Showing papers on "Stochastic simulation published in 2003"

Stiffness in stochastic chemically reacting systems: The implicit tau-leaping method

Abstract: We show how stiffness manifests itself in the simulation of chemical reactions at both the continuous-deterministic level and the discrete-stochastic level. Existing discrete stochastic simulation methods, such as the stochastic simulation algorithm and the (explicit) tau-leaping method, are both exceedingly slow for such systems. We propose an implicit tau-leaping method that can take much larger time steps for many of these problems.

Improved leap-size selection for accelerated stochastic simulation

Abstract: In numerically simulating the time evolution of a well-stirred chemically reacting system, the recently introduced “tau-leaping” procedure attempts to accelerate the exact stochastic simulation algorithm by using a special Poisson approximation to leap over sequences of noncritical reaction events. Presented here is an improved procedure for determining the maximum leap size for a specified degree of accuracy.

Kriging for interpolation in random simulation

Abstract: Whenever simulation requires much computer time, interpolation is needed. Simulationists use different interpolation techniques (eg linear regression), but this paper focuses on Kriging. This technique was originally developed in geostatistics by DG Krige, and has recently been widely applied in deterministic simulation. This paper, however, focuses on random or stochastic simulation. Essentially, Kriging gives more weight to ‘neighbouring’ observations. There are several types of Kriging; this paper discusses—besides Ordinary Kriging—a novel type, which ‘detrends’ data through the use of linear regression. Results are presented for two examples of input/output behaviour of the underlying random simulation model: Ordinary and Detrended Kriging give quite acceptable predictions; traditional linear regression gives the worst results.

Non-Gaussian Simulation: Cumulative Distribution Function Map-Based Spectral Correction

Abstract: Methods for stochastic simulation of sample functions have increasingly addressed the preservation of both spectral and probabilistic contents to offer an accurate description of the dynamic behavior of system input for reliability analysis. This study presents an efficient, flexible and easily applied stochastic non-Gaussian simulation method capable of reliably converging to a target power spectral density function and marginal probability density function, or a close relative thereof. Several existing spectral representation-based non-Gaussian simulation algorithms are first summarized. The new algorithm is then presented and compared with these methods to demonstrate its efficacy. The advantages and limitations of the new method are highlighted and shown to complement those of the existing algorithms.

Mixtures of factor analysers. Bayesian estimation and inference by stochastic simulation

Abstract: Factor Analysis (FA) is a well established probabilistic approach to unsupervised learning for complex systems involving correlated variables in high-dimensional spaces. FA aims principally to reduce the dimensionality of the data by projecting high-dimensional vectors on to lower-dimensional spaces. However, because of its inherent linearity, the generic FA model is essentially unable to capture data complexity when the input space is nonhomogeneous. A finite Mixture of Factor Analysers (MFA) is a globally nonlinear and therefore more flexible extension of the basic FA model that overcomes the above limitation by combining the local factor analysers of each cluster of the heterogeneous input space. The structure of the MFA model offers the potential to model the density of high-dimensional observations adequately while also allowing both clustering and local dimensionality reduction. Many aspects of the MFA model have recently come under close scrutiny, from both the likelihood-based and the Bayesian perspectives. In this paper, we adopt a Bayesian approach, and more specifically a treatment that bases estimation and inference on the stochastic simulation of the posterior distributions of interest. We first treat the case where the number of mixture components and the number of common factors are known and fixed, and we derive an efficient Markov Chain Monte Carlo (MCMC) algorithm based on Data Augmentation to perform inference and estimation. We also consider the more general setting where there is uncertainty about the dimensionalities of the latent spaces (number of mixture components and number of common factors unknown), and we estimate the complexity of the model by using the sample paths of an ergodic Markov chain obtained through the simulation of a continuous-time stochastic birth-and-death point process. The main strengths of our algorithms are that they are both efficient (our algorithms are all based on familiar and standard distributions that are easy to sample from, and many characteristics of interest are by-products of the same process) and easy to interpret. Moreover, they are straightforward to implement and offer the possibility of assessing the goodness of the results obtained. Experimental results on both artificial and real data reveal that our approach performs well, and can therefore be envisaged as an alternative to the other approaches used for this model.

