state," i.e., from any state of the Markov chain there exists a sample path of significant probability to the attractor state. There also exists a "rare set," which is accessible from the attractor state only by sample paths of very small probability. The problem is to estimate the probability that starting from the attractor state, the Markov chain hits the rare set before returning to the attractor state. Examples of this setting arise in the case of reliability models with highly reliable components as well as in the case of queueing networks with low traffic. Importance-sampling is a commonly used simulation technique for the fast estimation of rare-event probabilities. It involves simulating the Markov chain under a new probability measure that emphasizes the most likely paths to the rare set. Previous research focused on developing importance-sampling schemes for a special case of Markov chains that did not include "high-probability cycles." We show through examples that the Markov chains used to model many commonly encountered systems do have high-probability cycles, and existing importance-sampling schemes can lead to infinite variance in simulating such systems. We then develop the insight that in the presence of high-probability cycles care should be taken in allocating the new transition probabilities so that the variance accumulated over these cycles does not increase without bounds. Based on this observation we develop two importance-sampling techniques that have the bounded relative error property, i.e., the simulation run-length required to estimate the rare-event probability to a fixed degree of accuracy remains bounded as the event of interest becomes more rare.Simulation, Markov Chains, Reliability Models, Steady-State Measures, Importance-Sampling
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
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