Showing papers on "Stochastic simulation published in 1987"

Stochastic Simulation

Abstract: One fifth (4 of 20) of the research articles published in the Journal of Educational Statistics in 1988 include simulation studies that justify or illustrate the authors' conclusions. A similar fraction (6 of 33) of the articles in the 1988 volume of Psychometrika include simulations; comparable proportions could be expected in other journals at the boundary of theoretical statistics and social/psychological applications. Due in part to the complexity of the problems tackled today and in part to the availability of cheap, powerful computing—by no means independent influences—simulation and Monte Carlo methods have become both necessary and practical tools for statisticians and applied workers in quantitative areas of education and psychology. Simulation has become popular—not only in the quantitative social sciences, but in all of the mathematical sciences from physics to operations research to number theory—because it is almost always easy to do. This ease of use makes the simulation experimenter vulnerable to two common pitfalls. Selection of the basic source of "random numbers" is often passive: Whatever is available in the computer's standard subroutine library is used. However, the fact that a pseudo-random number generator appears in a popular software package or operating system is hardly reason to trust it, as is shown by the infamous RANDU generator, once popular on IBM mainframes and PDP mini-computers, and by the generators burned into RAM on today's PCs. Simulation design and reporting also deserve special care. Some attempt must be made to assess the accuracy of the simulation estimates: One should accurately estimate and report SE (6) as well as 6. In addition, enough detail should be reported that the interested reader can replicate the study and check the results, just as with other experiments. Yet these considerations are also easy to overlook. Brian D. Ripley's Stochastic Simulation is a short, yet ambitious, survey of modern simulation techniques. Three themes run throughout the book. First, one shoud not take basic simulation subroutines for granted, especially on minior microcomputers where they tend to be poor implementations, implementations of poor algorithms, or both. Second, design of experiments, or variance reduction as it is known in this field, deserves greater consideration. Third, modern methods make it possible to simulate and analyze processes that are dependent over time, and using such processes opens the door to new simulation techniques, such as simulated annealing in optimization. Ripley intends this book to be a "comprehensive guide," and it is indeed most accurately described as a researcher's handbook with examples and

An experimental procedure for simulation response surface model identification

Abstract: An experimental method for identifying an appropriate model for a simulation response surface is presented. This technique can be used for globally identifying those factors in a simulation that have a significant influence on the output. The experiments are run in the frequency domain. A simulation model is run with input factors that oscillate at different frequencies during a run. The functional form of a response surface model for the simulation is indicated by the frequency spectrum of the output process. The statistical significance of each term in a prospective response surface model can be measured. Conditions are given for which the frequency domain approach is equivalent to ranking terms in a response surface model by their correlation with the output. Frequency domain simulation experiments typically will require many fewer computer runs than conventional run-oriented simulation experiments.

Stochastic water quality optimization using imbedded chance constraints

Abstract: A chance-constrained stochastic programming model is developed for water quality optimization. It determines the least cost allocation of waste treatment plant biochemical oxygen demand (BOD) removal efficiencies, subject to probabilistic restrictions on maximum allowable instream dissolved oxygen deficit. The new model extends well beyond traditional approaches that assume streamflow is the sole random variable. In addition to streamflow, other random variables in the model are initial in-stream BOD level and dissolved oxygen (DO) deficit; waste outfall flow rates, BOD levels and DO deficits; deoxygenation k1, reaeration k2, and sedimentation-scour rate k3 coefficients of the Streeter-Phelps DO sag model; photosynthetic input-benthic depletion rates Ai, and nonpoint source BOD input rate Pi for the Camp-Dobbins extensions to the Streeter-Phelps model. These random variables appear in more highly aggregated terms which in turn form part of the probabilistic constraints of the water quality optimization model. Stochastic simulation procedures for estimating the probability density functions and covariances of these aggregated terms are discussed. A new chance-constrained programming variant, imbedded chance constraints, is presented along with an example application. In effect, this method imbeds a chance constraint within a chance constraint in a manner which is loosely associated with the distribution-free method of chance-constrained programming. It permits the selection of nonexpected value realizations of the mean and variance estimates employed in the deterministic equivalents of traditional chance-constrained models. As well, it provides a convenient mechanism for generating constraint probability response surfaces. A joint chance-constrained formulation is also presented which illustrates the possibility for prescription of an overall system reliability level, rather than reach-by-reach reliability assignment.

Random Signals and Systems

Abstract: Discussion of Probability and Stochastic Processes The Gaussian Distribution in One and Two Dimensions The Multidimensional Gaussian Distribution Finite Random Sequences Stationary Random Sequences Continuous-time Stationary Gaussian and Second-order Processes Nonstationary Continuous-time Processes Additional Topics in the Study of Continuous-time Processes Linear Systems in Conjunction with Memoryless Nonlinear Devices Nonstationary Random Sequences Discrete-time Kalman Filtering Appendixes References Index.

