Showing papers on "Monte Carlo method published in 1994"

Reliability Assessment of Electric Power Systems Using Monte Carlo Methods

Abstract: Introduction. Basic Concepts of Power System Reliability Evaluation. Elements of Monte Carlo Methods. Generating System Adequacy Assessment. Composite System Adequacy Assessment. Distribution System and Station Adequacy Assessment. Reliability Cost/Worth Assessment. Appendixes. Index.

Monte Carlo Methods In Ab Initio Quantum Chemistry

Abstract: Review of ab initio quantum chemistry introduction to Monte Carlo methods the variational Monte Carlo method quantum Monte Carlo exact Green's function methods released node methods excited states properties other than energy determination of interaction potentials, stationary geometries, energy derivatives valence-electron and acceleration methods.

Estimating Normal Means with a Dirichlet Process Prior

Abstract: In this article, the Dirichlet process prior is used to provide a nonparametric Bayesian estimate of a vector of normal means. In the past there have been computational difficulties with this model. This article solves the computational difficulties by developing a “Gibbs sampler” algorithm. The estimator developed in this article is then compared to parametric empirical Bayes estimators (PEB) and nonparametric empirical Bayes estimators (NPEB) in a Monte Carlo study. The Monte Carlo study demonstrates that in some conditions the PEB is better than the NPEB and in other conditions the NPEB is better than the PEB. The Monte Carlo study also shows that the estimator developed in this article produces estimates that are about as good as the PEB when the PEB is better and produces estimates that are as good as the NPEB estimator when that method is better.

A Primer for the Monte Carlo Method

Abstract: The Monte Carlo method is a numerical method of solving mathematical problems through random sampling. As a universal numerical technique, the method became possible only with the advent of computers, and its application continues to expand with each new computer generation. A Primer for the Monte Carlo Method demonstrates how practical problems in science, industry, and trade can be solved using this method. The book features the main schemes of the Monte Carlo method and presents various examples of its application, including queueing, quality and reliability estimations, neutron transport, astrophysics, and numerical analysis. The only prerequisite to using the book is an understanding of elementary calculus.

Diffuse reflectance of oceanic shallow waters: influence of water depth and bottom albedo

Abstract: We used simplifying assumptions to derive analytical formulae expressing the reflectance of shallow waters as a function of observation depth and of bottom depth and albedo. These formulae also involve two apparent optical properties of the water body: a mean diffise attenuation coefficient and a hypothetical reflectance which would be observed if the bottom was infinitely deep. The validity of these approximate formulae was tested by comparing their outputs with accurate solutions of the radiative transfer obtained under the same boundary conditions by Monte Carlo simulations. These approximations were also checked by comparing the reflectance spectra for varying bottom depths and compositions determined in coastal lagoons with those predicted by the formulae. These predictions were based on separate determinations of the spectral albedos of typical materials covering the floor, such as coral sand and various green or brown algae. The simple analytical expressions are accurate enough for most practical applications and also allow quantitative discussion of the limitations of remote-sensing techniques for bottom recognition and bathymetry. As early as 1944, Duntley used a spectrograph mounted in a glass-bottomed boat or flown in an airplane to analyze radiances emerging from the ocean and shallow waters. He evidenced the influence of the water depth on the spectral composition of the upward flux (Duntley 1963). Using a Monte Carlo technique, Plass and Kattawar (1972) calculated the radiative field in the atmosphere+cean system and in particular examined the dependence of the upward flux on the albedo of the ocean floor. Gordon and Brown (1974) studied the diffuse reflectance of a shallow ocean using Monte Carlo simulations and a probabilistic approach. Gordon and Brown provided an analysis based on photon history of the light field as modified by the presence of a reflecting bottom. In, addition, Ackleson and Klemas (1986) developed a two-flow model that simulated the light field within a canopy of bottom-adhering plants. A single scattering approximation for irradiance reflectance was also

Approximate Asymptotic Distribution Functions for Unit-Root and Cointegration Tests

Abstract: This article uses Monte Carlo experiments and response surface regressions in a novel way to calculate approximate asymptotic distribution functions for several well-known unit-root and cointegration test statistics. These allow empirical workers to calculate approximate P values for these tests. The results of the article are based on an extensive set of Monte Carlo experiments, which yield finite-sample quantiles for several sample sizes. Based on these, response surface regressions are used to obtain asymptotic quantiles for many different test sizes. Then approximate distribution functions with simple functional forms are estimated from these asymptotic quantiles.