Random Numbers

Abstract: 27.1 The RandomGen class, and the StdGen generator 23627.2 The Random class 23927.3 The global random number generator 240

Stochastic programming models for general redundancy-optimization problems

Abstract: This paper provides a unified modeling idea for both parallel and standby redundancy optimization problems. A spectrum of redundancy stochastic programming models is constructed to maximize the mean system-lifetime, /spl alpha/-system lifetime, or system reliability. To solve these models, a hybrid intelligent algorithm is presented. Some numerical examples illustrate the effectiveness of the proposed algorithm. This paper considers both parallel redundant systems and standby redundant systems whose components are connected with each other in a logical configuration with a known system structure function. Three types of system performance-expected system lifetime, /spl alpha/-system lifetime and system reliability-are introduced. A stochastic simulation is designed to estimate these system performances. In order to model general redundant systems, a spectrum of redundancy stochastic programming models is established. Stochastic simulation, NN and GA are integrated to produce a hybrid intelligent algorithm for solving the proposed models. Finally, the effectiveness of the hybrid intelligent algorithm is illustrated by some numerical examples.

Predictability and uncertainty in CFD

Abstract: SUMMARY CFD has reached some degree of maturity today, but the new question is how to construct simulation error bars that reect uncertainties of the physical problem, in addition to the usual numerical inaccura- cies. We present a fast Polynomial Chaos algorithm to model the input uncertainty and its propagation in incompressibleow simulations. The stochastic input is represented spectrally by Wiener-Hermite functionals, and the governing equations are formulated by employing Galerkin projections. The resulted system is deterministic, and therefore existing solvers can be used in this new context of stochastic simulations. The algorithm is applied to a second-order oscillator and to aow-structure interaction problems. Open issues and extensions to general random distributions are presented. Copyright ? 2003 John Wiley & Sons, Ltd.