Random set theory and problems of modeling

Abstract: The three- or four-dimensional world in which we live is full of objects to be measured and summarized. Very often a parsimonious finite collection of measurements is enough for scientific investigation into an object’s genesis and evolution. There is a growing need, however, to describe and model objects through their form as well as their size. The purpose of this article is to show the potentials and limitations of a probabilistic and statistical approach. Collections of objects (the data) are assimilated to a random set (the model), whose parameters provide description and/or explanation.

Semigroup solutions to stochastic unsteady groundwater flow subject to random parameters

Abstract: Two methods for the solution of partial differential equations (PDE) for the general case of random in time physical parameters are presented and their application to the solution of unsteady regional groundwater flow equations are illustrated. The first method is the semigroup approach which directly offers a solution without resorting to “closure approximations” (hierarchy techniques), perturbation techniques, or Montecarlo simulation techniques. The semigroup approach can also handle the general stochastic problem when randomness also appears as initial conditions, boundary conditions or forcing terms. The second method is an approximation scheme to obtain the semigroup solution in complex cases and permits the solution of equations with more than one random coefficient.

Stochastic simulation of spatially correlated geo-processes

Abstract: In this study, developments in the theory of stochastic simulation are discussed. The unifying element is the notion of Radon projection in Euclidean spaces. This notion provides a natural way of reconstructing the real process from a corresponding process observable on a reduced dimensionality space, where analysis is theoretically easier and computationally tractable. Within this framework, the concept of space transformation is defined and several of its properties, which are of significant importance within the context of spatially correlated processes, are explored. The turning bands operator is shown to follow from this. This strengthens considerably the theoretical background of the geostatistical method of simulation, and some new results are obtained in both the space and frequency domains. The inverse problem is solved generally and the applicability of the method is extended to anisotropic as well as integrated processes. Some ill-posed problems of the inverse operator are discussed. Effects of the measurement error and impulses at origin are examined. Important features of the simulated process as described by geomechanical laws, the morphology of the deposit, etc., may be incorporated in the analysis. The simulation may become a model-dependent procedure and this, in turn, may provide numerical solutions to spatial-temporal geologic models. Because the spatial simūlation may be technically reduced to unidimensional simulations, various techniques of generating one-dimensional realizations are reviewed. To link theory and practice, an example is computed in detail.

Stochastic simulation of Bayesian belief networks

Abstract: This paper examines the use of stochastic simulation of Bayesian belief networks as a method for computing the probabilities of values of variables. Specifically, it examines the use of a scheme described by Henrion, called logic sampling, and an extension to that scheme described by Pearl. The scheme devised by Pearl allows us to "clamp" any number of variables to given values and to conduct stochastic simulation on the resulting network. We have found that this algorithm, in certain networks, leads to much slower than expected convergence to the true posterior probability. This behavior is a result of the tendency for local areas in the graph to become fixed through many stochastic iterations. The length of this non-convergence can be made arbitrarily long by strengthening the dependency between two nodes. This paper describes the use of graph modification. By modifying a belief network through the use of pruning, arc reversal, and node reduction, it may be possible to convert the network to a form that is computationally more efficient for stochastic simulation.

Use of comb-like models to mimic anomalous diffusion on fractal structures

Abstract: We discuss some properties of random walks on comb-like structures. These have been used as analogues for the study of anomalous diffusion along a percolation cluster intersected by loopless dead-ends. It is shown that a number of transport properties along a backbone can be found by using an approximation method based on the continuous-time random walk (CTRW). The principal property resulting from this analysis is the asymptotic form of the probability distribution for the location of a random walker at step n. This allows the calculation of such quantities as the mean-squared displacement after n steps, the expected number of distinct sites visited, and changes in properties of the random walk in response to biasing fields. It is shown that when the times between successive visits to the backbone are random, and distributed according to a stable law different critical phenomena can occur in the model.

One-dimensional random field Ising model and discrete stochastic mappings

Abstract: Previous results relating the one-dimensional random field Ising model to a discrete stochastic mapping are generalized to a two-valued correlated random (Markovian) field and to the case of zero temperature. The fractal dimension of the support of the invariant measure is calculated in a simple approximation and its dependence on the physical parameters is discussed.

Stochastic response of nonlinear structures with parameter random fluctuations

Abstract: The random response of a nonlinear structural system is examined when its parameters are experiencing random fluctuations with time. The treatment is based on the recent developments in the mathematical theory of stochastic differential equations. These include the Ito stochastic calculus and the Fokker-Planck equation approach to derive a general differential equation that describes the evolution of the statistical moments of the response coordinates. The differential equation is found to constitute an infinite coupled set of differential equations that are closed via two different closure schemes. The system response is determined in the neighborhood of internal resonance condition and for various random intensities of the system parameters. It is found that the random modal interaction is governed mainly by the internal resonance ratio and the stiffness fluctuation intensity. The effect of the random damping fluctuation on the system response is found to be very small compared to the stiffness fluctuation effect.

