Use Of Monte-Carlo Method Research Articles

Pointwise and functional approximations in Monte Carlo maximum likelihood estimation

We consider the use of Monte Carlo methods to obtain maximum likelihood estimates for random effects models and distinguish between the pointwise and functional approaches. We explore the relationship between the two approaches and compare them with the EM algorithm. The functional approach is more ambitious but the approximation is local in nature which we demonstrate graphically using two simple examples. A remedy is to obtain successively better approximations of the relative likelihood function near the true maximum likelihood estimate. To save computing time, we use only one Newton iteration to approximate the maximiser of each Monte Carlo likelihood and show that this is equivalent to the pointwise approach. The procedure is applied to fit a latent process model to a set of polio incidence data. The paper ends by a comparison between the marginal likelihood and the recently proposed hierarchical likelihood which avoids integration altogether.

A generalized growth model for simulating initial migration of dense non‐aqueous phase liquids

Modeling the migration of spilled non–aqueous phase liquids (NAPLs) is currently difficult because the physics governing their movement is complex and knowledge of the local geology is always incomplete. NAPL movement is subject to buoyancy, capillary, and viscous forces in addition to being directed by the particular structural and hydraulic properties of the porous medium. Consideration of buoyancy forces suggests that the flow regime diagram of Lenormand et al. [1988] can be expanded to a third dimension. We develop a generalized growth model, based on invasion percolation, that captures the essential physics of initial NAPL migration but is simple enough computationally that simulations can be conducted much faster than by using continuum simulation models that attempt to capture all details of the physics. In comparison with available experimental data, our model realistically simulates movement of a NAPL for a wide range of values of Bond and capillary numbers, in any kind of porous medium. Because this approach allows much faster and simpler simulation than other approaches, a higher spatial resolution and/or the use of Monte Carlo methods to reduce the effect of geological uncertainty becomes a realistic possibility.

Studies of bilateral contracts with respect to steady-state security in a deregulated environment [of electricity supply

Under a deregulated environment, electricity consumers and suppliers will be permitted to establish various bilateral service contracts. The transmission company however will only have to honour and execute these bilateral contracts as far as the system design and operating conditions permit. A fundamental question is to what extent the system security could affect these contracts and what kinds of system reinforcements will be required to meet the future contract needs. This paper describes a series of studies modelling the bilateral contracts by using a transaction matrix (T). The concept of the transaction matrix is to expand the conventional load flow variables such as generations (Pg) and loads (Pd) into a 2-dimensional matrix (T). Each element of T, namely t/sub ij/, corresponds to a bilateral contract between a supplier (Pg/sub 1/) and consumer (Pd/sub j/). A generalized linear programming formulation is then proposed to solve various system operation and planning problems under a deregulated environment subjected to the steady-state security constraints (e.g. generation and line flow limits). Examples are presented to illustrate how to use this formulation to maximize any bilateral contract, individual generation or groups of generations; or to minimize the necessary correction needed for a proposed transaction matrix (T/spl deg/) in order to comply with the security requirements. Other studies such as the use of Monte Carlo methods to study the behaviour of random bilateral contracts are also presented and discussed. It was concluded that the proposed methodology will be an effective tool to study the intricate relationships between the bilateral contracts and system security.

Monte Carlo methods for modeling magnetostatic NDE phenomena: a feasibility study

Magnetostatic methods that are used for the nondestructive evaluation (NDE) of ferromagnetic materials can be modeled by partial differential equations. Conventional numerical methods such as finite difference, finite elements or boundary integral methods for large problems typically require an iterative matrix inversion scheme to solve the system of equations. Parallel implementation of such schemes is extremely difficult due to the data dependencies in the matrices. Monte Carlo methods offer an alternative approach by reducing the differential equation to simple, independent, random processes that are inherently amenable to parallel implementation. This paper investigates the use of Monte Carlo methods for modeling magnetostatic flux leakage NDE phenomena. The model is validated by comparing the results with those obtained with finite element models. The approach offers significant reduction in computational burden especially for 3-D problems.

The use of Monte Carlo methods to determine the distribution of Al and Si cations in framework aluminosilicates from29Si MAS NMR data

A Monte Carlo method was developed to determine the distribution of Al and Si cations from 29SiMAS NMR data for framework aluminosilicates. The method was used to analyze data obtained from Cs-exchanged leucite in its high-temperature cubic phase and from cubic analcime samples. It was also used to determine the number of AI-O-Allinkages in cordierite for different degrees of Al-Si order. The results for cordierite were correlated with the calorimetric data of Carpenter et al. (1983) to estimate the energy for the reaction (AI-O-Al) + (Si-O-Si) ~ 2(AI-O-Si) of -40 kJ/mol.