Introduction to Probability Models

Abstract: 1. REVIEW OF CALCULUS AND PROBABILITY. Review of Differential Calculus. Review of Integral Calculus. Differentiation of Integrals. Basic Rules of Probability. Bayes" Rule. Random Variables. Mean Variance and Covariance. The Normal Distribution. Z-Transforms. Review Problems. 2. DECISION MAKING UNDER UNCERTAINTY. Decision Criteria. Utility Theory. Flaws in Expected Utility Maximization: Prospect Theory and Framing Effects. Decision Trees. Bayes" Rule and Decision Trees. Decision Making with Multiple Objectives. The Analytic Hierarchy Process. Review Problems. 3. DETERMINISTIC EOQ INVENTORY MODELS. Introduction to Basic Inventory Models. The Basic Economic Order Quantity Model. Computing the Optimal Order Quantity When Quantity Discounts Are Allowed. The Continuous Rate EOQ Model. The EOQ Model with Back Orders Allowed. Multiple Product Economic Order Quantity Models. Review Problems. 4. PROBABILISTIC INVENTORY MODELS Single Period Decision Models. The Concept of Marginal Analysis. The News Vendor Problem: Discrete Demand. The News Vendor Problem: Continuous Demand. Other One-Period Models. The EOQ with Uncertain Demand: the (r, q) and (s, S models). The EOQ with Uncertain Demand: The Service Level Approach to Determining Safety Stock Level. Periodic Review Policy. The ABC Inventory Classification System. Exchange Curves. Review Problems. 5. MARKOV CHAINS. What is a Stochastic Process. What is a Markov Chain? N-Step Transition Probabilities. Classification of States in a Markov Chain. Steady-State Probabilities and Mean First Passage Times. Absorbing Chains. Work-Force Planning Models. 6. DETERMINISTIC DYNAMIC PROGRAMMING. Two Puzzles. A Network Problem. An Inventory Problem. Resource Allocation Problems. Equipment Replacement Problems. Formulating Dynamic Programming Recursions. The Wagner-Whitin Algorithm and the Silver-Meal Heuristic. Forward Recursions. Using Spreadsheets to Solve Dynamic Programming Problems. Review Problems. 7. PROBABILISTIC DYNAMIC PROGRAMMING. When Current Stage Costs are Uncertain but the Next Period"s State is Certain. A Probabilistic Inventory Model. How to Maximize the Probability of a Favorable Event Occurring. Further Examples of Probabilistic Dynamic Programming Formulations. Markov Decision Processes. Review Problems. 8. QUEUING THEORY. Some Queuing Terminology. Modeling Arrival and Service Processes. Birth-Death Processes. M/M/1/GD/"V/"V Queuing System and the Queuing Formula L=?U W, The M/M/1/GD/"V Queuing System. The M/M/S/ GD/"V/"V Queuing System. The M/G/ "V/GD/"V"V and GI/G/"V/GD/"V/"VModels. The M/ G/1/GD/"V/"V Queuing System. Finite Source Models: The Machine Repair Model. Exponential Queues in Series and Opening Queuing Networks. How to Tell whether Inter-arrival Times and Service Times Are Exponential. The M/G/S/GD/S/"V System (Blocked Customers Cleared). Closed Queuing Networks. An Approximation for the G/G/M Queuing System. Priority Queuing Models. Transient Behavior of Queuing Systems. Review Problems. 9. SIMULATION. Basic Terminology. An Example of a Discrete Event Simulation. Random Numbers and Monte Carlo Simulation. An Example of Monte Carlo Simulation. Simulations with Continuous Random Variables. An Example of a Stochastic Simulation. Statistical Analysis in Simulations. Simulation Languages. The Simulation Process. 10. SIMULATION WITH PROCESS MODEL. Simulating an M/M/1 Queuing System. Simulating an M/M/2 System. A Series System. Simulating Open Queuing Networks. Simulating Erlang Service Times. What Else Can Process Model Do? 11. SPREADSHEET SIMULATION WITH @RISK. Introduction to @RISK: The Newsperson Problem. Modeling Cash Flows from a New Product. Bidding Models. Reliability and Warranty Modeling. RISKGENERAL Function. RISKCUMULATIVE Function. RISKTRIGEN Function. Creating a Distribution Based on a Point Forecast. Forecasting Income of a Major Corporation. Using Data to Obtain Inputs For New Product Simulations. Playing Craps with @RISK. Project Management. Simulating the NBA Finals. 12. SPREADSHEET SIMULATION AND OPTIMIZATION WITH RISKOPTIMIZER. The Newsperson Problem. Newsperson Problem with Historical Data. Manpower Scheduling Under Uncertainty. Product Mix Problem. Job Shop Scheduling. Traveling Salesperson Problem. 13. OPTION PRICING AND REAL OPTIONS. Lognormal Model for Stock Prices. Option Definitions. Types of Real Options. Valuing Options by Arbitrage Methods. Black-Scholes Option Pricing Formula. Estimating Volatility. Risk Neutral Approach to Option Pricing. Valuing an Internet Start Up and Web TV. Relation Between Binomial and Lognormal Models. Pricing American Options with Binomial Trees. Pricing European Puts and Calls with Simulation. Using Simulation to Model Real Options. 14. PORTFOLIO RISK, OPTIMIZATION AND HEDGING. Measuring Value at Risk (VAR). Scenario Approach to Portfolio Optimization. 15. FORECASTING. Moving Average Forecasting Methods. Simple Exponential Smoothing. Holt"s Method: Exponential Smoothing with Trend. Winter"s Method: Exponential Smoothing with Seasonality. Ad Hoc Forecasting, Simple Linear Regression. Fitting Non-Linear Relationships. Multiple Regression. 16. BROWNIAN MOTION, STOCHASTIC CALCULUS, AND OPTIMAL CONTROL. What Is Brownian Motion? Derivation of Brownian Motion as a Limit of Random Walks. Stochastic Differential Equations. Ito"s Lemma. Using Ito"s Lemma to Derive the Black-Scholes Equation. An Introduction to Stochastic Control.

