Monte Carlo Integration Method Research Articles

Femtosecond protein nanocrystallography—data analysis methods

X-ray diffraction patterns may be obtained from individual submicron protein nanocrystals using a femtosecond pulse from a free-electron X-ray laser. Many "single-shot" patterns are read out every second from a stream of nanocrystals lying in random orientations. The short pulse terminates before significant atomic (or electronic) motion commences, minimizing radiation damage. Simulated patterns for Photosystem I nanocrystals are used to develop a method for recovering structure factors from tens of thousands of snapshot patterns from nanocrystals varying in size, shape and orientation. We determine the number of shots needed for a required accuracy in structure factor measurement and resolution, and investigate the convergence of our Monte-Carlo integration method.

Application of a Monte Carlo integration method to collision and coagulation growth processes of hydrometeors in a bin‐type model

New algorithms for calculating the collision‐coagulation growth process of hydrometeors were developed and implemented into a bin cloud microphysics model in order to improve its computational efficiency. Computation of collision‐coagulation growth is a bottleneck in the bin‐type cloud microphysics calculation that takes a large amount of computing time. Improvement in the efficiency of the process can significantly reduce computing time. In this study, a new stochastic algorithm was developed and implemented into the collision‐coagulation growth process of a nonhydrostatic cloud model. Simulations showed that the computing time was reduced by about 90%. We verified that the error range of the simulation results from the new scheme is much smaller than the internal variability involved the traditional bin‐type model and also in the real atmosphere. The newly developed scheme was implemented into the mesoscale operational model of the Japan Meteorological Agency. The precipitation field was accurately simulated in a numerical weather prediction simulation.

Influence of Random Effects Incorporated in the Analysis of Pharmacological Data Based on a Four-parameter Logistic Model

In the later phases of selecting candidate chemicals for drug development, pharmacological experiments are conducted using animal organs or human peripheral blood cells. In these experiments, data analysis is often performed on the basis of mixed-effect models so that the individuality effect can be incorporated in the dose-response relationship. This paper studied the influence of the incorporation of random effects on parameters in a logistic model intended for analysis, with the assumption that the dose-response relationship is really described by a four-parameter logistic model. Using Monte-Carlo simulation experiments, we compared the performances of eight models in which various mixed-effects were incorporated. In each of the eight analysis models, five methods of calculation, namely, the standard two-stage method (STS), first-order approximation method (FOA), Laplacian approximation method (LAP), Monte Carlo integration method (MCI), and Gaussian quadrature method (GAU), were applied to the simulation data. The eight analysis models and five estimation methods were compared, using estimability and the deviation of estimates from the true value as the criteria. The results revealed the analysis model incorporating the random effect on only the maximum response to be the best. The results also indicated that the FOA, LAP, MCI, and GAU methods had almost the same performances for this analysis model. The authors recommend LAP as the preferred method because of the simplicity of its calculation.

Modified Weibull-derived spectrum for deep water significant wave height estimation

The modified Weibull spectrum is utilized to calculate the zeroth spectral moment (mo) using Monte Carlo integration methods. Then significant wave height (Hs) is calculated using the formula $$ {\text{H}}_{\text{s}} = 4\sqrt {{\text{m}}_{\text{o}} } . $$ This is validated with observed buoy data and numerical wave model (WAM) predicted significant wave heights. The Weibull parameters have been calculated using energy densities from observed spectra recorded by DS5 buoy (13.80° N, 82.52° E, depth 3355.48 m) by the method of maximum likelihood (MLE).The relative root mean square error (RRMS) and relative bias error criteria show that modified Weibull spectrum estimated significant wave heights are better than those predicted by WAM model. The monthly averaged observed wave power spectra for the year 2005 recorded by deep water buoy DS5 is considered in this work. The spectra exhibit bimodal sea states for several months of the year.

Benchmark calculations from summarized data: an example

Benchmark calculations often are made from data extracted from publications. Such data may not be in a form most appropriate for benchmark analysis, and, as a result, suboptimal and/or non-standard benchmark analyses are often applied. This problem can be mitigated in some cases using Monte Carlo computational methods that allow the likelihood of the published data to be calculated while still using an appropriate benchmark dose (BMD) definition. Such an approach is illustrated herein using data from a study of workers exposed to styrene, in which a hybrid BMD calculation is implemented from dose response data reported only as means and standard deviations of ratios of scores on neuropsychological tests from exposed subjects to corresponding scores from matched controls. The likelihood of the data is computed using a combination of analytic and Monte Carlo integration methods.