モンテカルロ法を活用した平衡状態図と変態組織形成のシミュレーション

モンテカルロ法を活用した平衡状態図と変態組織形成のシミュレーション

A Monte Carlo Study of Distribution Function P(S) of a Polymer Chain

The distribution function P(S) of the radius of gyration of linear polyethylene (PE) is studied by use of Monte Carlo method in tetrahedral lattice. Three different cases, according to different interactions between polymer chain molecules, are investigated. The P(S)s of three different cases are compared with the exact distribution function P0(S) for random flight chain obtained by Yamakawa. At θ-state, the P(S) of N=260 (N is the length of polymer chain) is similar to P0(S), but that of N=20 deviates largely from P0(S). When the chain perturbed by an excluded volume, the difference between P(S) and P0(S) becomes large, but when we introduce long-range interaction (Van der Waals potential) at the same time, the difference becomes smaller. The results show that not only can short chain effect affect the distribution function P(S), excluded volume and long-range interaction can also affect P(S) of the chain.

Elastomers having high functionality cross links viewed as bimodal networks. An alternative interpretation in terms of bimodal chain‐length distributions

AbstractSeveral groups have now prepared poly(dimethylsiloxane) networks of high cross‐link functionality by end‐linking vinyl‐terminated chains by means of SiH groups in siloxane oligomers (CH3)3SiO[SiHCH3O]xSi(CH3)3. The elongation moduli of these networks were generally found to be considerably larger than the values predicted from the functionality and number density of the cross links (based on the stoichiometry of the end‐linking reaction). Not all the SiH groups in an oligomer are used in the end‐linking reaction, however, and the segments between cross‐links can themselves act as short network chains. The connectivity of these short chains to the long ones, in what is essentially a bimodal distribution, has been neglected in analyses to date. They are taken into account in the present analysis, giving much better agreement between experiment and theory. The stress‐strain behavior for such very short chains can be characterized by the use of Monte Carlo methods and the Fixman‐Alben non‐Gaussian distribution. This alternative analysis seems useful in reproducing the experimental observations, but further experimental and theoretical will be required to remove some remaining ambiguities. © 1995 John Wiley & Sons, Inc.

The use of Monte Carlo methods in factor analysis

Monte Carlo techniques are introduced in target transformation factor analysis (TTFA), in combination with the concept of the principal factor model, in order to account for local variances in the data set and to estimate the uncertainties in the obtained source profiles. The new method is validated using several types of artificial data sets. It was found that application of the Monte Carlo method leads to a significant improvement of the accuracy of the derived source profiles in comparison with standard TTFA. From the introduction of (known) error sources to the artificial data sets it was found that the source-profile reproduction quality is optimal if the magnitudes of the Monte Carlo variations are chosen equal to the magnitudes of the introduced errors.

Whole Core Calculations of Power Reactors by Use of Monte Carlo Method

Whole Core Calculations of Power Reactors by Use of Monte Carlo Method

Whole Core Calculations of Power Reactors by Use of Monte Carlo Method.

Abstract Whole core calculations have been performed for a commercial size PWR and a prototype LMFBR by using vectorized Monte Carlo codes. Geometries of cores were precisely represented in a pin by pin model. The calculated parameters were k eff, control rod worth, power distribution and so on. Both multigroup and continuous energy models were used and the accuracy of multigroup approximation was evaluated through the comparison of both results. One million neutron histories were tracked to considerably reduce variances. It was demonstrated that the high speed vectorized codes could calculate k eff, assembly power and some reactivity worths within practical computation time. For pin power and small reactivity worth calculations, the order of 10 million histories would be necessary. It would be difficult for the conventional scalar code to solve such large scale problems while the present codes consumed computation time less than 30 min for a PWR and 1 hour for an LMFBR. Required number of histories to achieve target design accuracy were estimated for those neutronic parameters.

The conformation of fluid membranes: Monte Carlo simulations.

The conformation and scaling properties of self-avoiding fluid membranes with an extrinsic bending rigidity kappa were studied with the use of Monte Carlo methods. For kappa = 0, the results are consistent with branched polymer behavior at large length scales. There is a smooth crossover from a crumpled to an extended state with increasing kappa, with a peak in the specific heat when the persistence length reaches the system size. The scale-dependent effective bending rigidity is a decreasing function of system size for all bare rigidities. These results indicate that fluid membranes are always crumpled at sufficiently long length scales.