Evolution of Biological Systems in Random Media: Limit Theorems and Stability

Abstract: Preface. List of Notations. 1: Random Media. 1.1. Markov Chains. 1.2. Ergodicity and Reducibility of Markov Chains. 1.3. Markov Renewal Processes. 1.4. Semi-Markov Processes. 1.5. Jump Markov Processes. 1.6. Wiener Processes and Diffusion Processes. 1.7. Martingales. 1.8. Semigroups of Operators and their Generators. 1.9. Martingale Characterization of Markov and Semi-Markov Processes. 1.10. General Representation and Measurability of Biological Systems in Random Media. 2: Limit Theorems for Difference Equations in Random Media. 2.1. Limit Theorems for Random Evolutions. 2.2. Averaging of Difference Equations in Random Media. 2.3. Diffusion Approximation of Difference Equations in Random Media. 2.4. Normal Deviations of Difference Equations in Random Media. 2.5. Merging of Difference Equations in Random Media. 2.6. Stability of Difference Equations in Random Media. 2.7. Limit Theorems for Vector Difference Equations in Random Media. 3: Epidemic Models. 3.1. Deterministic Epidemic Models. 3.2. Stochastic Epidemic Model (Epidemic Model in Random Media). 3.3. Averaging of Epidemic Model in Random Media. 3.4. Merging of Epidemic Models in Random Media. 3.5. Diffusion Approximation of Epidemic Models in Random Media. 3.6. Normal Deviations of Epidemic Model in Random Media. 3.7. Stochastic Stability of Epidemic Model. 4: Genetic Selection Models. 4.1. Deterministic Genetic Selection Models. 4.2. Stochastic Genetic Selection Model (Genetic Selection Model in Random Media). 4.3. Averaging of Slow Genetic Selection Model in Random Media. 4.4. Merging of Slow Genetic Selection Model in Random Media. 4.5. Diffusion Approximation of Slow Genetic Selection Model in Random Media. 4.6. Normal Deviations of Slow Genetic Selection Model in Random Media. 4.7. Stochastic Stability of Slow Genetic Selection Model. 5: Branching Models. 5.1. Branching Models with Deterministic Generating Function. 5.2. Branching Models in Random Media. 5.3. Averaging of Branching Models in Random Media. 5.4. Merging of Branching Model in Random Media. 5.5. Diffusion Approximation of Branching Process in Random Media. 5.6. Normal Deviations of Branching Process in Random Media. 5.7. Stochastic Stability of Branching Model in Averaging and Diffusion Approximation Schemes. 6: Demographic Models. 6.1. Deterministic Demographic Model. 6.2. Stochastic Demographic Models (Demographic Models in Random Media). 6.3. Averaging of Demographic Models in Random Media. 6.4. Merging of Demographic Model. 6.5. Diffusion Approximation of Demographic Model. 6.6. Normal Deviations of Demographic Models in Random Media. 6.7. Stochastic Stability of Demographic Model in Averaging and Diffusion Approximation Schemes. 7: Logistic Growth Models. 7.1. Deterministic Logistic Growth Model. 7.2. Stochastic Logistic Growth Model (Logistic Growth Model in Random Media). 7.3. Averaging of Logistic Growth Model in Random Media. 7.4. Merging of Logistic Growth Model in Random Media. 7.5. Diffusion Approximation of Logistic Growth Model in Random Media. 7.6. Normal De

An efficient and accurate algorithm for generating spatially‐correlated random fields

Abstract: Reference GEOLEP-ARTICLE-2003-004doi:10.1002/cnm.621View record in Web of Science Record created on 2008-02-13, modified on 2016-08-08