Ancestral Inference in Population Genetics

Abstract: Mitochondrial DNA sequence variation is now being used to study the history of our species. In this paper we discuss some aspects of estimation and inference that arise in the study of such variability, focusing in particular on the estimation of substitution rates and their use in calibrating estimates of the time since the most recent common ancestor of a sample of sequences. Observed DNA sequence variation is generated by superimposing the effects of mutation on the ancestral tree of the sequences. For data of the type studied here, this ancestral tree has to be modeled as a random process. Superimposing the effects of mutation produces complicated sampling distributions that form the basis of any statistical model for the data. Using such distributions--for example, for maximum likelihood estimation of rates--poses some difficult computational problems. We describe a Monte Carlo method, a cousin of the popular "Markov chain Monte Carlo," that has proved very useful in addressing some of these issues.

The solution and estimation of discrete choice dynamic programming models by simulation and interpolation: monte carlo evidence

Abstract: Over the past decade, a substantial literature on methods for the estimation of discrete choice dynamic programming (DDP) models of behavior has developed. However, the implementation of these methods can impose major computational burdens because solving for agents' decision rules often involves high dimensional integrations that must be performed at each point in the state space. In this paper we develop an approximate solution method that consists of: (1) using Monte Carlo integration to stimulate the required multiple integrals at a subset of the state points, and (2) interpolating the non-simulated values using a regression function. The overall performance of this approximation method appears to be excellent. Copyright 1994 by MIT Press.

The solution and estimation of discrete choice dynamic programming models by simulation and interpolation: Monte Carlo evidence

Abstract: Over the past decade, a substantial literature on the estimation of discrete choice dynamic programming (DC-DP) models of behavior has developed. However, this literature now faces major computational barriers. Specifically, in order to solve the dynamic programming (DP) problems that generate agents' decision rules in DC-DP models, high dimensional integrations must be performed at each point in the state space of the DP problem. In this paper we explore the performance of approximate solutions to DP problems. Our approximation method consists of: 1) using Monte Carlo integration to simulate the required multiple integrals at a subset of the state points, and 2) interpolating the non-simulated values using a regression function. The overall performance of this approximation method appears to be excellent, both in terms of the degree to which it mimics the exact solution, and in terms of the parameter estimates it generates when embedded in an estimation algorithm.

Comparison of numerical models for computing underwater light fields

Abstract: Seven models for computing underwater radiances and irradiances by numerical solution of the radiative transfer equation are compared. The models are applied to the solution of several problems drawn from optical oceanography. The problems include highly absorbing and highly scattering waters, scattering by molecules and by particulates, stratified water, atmospheric effects, surface-wave effects, bottom effects, and Raman scattering. The models provide consistent output, with errors (resulting from Monte Carlo statistical fluctuations) in computed irradiances that are seldom larger, and are usually smaller, than the experimental errors made in measuring irradiances when using current oceanographic instrumentation. Computed radiances display somewhat larger errors.

Annual Reviews of Computational Physics VII

Abstract: Empirical Potential Energy Functions Used in the Simulations of Materials Properties (TM Erkoc) Thermally Activated Reversal in Magnetic Nanostructures (U Nowak) A Tutorial on Advanced Dynamic Monte Carlo Methods for Systems with Discrete State State Spaces (M A Novotny) Beyond Navier-Stokes: Burnett Equations for Flow Simulations in the Contunuum-Transition Regimes (R K Agarwal et al.) Social Impact Models of Opinion Ddynamics (J A Holyst et al.) Teaching Computational Physics to Undergraduates (J Tobochnik & H Gould).

Ordering and phase transitions of charged particles in a classical finite two-dimensional system.

Abstract: We report a Monte Carlo study of phase transitions in a finite two-dimensional (2D) system of charged classical particles which are confined by a circular parabolic or hard-wall well. The ground-state configurations are found by static energy calculations and their structures are analyzed using the Voronoi constructions. A Mendeleev table for these classical 2D-like atoms is obtained. We calculate the radial and angular components of the displacements of the particles as functions of temperature and determine the critical temperatures for the order-disorder phase transitions. The intershell rotation and intershell diffusion transitions are investigated. The results are compared with Wigner crystallization in the infinite 2D system.

Determination of phase diagrams for the hard-core attractive Yukawa system

Abstract: The phase diagram of a system consisting of hard particles with an attractive Yukawa interaction is computed by Monte Carlo simulation. From the results of these simulations we can estimate that the liquid–vapor coexistence curve disappears when the range of the attractive part of the Yukawa potential is less than approximately one‐sixth of the hard‐core diameter. The results of the simulations are compared with predictions based on first order perturbation theory.

Computer simulation of the domain dynamics of a quenched system with a large number of nonconserved order parameters: The grain-growth kinetics

Abstract: The domain dynamics of a quenched system with many nonconserved order parameters was investigated by using the time-dependent Ginzburg-Landau kinetic equations. Our computer simulation of a model two-dimensional system produced microstructures remarkably similar to experimental observations of normal grain growth. After a short transient, the average domain or grain radius was found to increase with time as ${\mathit{t}}^{1/2}$, in agreement with most of previous mean-field predictions and more recent Q-state Potts model Monte Carlo simulations.