Modeling continuous noise sources in digital simulations

Abstract: Physical systems often contain subsystems that are "best" model ed as continuous random processes. When these processes are included in digital simulations, the statistics of the random num ber generator used in the simulation must be selected such that the continuous random process is modeled faithfully. In general the statistics of the random number generator will be drastically different from the statistics of the continuous random process. This paper presents the functional relationship between the sta tistics of the random number generator and the statistics of the continuous random process for simulations using two commonly employed integration methods.

Simple stochastic simulation models to sharpen mine management

Abstract: Essentially any dynamic process can be modeled mathematically. Simple stochastic modelling, sometimes called Monte-Carlo, is available to anyone with even a small computer. Construction of a mine management model should start with a few broad parameters. After these are tested, they can be broken down into sub-elements; more parameters can be added; and the model is thus expanded to embrace all decision variables in the organization. In the following discussion, statistical jargon is avoided where possible in order to focus attention on the essentials of modelling.

Weak convergence of approximate solutions of stochastic equations with applications to random differential and integral equations

Abstract: In this paper, we considerably extend our earlier ~esult about convergence in distribution of approximate solutions of random operator equations, where the stochastic inputs and the underlying deterministic equation are simltaneously approximated. As a by-product, we obtain convergence results for approximate solutions of equations between spaces of probability measures. We apply our results to random Fredholm integral equations of the second kind and to a random iionlinear ellintic boundary value problem.

A modified version of handscomb's antithetic variates theorem

Abstract: We consider a modified version of Handscomb’s Antithetic Variates theorem and prove the existence of exact minimum rather than infinimum and that this minimum is achieved by using only one random number. Practical procedures for finding the optimal cumulative distribution function are given, for estimating the expected value of the response difference of a pair of arbitrary functions of scalar arguments.

Asymptotic optimization of stochastic simulation in problems of atmospheric optics

Abstract: The main results on the optimization of Monte Carlo algorithms based on the asymptotic solutions of the transport theory are presented. The methods of constructing such algorithms for a number of problems in atmospheric optics are analysed. Approaches to optimizing the simulation of radiative transfer with non-exponential absorption are described. The algorithms are aimed at computing the transmission of IR radiation through cloud layers in the absorption bands of atmospheric gases. 1. IMPORTANCE SAMPLING In terms of the ray-optics approximation, the transfer of optic radiation in scattering and absorbing media can be described (see, for example, [9]) by an integral equation of the second kind f J /(x)= /c(x',x)/(x')dx' + iA(x) (1.1) x where /(x) is the density of collisions or scattering events for particles (light quanta) in the medium in the phase space Χ; χ and χΈΧ\ and ψ(χ) is the density of'collisions' in the source. We shall consider problems whose solutions can be reduced to estimating functional of the type J* = (/, Φ) = I /(*)#*) dx, φ(χ) > 0. (1.2) Jx It is well known (see, for example, [4]) that

A simple approximation for the simulation of continuous random variables

Abstract: A simple technique is described for simulations and analytical studies where the indication is of a unimodal, right-skewed dis tribution of a continuous random variable, the type of distribu tion often approximated by a gamma distribution. The technique is more realistic and more general than the "simple" techniques described in the simulation literature in that it does not require integer parameters.

Minimax control of a stochastic system with the loss fun ction dependent on parameter of distrubances

Abstract: A discrete time linear stochastic system with random horizon of control is considered. Disturbances in the system have distribution belonging to an exponential family with a parameter. The loss function depends on state variables, controls and it is given by (3). A horizon of control is a random variable independent of disturbances with given distribution. For a conjugate a priori distribution of the parameter the BAYES control is obtained. Next, a problem of determining the minimax control of the system is considered.

Monte Carlo simulations of random walks and surfaces in parallel

Abstract: The theory of Monte Carlo simulation of random geometric objects such as random walks and random surfaces is considered on a sequential and a parallel computer. The partition functions generated for simple Monte Carlo rules are derived and the difference between sequential and parallel computing is discussed for the case of random walks with fixed endpoints or for random loops. The implications for random surface calculations in parallel is considered in short.

Generation of normally distributed random sequences in stochastic dynamic models

Abstract: The generation of white normal sequences in stochastic dynamic models is investigated. A normal white generator is proposed and its performance evaluated. The normal sequences are tested on artificial models, prior to their use in system identification. The results of these tests indicate a close agreement with the white normal theory.

Some methods for simulating random fields

Abstract: Several methods exist for simulating random fields. This paper reviews some of the methods used to simulate stationary random fields in Rn, n ≥ 1. A recent study comparing the traditional turning bands method to a method called the random impact method is given. The results of this study indicate that the random impact model is comparable to the turning bands method in terms of execution time, and in terms of reproducibility of the covariance functions.