Download or read book Fast Simulation of Rare Events in Markov Level phase Processes written by and published by . This book was released on 2004 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Methods of efficient Monte-Carlo simulation when rare events are involved have been studied for several decades. Rare events are very important in the context of evaluating high quality computer/communication systems. Meanwhile, the efficient simulation of systems involving rare events poses great challenges. A simulation method is said to be efficient if the number of replicas required to get accurate estimates grows slowly, compared to the rate at which the probability of the rare event approaches zero. Despite the great success of the two mainstream methods, importance sampling (IS) and importance splitting, either of them can become inefficient under certain conditions, as reported in some recent studies. The purpose of this study is to look for possible enhancement of fast simulation methods. I focus on the ``level/phase process', a Markov process in which the level and the phase are two state variables. Furthermore, changes of level and phase are induced by events, which have rates that are independent of the level except at a boundary. For such a system, the event of reaching a high level occurs rarely, provided the system typically stays at lower levels. The states at those high levels constitute the rare event set. Though simple, this models a variety of applications involving rare events. In this setting, I have studied two efficient simulation methods, the rate tilting method and the adaptive splitting method, concerning their efficiencies. I have compared the efficiency of rate tilting with several previously used similar methods. The experiments are done by using queues in tandem, an often used test bench for the rare event simulation. The schema of adaptive splitting has not been described in literature. For this method, I have analyzed its efficiency to show its superiority over the (conventional) splitting method. The way that a system approaches a designated rare event set is called the system's large deviation behavior. Toward the end of gaining in.

Download or read book Fast Simulation of Rare Events in Markov Level phase Processes written by and published by . This book was released on 2004 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Methods of efficient Monte-Carlo simulation when rare events are involved have been studied for several decades. Rare events are very important in the context of evaluating high quality computer/communication systems. Meanwhile, the efficient simulation of systems involving rare events poses great challenges. A simulation method is said to be efficient if the number of replicas required to get accurate estimates grows slowly, compared to the rate at which the probability of the rare event approaches zero. Despite the great success of the two mainstream methods, importance sampling (IS) and importance splitting, either of them can become inefficient under certain conditions, as reported in some recent studies. The purpose of this study is to look for possible enhancement of fast simulation methods. I focus on the ``level/phase process', a Markov process in which the level and the phase are two state variables. Furthermore, changes of level and phase are induced by events, which have rates that are independent of the level except at a boundary. For such a system, the event of reaching a high level occurs rarely, provided the system typically stays at lower levels. The states at those high levels constitute the rare event set. Though simple, this models a variety of applications involving rare events. In this setting, I have studied two efficient simulation methods, the rate tilting method and the adaptive splitting method, concerning their efficiencies. I have compared the efficiency of rate tilting with several previously used similar methods. The experiments are done by using queues in tandem, an often used test bench for the rare event simulation. The schema of adaptive splitting has not been described in literature. For this method, I have analyzed its efficiency to show its superiority over the (conventional) splitting method. The way that a system approaches a designated rare event set is called the system's large deviation behavior. Toward the end of gaining in.

Download or read book Computing Rare event Probabilities for Affine Models and General State Space Markov Processes written by Xiaowei Zhang and published by Stanford University. This book was released on 2011 with total page 129 pages. Available in PDF, EPUB and Kindle. Book excerpt: Rare-event simulation concerns computing small probabilities, i.e. rare-event probabilities. This dissertation investigates efficient simulation algorithms based on importance sampling for computing rare-event probabilities for different models, and establishes their efficiency via asymptotic analysis. The first part discusses asymptotic behavior of affine models. Stochastic stability of affine jump diffusions are carefully studied. In particular, positive recurrence, ergodicity, and exponential ergodicity are established for such processes under various conditions via a Foster-Lyapunov type approach. The stationary distribution is characterized in terms of its characteristic function. Furthermore, the large deviations behavior of affine point processes are explicitly computed, based on which a logarithmically efficient importance sampling algorithm is proposed for computing rare-event probabilities for affine point processes. The second part is devoted to a much more general setting, i.e. general state space Markov processes. The current state-of-the-art algorithm for computing rare-event probabilities in this context heavily relies on the solution of a certain eigenvalue problem, which is often unavailable in closed form unless certain special structure is present (e.g. affine structure for affine models). To circumvent this difficulty, assuming the existence of a regenerative structure, we propose a bootstrap-based algorithm that conducts the importance sampling on the regenerative cycle-path space instead of the original one-step transition kernel. The efficiency of this algorithm is also discussed.