Characterization of Virtual Nano-Structures through the Use of Monte Carlo Integration

The determination of the properties of porous solids remains an integral element to the understanding of adsorption, transport and reaction processes in new and novel materials. The advent of molecular simulation has led to an improved understanding and prediction of adsorption processes using molecular models. These molecular models have removed the constraints of traditional adsorption theories, which require rigid assumptions about the structure of a material. However, even if we possess a full molecular model of a solid, it is still desirable to define the properties of this solid in a standard manner with quantities such as the accessible volume, surface area and pore size distribution. This talk will present Monte Carlo integration methods for calculating these quantities in a physically meaningful and unambiguous way. The proposed methods for calculating the surface area and pore size distribution were tested on an array of idealised solid configurations including cylindrical and cubic pores. The method presented is adequate for all configurations tested giving confidence to its applicability to disordered solids. The method is further tested by using several different noble gas probe molecules. Finally, the results of this technique are compared against those obtained by applying the BET equation for a range of novel materials.

Stochastic Graph Processes for Performance Evaluation of Content Delivery Applications in Overlay Networks

This paper proposes a new methodology to model the distribution of finite size content to a group of users connected through an overlay network.Our methodology describes the distribution process as a constrained stochastic graph process (CSGP), where the constraints dictated by the content distribution protocol and the characteristics of the overlay network define the interaction among nodes. A CSGP is a semi-Markov process whose state is described by the graph itself. CSGPs offer a powerful description technique that can be exploited by Monte Carlo integration methods to compute in a very efficient way not only the mean but also the full distribution of metrics such as the file download times or number of hops from the source to the receiving nodes.We model several distribution architectures based on trees and meshes as CSGPs and solve them numerically. We are able to study scenarios with a very large number of nodes and we can precisely quantify the performance differences between the treeand mesh-based distribution architectures.

Improved strategies for coverage estimation by using replicated line-intercept sampling

Coverage, i.e., the area covered by the target attribute in the study region, is a key parameter in many surveys. Coverage estimation is usually performed by adopting a replicated protocol based on line-intercept sampling coupled with a suitable linear homogeneous estimator. Since coverage is a parameter which may be interestingly represented as the integral of a suitable function, improved Monte Carlo strategies for implementing the replicated protocol are introduced in order to achieve estimators with small variance rates. In addition, new specific theoretical results on Monte Carlo integration methods are given to deal with the integrand functions arising in the special coverage estimation setting.

Lower virial coefficients of primitive models of polar and associating fluids

With respect to technical problems associated with simulations of primitive models of polar and associating fluids at low temperatures and/or high densities, another possibility to determine numerically their phase behavior and estimate the location of the critical point is via the virial expansion. However, neither the determination of the virial coefficients is straightforward. The second and third virial coefficients of primitive models of four associating fluids (ammonia, ethanol, methanol and water) and three polar fluids (acetone, carbon dioxide and hydrogen sulfide) were therefore determined using a recently developed Metropolis-like Monte Carlo integration method.

Comparison of Methods for Parameter Estimation in a Circular Linear Mixed Effect Model Incorporating the Diurnal Variation for Evaluating the Treatment Effects of Glaucoma Therapy

Glaucoma is the primary cause of vision loss in Japan. The most important glaucoma therapy is to decrease intraocular pressure (IOP) for preventing visual field defects in the pre-stage of vision loss. Considering a systematic diurnal variation of IOP, Kuwayama et al. (2006) proposed to use a circular linear mixed effect (CLME) model for evaluating the efficacy of therapy on IOP decrease for patients with normal tension glaucoma (NTG) and applied it to the data analysis in a clinical trial (Nipradilol trial) with 28 NTG patients. In this application, there occurred an issue that the parameter estimates were different depending on the method of estimation and the best method was not identified. We, therefore, compared six methods for parameter estimation (standard two-stage (STS) method, global two-stage (GTS) method, first order approximation (FOA) method, Laplacian approximation (LAP) method, Monte Carlo integration (MCI) method and Gaussian quadrature (GAUS) method) through a simulation experiment with the bias and square root of mean squared error as the criteria for evaluation. The GAUS method proved to be superior to others in realizing least bias and mean squared error under various simulation conditions, although it was most time consuming.