An Exact Application of Maximum Likelihood Method to Pharmacokinetic Analysis.

It is well known that there exist inter-individual variations of pharmacokinetic parameters. We can analyze pharmacokinetic data by Bayesian models expressing these variations by a prior distribution. Some programs, such as MULTI(ELS), are developed on this method and population distribution of pharmacokinetic parameters are estimated by maximizing log likelihood. In this program, however, the linear approximation by Taylor expansion is used in calculation of log likelihood and this linear approximation brings significant error in calculation of maximum log likelihood. We need to calculate maximum log likelihood unbiassedly for model selection by AIC.In this paper, we employ Monte Carlo method to calculate the likelihood of Bayesian models. We find that the estimate of maximum log likelihood by MULTI(ELS) has bias caused by the linear approximation in calculation of log likelihood. We propose the use of Monte Carlo method for unbiassed calculation of the log likelihood of Bayesian models.

Use of Monte Carlo method in planning expensive experiments

Thus, the numerical method proposed here for constructing the experiment plan is intended for the construction of a mathematical model of a technological process with the aim of “adjusting” it in optimal conditions. The distinctive feature of the method is the use of the information value parameter as the quality index of the experiment plan. The advantage of the method is the possibility of determining the optimal parameters of the technological process with a small number of experiments, which is especially important when the experiments are expensive.

An epidemiological model of rinderpest. I. Description of the model.

The development of an epidemiological model of rinderpest in cattle and wildlife populations is described. The model uses a state-transition structure, incorporating a stochastic element through the use of Monte-Carlo methods modified to allow large populations to be simulated. The potential applications include the estimation of "safe" host population immunity rates and the design of cost-effective rinderpest vaccination programmes.

Development of an electron avalanche and its transition into streamers.

In this paper results are presented from an investigation of the growth of ionization in nitrogen, in a uniform electric field, starting from one or more initiatory electrons. The electrons are described by the distribution function f(vrt) while the ions are assumed stationary. The electron distribution function is obtained with use of Monte Carlo methods, taking into account, self-consistently, collective effects due to the space-charge electric field generated by the electrons and ions. From this kinetic investigation, we have gained insight into the avalanche-to-streamer transition and the role that the velocity distribution and photoionization play in the dynamics of streamers.

A random surface representation of Wilson loops in Z(2) gauge theory

We study a random surface representation of Wilson loops in Z(2) gauge theory. The weights consist of an area factor, which dominates at strong coupling, and an excluded volume factor flavouring crumpled surfaces. We examine the latter one in some detail in three as well as four dimensions by use of Monte Carlo methods. In three dimensions, the critical behaviour of the surfaces is found to be determined to a large extent by the excluded volume factor.

Strings, Fields and Critical Phenomena

The connection between field theory and critical phenomena is reviewed. Emphasis is put on the use of Monte Carlo methods in the study of non-perturbative aspects of field theory. String theory is then described as a statistical theory of random surfaces and the critical behaviour is analyzed both by analytical and numerical methods.

Stochastic development of an electron avalanche.

The stochastic evolution in space of an electron avalanche has been investigated with the use of Monte Carlo methods. From these investigations we have obtained the energy distribution as a function of distance from the cathode and avalanche size, f(n,\ensuremath{\epsilon},x); the probability distribution for avalanche size, P(n,x); and the ionization probability, per unit distance at x, for electrons belonging to an avalanche of size n, ${\ensuremath{\alpha}}_{s}$(n,x). We believe that this is the first time that any information has been presented on f(n,\ensuremath{\epsilon},x) and ${\ensuremath{\alpha}}_{s}$(n,x) which takes microscopic processes into account. The investigations were done in nitrogen for E/N\ensuremath{\ge}300 Td. We suggest that pulse-height distribution experiments may be a sensitive technique for determining the E/N conditions at which runaway electrons appear.

The use of Monte Carlo methods in natural resource management models

The Monte Carlo method provides a means of introducing natural variability in data, uncertainty of parameter estimation, chance occurrences and model reliability, into the process of simulation modeling for resource management. The technique is described and demonstrated for a hypothetical application of a Gaussian Plume Dispersion Model to a case of atmospheric pollution. It is concluded that the utility of the Monte Carlo approach lies mainly in providing decision makers with information on the likelihood of extreme occurrences and the inherent reliability of simulation modeling.