Towards Credible and Fast Quantitative Stochastic Simulation

Abstract: The computer revolution initiated in the second half of the twentieth century has resulted in the adoption of computer simulation as the most popular paradigm of scientic investigations. It has become the most commonly used tool in performance evaluation studies of various complex dynamic stochastic systems. Such reliance on simulation studies raises the question of credibility of the results they yield. Unfortunately, there is evidence that many reported simulation results cannot be considered as credible. In this paper, having briey overviewed the main necessary conditions of any trustworthy simulation study, we will focus on the issue of sequential on-line analysis of simulation output data, the most practical way for obtaining statistically accurate results from simulation studies. The perils and pitfalls of quantitative sequential simulation will be considered, together with its fast distributed version, based on concurrent execution of simulation on multiple processors and known as Multiple Replications in Parallel (MRIP). We will discuss main properties and limitations of MRIP, as well as its implementation in Akaroa2, a simulation controller designed at University of Canterbury in Christchurch, New Zealand, automatically executing MRIP on clusters of computers in local area networks.

Efficient random fields simulation for stochastic FEM analyses

Abstract: Publisher Summary This chapter presents a paper that discusses efficient random field's simulation for stochastic finite element method analyzes. Simulation of random fields is the fundamental task in stochastic finite element method (SFEM). There are many techniques available nowadays, but for computationally intensive problems, one is constrained by small number of Monte Carlo type simulations. This paper proposes a method that combines spectral decomposition of covariance matrix and improved Latin hypercube sampling (LHS). It uses a method for diminishing spurious correlation based on stochastic optimization method. This leads to decrease of the scatter of autocorrelation function of simulated random fields. An advantage is that there is no strict restriction concerning small number of random field simulations. This paper assesses the quality of simulated random fields. The best performance, the convergence to target values of statistics with low variability is achieved in case of LHS.

Estimation of Markovian jump systems with unknown transition probabilities through Bayesian sampling

Abstract: Addressed is the problem of state estimation for dynamic Markovian jump systems (MJS) with unknown transitional probability matrix (TPM) of the embedded Markov chain governing the system jumps. Based on recent authors' results, proposed is a new TPM-estimation algorithm that utilizes stochastic simulation methods (viz. Bayesian sampling) for finite mixtures' estimation. Monte Carlo simulation results of TMP-adaptive interacting multiple model algorithms for a system with failures and maneuvering target tracking are presented.

Optimal Control and Stochastic Simulation of Large Nonlinear Models withRational Expectations

Abstract: This paper presents a computationally fesible procedure for the optimal control and stochastic simulation of large nonlinear models with rational expectations under the assumption of certainty equivalence.

Random number generation method based on multivariate non-normal distribution, parameter estimation method thereof, and application to simulation of financial field and semiconductor ion implantation

Abstract: Random number generating method for generating random numbers in accordance with multivariate non-normal distributions based on the Yuan and Bentler method I on computer. The method includes application steps for applying n-dimensional multivariate non-normal distributions to n-dimensional experience distribution by using computer and steps for generating random numbers including pseudo-random numbers, quasi-random numbers, low discrepancy sequences, and physical random numbers by methods including additive generator method, M-sequence, generalized feedback shift-register method, and Mersenne Twister, and excluding congruential method, by using computer. The application steps use predetermined relationship equations for the third and fourth order moments to perform application associated with the third and fourth order moments of the empirical distributions. Moreover, by using random numbers generation method, parameters are estimated by maximum likelihood method. Furthermore, the random number generation method and the parameters estimated method are applied to simulation of financial field, semiconductor ion implantation, and the like.