Muon simulations for Super-Kamiokande, KamLAND, and CHOOZ

Muon backgrounds at Super-Kamiokande, KamLAND, and CHOOZ are calculated using $\mathtt{M}\mathtt{U}\mathtt{S}\mathtt{I}\mathtt{C}$. A modified version of the Gaisser sea-level muon distribution and a well-tested Monte Carlo integration method are introduced. Average muon energy, flux, and rate are tabulated. Plots of average energy and angular distributions are given. Implications for muon tracker design in future experiments are discussed.

On the shape of posterior densities and credible sets in instrumental variable regression models with reduced rank: An application of flexible sampling methods using neural networks

Likelihoods and posteriors of instrumental variable (IV) regression models with strong endogeneity and/or weak instruments may exhibit rather non-elliptical contours in the parameter space. This may seriously affect inference based on Bayesian credible sets. When approximating posterior probabilities and marginal densities using Monte Carlo integration methods like importance sampling or Markov chain Monte Carlo procedures the speed of the algorithm and the quality of the results greatly depend on the choice of the importance or candidate density. Such a density has to be ‘close’ to the target density in order to yield accurate results with numerically efficient sampling. For this purpose we introduce neural networks which seem to be natural importance or candidate densities, as they have a universal approximation property and are easy to sample from. A key step in the proposed class of methods is the construction of a neural network that approximates the target density. The methods are tested on a set of illustrative IV regression models. The results indicate the possible usefulness of the neural network approach.

Profile Likelihood-Based Confidence Intervals Using Monte Carlo Integration for Population Pharmacokinetic Parameters

ABSTRACT Population pharmacokinetic (PPK) analysis usually employs nonlinear mixed effects models using first-order linearization methods. It is well known that linearization methods do not always perform well in actual situations. To avoid linearization, the Monte Carlo integration method has been proposed. Moreover, we generally utilize asymptotic confidence intervals for PPK parameters based on Fisher information. It is known that likelihood-based confidence intervals are more accurate than those from the usual asymptotic confidence intervals. We propose profile likelihood-based confidence intervals using Monte Carlo integration. We have evaluated the performance of the proposed method through a simulation study, and analyzed the erythropoietin concentration data set by the method.

On the Shape of Posterior Densities and Credible Sets in Instrumental Variable Regression Models with Reduced Rank: An Application of Flexible Sampling Methods using Neural Networks

Likelihoods and posteriors of instrumental variable regression models with strong endogeneity and/or weak instruments may exhibit rather non-elliptical contours in the parameter space. This may seriously affect inference based on Bayesian credible sets. When approximating such contours using Monte Carlo integration methods like importance sampling or Markov chain Monte Carlo procedures the speed of the algorithm and the quality of the results greatly depend on the choice of the importance or candidate density. Such a density has to be 'close' to the target density in order to yield accurate results with numerically efficient sampling. For this purpose we introduce neural networks which seem to be natural importance or candidate densities, as they have a universal approximation property and are easy to sample from. A key step in the proposed class of methods is the construction of a neural network that approximates the target density accurately. The methods are tested on a set of illustrative models. The results indicate the feasibility of the neural network approach.

Distribution of relaxation times in α-phase polyvinylidene fluoride

In this paper, a recently developed numerical method to analyze dielectric-spectroscopy data is applied to α-phase polyvinylidene fluoride (PVDF). The numerical procedure is non-parametric and does not contain any of the extensively used empirical formulas mentioned in the literature. The method basically recovers the unknown distribution of relaxation times of the generalized dielectric function representation by simultaneous application of the Monte Carlo integration method and of the constrained least-squares optimization. The relaxation map constructed after the numerical analysis is compared to α-phase PVDF data presented in the literature and results of the parametric analysis with a well-known empirical formula.

Monte Carlo integration strategies for design‐based regression estimators of the spatial mean

AbstractWhen a continuous population is sampled, the spatial mean is often the target parameter if the design‐based approach is assumed. In this case, auxiliary information may be suitably used to increase the accuracy of the spatial mean estimators. To this end, regression models are usually considered at the estimation stage in order to implement regression estimators. Since the spatial mean may be obviously represented as a bivariate integral, the strategies for placing the sampling locations are actually Monte Carlo integration methods. Hence, the regression‐based estimation is equivalent to the control‐variate integration method. In this setting, we suggest more refined Monte Carlo integration strategies which may drastically increase the regression estimator accuracy. Copyright © 2005 John Wiley & Sons, Ltd.