Comments on cross-correlation methodology in variability studies of active galactic nuclei

Abstract: We discuss two separate cross-correlation methdologies, the interpolation method of Gaskell and Sparkle and the discrete correlation function of Edelson and Krolik, that are commonly used to quantify the lags between continuum and emission-line flux variations in active galactic nuclei (AGNs). We show that if similar assumptions are made to normalize the cross-correlation functions, the two methods are in good agreement for well-sampled AGN light curves. We also investigate the performance of cross-correlation methodology for less well-sampled data sets through Monte Carlo simulations that employ realistic models of the continuum behavior (based on well-observed Seyfert galaxies) and typical emission-line response times. We find that the interpolation method fairly accurately recovers the emission-line lags as the sampling is degraded (i.e., as the number of observed points is reduced). We find that for the cases investigated, the emission-line lags can be determined with reasonable accuracy even with mean sampling intervals as large as around two weeks.

Two‐dimensional modeling of high plasma density inductively coupled sources for materials processing

Abstract: Inductively coupled plasma sources are being developed to address the need for high plasma density (1011–1012 cm−3), low pressure (a few to 10–20 mTorr) etching of semiconductor materials. One such device uses a flat spiral coil of rectangular cross section to generate radio‐frequency (rf) electric fields in a cylindrical plasma chamber, and capacitive rf biasing on the substrate to independently control ion energies incident on the wafer. To investigate these devices we have developed a two‐dimensional hybrid model consisting of electromagnetic, electron Monte Carlo, and hydrodynamic modules; and an off line plasma chemistry Monte Carlo simulation. The results from the model for plasma densities, plasma potentials, and ion fluxes for Ar, O2, Ar/CF4/O2 gas mixtures will be presented.

The formulation of quantum statistical mechanics based on the Feynman path centroid density. IV. Algorithms for centroid molecular dynamics

Abstract: Numerical algorithms are developed for the centroid molecular dynamics (centroid MD) method to calculate dynamical time correlation functions for general many‐body quantum systems. Approaches based on the normal mode path integral molecular dynamics and staging path integral Monte Carlo methods are described to carry out a direct calculation of the force on the centroid variables in the centroid MD algorithm. A more efficient, but approximate, scheme to compute the centroid force is devised which is based on the locally optimized harmonic approximation for the centroid potential. The centroid MD equations in the latter method can be solved with the help of an iterative procedure or through extended Lagrangian dynamics. A third algorithm introduces an effective centroid pseudopotential to approximate the full many‐body centroid mean force potential by effective pairwise centroid interactions. Numerical simulations for both prototype models and more realistic many‐body systems are performed to explore the feasibility and limitations of each algorithm.

Inversion of seismoacoustic data using genetic algorithms and a posteriori probability distributions

Abstract: The goal of many underwater acoustic modeling problems is to find the physical parameters of the environment. With the increase in computer power and the development of advanced numerical models it is now feasible to carry out multiparameter inversion. The inversion is posed as an optimization problem, which is solved by a directed Monte Carlo search using genetic algorithms. The genetic algorithm presented in this paper is formulated by steady‐state reproduction without duplicates. For the selection of ‘‘parents’’ the object function is scaled according to a Boltzmann distribution with a ‘‘temperature’’ equal to the fitness of one of the members in the population. The inversion would be incomplete if not followed by an analysis of the uncertainties of the result. When using genetic algorithms the response from many environmental parameter sets has to be computed in order to estimate the solution. The many samples of the models are used to estimate the a posteriori probabilities of the model parameters. T...

Noise properties of the EM algorithm: II. Monte Carlo simulations.

Abstract: For pt.I see ibid., vol.39, no.5, p.833-46 (1994). In pt.I the authors derived a theoretical formulation for estimating the statistical properties of images reconstructed using the iterative maximum-likelihood expectation-maximization (ML-EM) algorithm. To gain insight into this complex problem, two levels of approximation were considered in the theory. These techniques revealed the dependence of the variance and covariance of the reconstructed image noise on the source distribution, imaging system transfer function, and iteration number. Here, a Monte Carlo approach was taken to study the noise properties of the ML-EM algorithm and to test the predictions of the theory. The study also served to evaluate the approximations used in the theory. Simulated data from phantoms were used in the Monte Carlo experiments. The ML-EM statistical properties were calculated from sample averages of a large number of images with different noise realizations. The agreement between the more exact form of the theoretical formulation and the Monte Carlo formulation was better than 10% in most cases examined, and for many situations the agreement was within the expected error of the Monte Carlo experiments. Results from the studies provide valuable information about the noise characteristics of ML-EM reconstructed images. Furthermore, the studies demonstrate the power of the theoretical and Monte Carlo approaches for investigating noise properties of statistical reconstruction algorithms.