Download or read book Dissertation Abstracts International written by and published by . This book was released on 2008 with total page 946 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Sequential Methods for Rare Event Simulations written by Shaojie Deng and published by . This book was released on 2010 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: We consider rare events modeled as a Markov Chain hitting a certain rare set. A sequential importance sampling with resampling (SISR) method is introduced to provide a versatile approach for computing such probabilities of rare events. The method uses resampling to track the zero-variance importance measure associated with the event of interest. A general methodology for choosing the importance measure and resampling scheme to come up with an efficient estimator of the probability of occurrence of the rare event is developed and the distinction between light-tailed and heavy-tailed problems is highlighted. Applications include classic tail probabilities for sums of independent light-tailed or heavy-tailed random variables. Markovian extensions and simultaneous simulation are also given. The heuristics and the methodology can also be applied to more complex Monte Carlo problems that arise in recent works on the dynamic portfolio credit risk model.

Download or read book Path Properties of Rare Events written by Jesse Collingwood and published by . This book was released on 2015 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Simulation of rare events can be costly with respect to time and computational resources. For certain processes it may be more efficient to begin at the rare event and simulate a kind of reversal of the process. This approach is particularly well suited to reversible Markov processes, but holds much more generally. This more general result is formulated precisely in the language of stationary point processes, proven, and applied to some examples. An interesting question is whether this technique can be applied to Markov processes which are substochastic, i.e. processes which may die if a graveyard state is ever reached. First, some of the theory of substochastic processes is developed; in particular a slightly surprising result about the rate of convergence of the distribution pi(n) at time n of the process conditioned to stay alive to the quasi-stationary distribution, or Yaglom limit, is proved. This result is then verified with some illustrative examples. Next, it is demonstrated with an explicit example that on infinite state spaces the reversal approach to analyzing both the rate of convergence to the Yaglom limit and the likely path of rare events can fail due to transience.

Download or read book Introduction to Rare Event Simulation written by James Bucklew and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a unified theory of rare event simulation and the variance reduction technique known as importance sampling from the point of view of the probabilistic theory of large deviations. It allows us to view a vast assortment of simulation problems from a unified single perspective.

Download or read book Computing Rare event Probabilities for Affine Models and General State Space Markov Processes written by Xiaowei Zhang and published by . This book was released on 2011 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Rare-event simulation concerns computing small probabilities, i.e. rare-event probabilities. This dissertation investigates efficient simulation algorithms based on importance sampling for computing rare-event probabilities for different models, and establishes their efficiency via asymptotic analysis. The first part discusses asymptotic behavior of affine models. Stochastic stability of affine jump diffusions are carefully studied. In particular, positive recurrence, ergodicity, and exponential ergodicity are established for such processes under various conditions via a Foster-Lyapunov type approach. The stationary distribution is characterized in terms of its characteristic function. Furthermore, the large deviations behavior of affine point processes are explicitly computed, based on which a logarithmically efficient importance sampling algorithm is proposed for computing rare-event probabilities for affine point processes. The second part is devoted to a much more general setting, i.e. general state space Markov processes. The current state-of-the-art algorithm for computing rare-event probabilities in this context heavily relies on the solution of a certain eigenvalue problem, which is often unavailable in closed form unless certain special structure is present (e.g. affine structure for affine models). To circumvent this difficulty, assuming the existence of a regenerative structure, we propose a bootstrap-based algorithm that conducts the importance sampling on the regenerative cycle-path space instead of the original one-step transition kernel. The efficiency of this algorithm is also discussed.

Download or read book Estimation of the Statistics of Rare Events in Data Communications Systems written by Michael R. Frater and published by . This book was released on 1990 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Rare Event Simulation using Monte Carlo Methods written by Gerardo Rubino and published by John Wiley & Sons. This book was released on 2009-03-18 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: In a probabilistic model, a rare event is an event with a very small probability of occurrence. The forecasting of rare events is a formidable task but is important in many areas. For instance a catastrophic failure in a transport system or in a nuclear power plant, the failure of an information processing system in a bank, or in the communication network of a group of banks, leading to financial losses. Being able to evaluate the probability of rare events is therefore a critical issue. Monte Carlo Methods, the simulation of corresponding models, are used to analyze rare events. This book sets out to present the mathematical tools available for the efficient simulation of rare events. Importance sampling and splitting are presented along with an exposition of how to apply these tools to a variety of fields ranging from performance and dependability evaluation of complex systems, typically in computer science or in telecommunications, to chemical reaction analysis in biology or particle transport in physics. Graduate students, researchers and practitioners who wish to learn and apply rare event simulation techniques will find this book beneficial.