Some large-sample results on a modified Monte Carlo integration method

The large-sample properties of the modified Monte Carlo integration method with locally antithetic variates proposed by Haber (Math. Comput. 21 (1967) 388) are provided under the mild assumption that the integrand is a C 1 function. Moreover, the asymptotic distribution of the modified Monte Carlo estimator is obtained under the same condition. Furthermore, we propose a consistent variance estimation method, which avoids the replicated procedure considered by Haber (1967) which reduces the efficiency of this integration technique. On the basis of the achieved results, in addition to the integration framework, the method may be conveniently applied in the environmental sampling setting.

First order QCD corrections to the weak gauge boson pair production in hadronic collisions

A complete next-to-leading logarithm (NLL) to the weak gauge boson pair production in hadron colliders pp → ZZ + X, which involves computing the contributions from the 2 → 3 real gluon emission as well as the one loop correction to the 2 → 2 process are presented. The calculation utilizes a combination of analytic and Monte Carlo integration methods.

A program for confidence interval calculations for a Poisson process with background including systematic uncertainties: POLE 1.0

A Fortran 77 routine has been developed to calculate confidence intervals with and without systematic uncertainties using a frequentist confidence interval construction with a Bayesian treatment of the systematic uncertainties. The routine can account for systematic uncertainties in the background prediction and signal/background efficiencies. The uncertainties may be separately parametrized by a Gauss, log-normal or flat probability density function (PDF), though since a Monte Carlo approach is chosen to perform the necessary integrals a generalization to other parameterizations is particularly simple. Full correlation between signal and background efficiency is optional. The ordering schemes for frequentist construction currently supported are the likelihood ratio ordering (also known as Feldman–Cousins) and Neyman ordering. Optionally, both schemes can be used with conditioning, meaning the probability density function is conditioned on the fact that the actual outcome of the background process can not have been larger than the number of observed events. Program summary Title of program: POLE version 1.0 Catalogue identifier: ADTA Program summary URL: http://cpc.cs.qub.ac.uk/summaries/ADTA Program available from: CPC Program Library, Queen's University of Belfast, N. Ireland Licensing provisions: None Computer for which the program is designed: DELL PC 1 GB 2.0 Ghz Pentium IV Operating system under which the program has been tested: RH Linux 7.2 Kernel 2.4.7-10 Programming language used: Fortran 77 Memory required to execute with typical data: ∼1.6 Mbytes No. of bytes in distributed program, including test data, etc.: 373745 No. of lines in distributed program, including test data, etc.: 2700 Distribution format: tar gzip file Keywords: Confidence interval calculation, Systematic uncertainties Nature of the physical problem: The problem is to calculate a frequentist confidence interval on the parameter of a Poisson process with known background in presence of systematic uncertainties in experimental parameters such as signal efficiency or background prediction. Method of solution: A PDF for the confidence interval construction is constructed by folding a Poisson density function with a parametrization describing the posterior PDF of the systematic uncertainties. The construction is then performed with this new PDF according to different ordering schemes. The convolution is performed using a Monte Carlo integration method, providing greatest possible flexibility with respect to the parametrization. Restriction on the complexity of the problem: No restrictions. Typical running time: for calculation of a single confidence interval with 1000 steps in signal hypothesis space the wall clock time on a DELL PC 1 GB 2.0 Ghz Pentium IV with 4 GB swap is ca. 500 seconds. The wall clock time scales roughly linear with the number of steps in signal space. Unusual features of the program: POLE uses routines from the CERNLIB library [ http://wwwasd.web.cern.ch/wwwasd/cernlib], which have to be linked in during compilation. It should be noted that the number of steps in signal space (maximal s required divided by the step-width) should not exceed 1000, since the corresponding arrays are predimensioned.

Adaptive radial-based direction sampling: some flexible and robust Monte Carlo integration methods

Adaptive radial-based direction sampling (ARDS) algorithms are specified for Bayesian analysis of models with non-elliptical, possibly, multimodal target distributions. A key step is a radial-based transformation to directions and distances. After the transformation a Metropolis-Hastings method or, alternatively, an importance sampling method is applied to evaluate generated directions. Next, distances are generated from the exact target distribution. An adaptive procedure is applied to update the initial location and covariance matrix in order to sample directions in an efficient way. The ARDS algorithms are illustrated on a regression model with scale contamination and a mixture model for economic growth of the USA.