Two Examples of Deterministic versus Stochastic Modeling of Chemical Reactions

Abstract: The numerical simulation of chemical reactions can be carried out using deterministic or stochastic models. The deterministic simulation gives the average behavior of the system, which is a suitable representation of the reaction when the number of molecules involved is large. The stochastic simulation requires stronger mathematical foundations, mainly from probability theory but allows prediction of the so-called stochastic effects, which are relevant when the number of molecules is small. A more accurate representation of processes dependent on the behavior of a small number of molecules is of increasing importance in current chemistry and can be achieved through stochastic modeling. From an educational point of view, the simultaneous use of stochastic and deterministic models in the simulation of chemical reactions results in a better understanding of the chemical dynamics. The two approaches are reviewed in this paper by using two selected examples of chemical reactions and four MATLAB programs, which...

Study of the Probabilistic Information of a Random Set.

Abstract: Given a random set coming from the imprecise observation of a random variable, we study how to model the information about the distribution of this random variable. Specifically, we investigate whether the information given by the upper and lower probabilities induced by the random set is equivalent to the one given by the class of the distributions of the measurable selections; together with sufficient conditions for this, we also give examples showing that they are not equivalent in all cases.

Queueing-network stability: simulation-based checking

Abstract: Queueing networks are either stable or unstable, with stable networks having finite performance measures and unstable networks having asymptotically many customers as time goes to infinity. Stochastic simulation methods for estimating steady-state performance measures often assume that the network is stable. Here, we discuss the problem of checking whether a given network is stable when the stability-checking algorithm is allowed only to view arrivals and departures from the network.

Stochastic simulation of inhomogeneous metocean fields: part I: annual variability

Abstract: The paper discusses stochastic models of scalar and vector metocean fields based on time varying Empirical Orthogonal Functions in space, and autoregressive time series models for the coefficients in the expansions. The models are fitted to an extensive data set from the Barents Sea and verified by studying field extreme value properties.

Rare-event, heavy-tailed simulations using hazard function transformations, with applications to value-at-risk

Abstract: We develop an observation that a simulation method introduced recently for heavy-tailed stochastic simulation, namely hazard-rate twisting, is equivalent to doing exponential twisting on a transformed version of the heavy-tailed random-variable; the transforming function is the hazard function. Using this approach, the paper develops efficient methods for computing portfolio value-at-risk (VAR) when changes in the underlying risk factors have the multivariate Laplace distribution.

Two-dimensional model for binary fragmentation process with random system of forces, random stopping and material resistance

Abstract: This work presents the numerical results obtained from large-scale parallel distributed simulations of a self-similar model for two-dimensional discrete in time and continuous in space binary fragmentation. Its main characteristics are: (1) continuous material; (2) uniform and independent random distribution of the net forces, denoted by f x and f y , that produce the fracture; (3) these net forces act at random positions of the fragments and generate the fracture following a maximum criterion; (4) the fragmentation process has the property that every fragment fracture stops at each time step with an uniform probability p ; (5) the material presents an uniform resistance r to the fracture process. Through a numerical study was obtained an approximate power law behavior for the small fragments size distribution for a wide range of the main parameters of the model: the stopping probability p and the resistance r . The visualizations of the model resemble real systems. The approximate power law distribution is a non-trivial result, which reproduces empirical results of some highly energetic fracture processes.

Poisson Simulation as an Extension of Continuous System Simulation for the Modeling of Queuing Systems

Abstract: Poisson simulation is an extension of continuous system simulation whereby randomness is modeled as opposed to just adding noise. This article treats how Poisson simulation can be used for modeling queuing systems. The focus is on the implementation of queues in Poisson simulation and the connections to queuing theory. This approach also has theoretical and practical implications. Dynamic and stochastic systems, especially when queues are involved, are often treated by discrete event simulation using a microscopic view in which individual entities are modeled. Poisson simulation makes it possible to handle many such systems on a macroscopic level using aggregated states. It is therefore interesting to compare these approaches. Parallel approaches can then be sketched with discrete event simulation in one branch and Poisson simulation in the other. A fundamental difference between the approaches is whether one prefers to base a model on individual, distinguishable entities or on lumped entities.