Download or read book Fast Simulation of Rare Events in Queueing and Reliability Models written by International Business Machines Corporation. Research Division and published by . This book was released on 1993 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book ACM Transactions on Modeling and Computer Simulation written by and published by . This book was released on 1995 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Splitting for Rare Event Simulation A Large Deviations Approach to Design and Analysis written by and published by . This book was released on 2007 with total page 35 pages. Available in PDF, EPUB and Kindle. Book excerpt: Particle splitting methods are considered for the estimation of rare events. The probability of interest is that a Markov process first enters a set B before another set A, and it is assumed that this probability satisfies a large deviation scaling. A notion of subsolution is defined for the related calculus of variations problem, and two main results are proved under mild conditions. The first is that the number of particles generated by the algorithm grows subexponentially if and only if a certain scalar multiple of the importance function is a subsolution. The second is that, under the same condition, the variance of the algorithm is characterized "asymptotically" in terms of the subsolution. The design of asymptotically optimal schemes is discussed, and numerical examples are presented.

Download or read book Rare event Simulation with Markov Chain Monte Carlo written by and published by . This book was released on 2015 with total page 109 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Hamiltonian Markov Chain Monte Carlo Schemes for Rare Event Estimation written by Hamed Nikbakht and published by . This book was released on 2020 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Estimating rare event probabilities is a commonly encountered important problem in several engineering and scientific applications, most often observed in the form of probability of failure (PF) estimation or, alternatively and better sounding for the public, reliability estimation. In many practical applications, such as for structures, airplanes, mechanical equipment, and many more, failure probabilities are fortunately very low, from 10-4 to even 10-9 and less. Such estimations are of utmost importance for design choices, emergency preparedness, safety regulations, maintenance suggestions and more. Calculating such small numbers with accuracy however presents many numerical and mathematical challenges. To make matters worse, these estimations in realistic applications are usually based on high dimensional random spaces with numerous random variables and processes involved. A single simulation of such a model, or else a single model call, may also require several minutes to hours of computing time. As such, reducing the number of model calls is of great importance in these problems and one of the critical parameters that limits or prohibits use of several available techniques in the literature. This research is motivated by efficiently and precisely quantifying these probabilities, often encountered in reliability analysis of complex engineering systems, based on a developed framework termed Approximate Sampling Target with Postprocessing Adjustment (ASTPA), which herein is integrated with and supported by gradient-based Hamiltonian Markov Chain Monte Carlo (HMCMC) methods. Hamiltonian Markov Chain Monte Carlo sampling is characterized by much better scalability, faster mixing rates, is capable of generating samples with much weaker auto-correlation, even in complex high-dimensional parameter spaces, and has enjoyed broad-spectrum successes in most general settings. HMCMC adopts physical system dynamics, rather than a proposal probability distribution, and can be used to produce distant proposal samples for the integrated Metropolis step, thereby avoiding the slow exploration of the state space that results from the diffusive behavior of simple random-walk proposals. In this work, we aim to advance knowledge on Hamiltonian Markov Chain Monte Carlo methods, in general, with particular emphasis on its efficient utilization for rare event probability estimation in both Gaussian and Non-Gaussian spaces. This research also seeks to offer significant advancements in probabilistic inference and reliability predictions. Thus, in this context, we develop various Quasi-Newton based HMCMC schemes, which can sample very adeptly, particularly in difficult cases of high curvature, high-dimensionality and very small failure probabilities. The methodology is formally introduced, and the key theoretical aspects, and the underlying assumptions are discussed. Performance of the proposed methodology is then compared against state-of-the-art Subset Simulation in a series of challenging static and dynamic (time-dependent reliability) low- and high-dimensional benchmark problems. In the last phase of this work, with an aim to avoid using analytical gradients, within the proposed HMCMC-based framework, we investigate application of the Automatic Differentiation (AD) technique. In addition, to avoid use of gradients altogether and to improve the performance of the original SuS algorithm, we study the application of Quasi-Newton based HMCMC within the Subset Simulation framework. Various numerical examples are then presented to showcase the performance of the aforementioned approaches.

Download or read book Collection of Pamphlets Relating to Zoology and written by and published by . This book was released on 1873 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Fast Simulation of Packet Loss Rates in a Shared Buffer Communications Switch written by Cheng-Shang Chang and published by . This book was released on 1993 with total page 28 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: "This paper describes an efficient technique for estimating, via simulation, the probability of buffer overflows in a queueing model that arises in the analysis of ATM (Asynchronous Transfer Mode) communication switches. There are multiple streams of (autocorrelated) traffic feeding the switch that has a buffer of finite capacity. Each stream is designated as either being of high or low priority. When the queue length reaches a certain threshold, only high priority packets are admitted to the switch's buffer. The problem is to estimate the loss rate of high priority packets. An asymptotically optimal importance sampling approach is developed for this rare event simulation problem. In this approach, the importance sampling is done in two distinct phases. In the first phase, an importance sampling change of measure is used to bring the queue length up to the threshold at which low priority packets get rejected. In the second phase, a different importance sampling change of measure is used to move the queue length from the threshold to the buffer capacity."