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In the reliability analysis of the landslide-stabilizing piles system (LSP), the most commonly used uncertainty models of geotechnical parameters mainly include the homogeneity model (HM) and unconditional random field (UCRF). However, neither of these models considers the existence of borehole data, which may lead to overestimation of the degree of site uncertainty. Based on borehole data in situ, the conditional random field (CRF) of the shear strength of the sliding surface was established through random field theory and the Kriging estimation method. By combining the limit equilibrium method (LEM) and Monte Carlo simulation (MCS), a novel procedure was introduced that can calculate the stability coefficient and design thrust of pile stabilization at the same time. By considering multiple failure modes comprehensively, a calculation flowchart for the failure probability of the LSP was proposed. The spatial layout parameters of pile stabilization, including the pile location, pile spacing, and pile length, significantly impact the calculation results. Compared with using HM and UCRF, the failure probability of the LSP may be lower when using CRF. Based on the allowable failure probability, feasible design solutions were provided. Further comparisons were made on the number of feasible solutions under these three uncertainty models. The research results in this paper might provide some assistance for the optimization of pile stabilization. [ABSTRACT FROM AUTHOR]

We revisit the Bayesian Context Trees (BCT) modelling framework for discrete time series, which was recently found to be very effective in numerous tasks including model selection, estimation and prediction. A novel representation of the induced posterior distribution on model space is derived in terms of a simple branching process, and several consequences of this are explored in theory and in practice. First, it is shown that the branching process representation leads to a simple variable-dimensional Monte Carlo sampler for the joint posterior distribution on models and parameters, which can efficiently produce independent samples. This sampler is found to be more efficient than earlier MCMC samplers for the same tasks. Then, the branching process representation is used to establish the asymptotic consistency of the BCT posterior, including the derivation of an almost-sure convergence rate. Finally, an extensive study is carried out on the performance of the induced Bayesian entropy estimator. Its utility is illustrated through both simulation experiments and real-world applications, where it is found to outperform several state-of-the-art methods. [ABSTRACT FROM AUTHOR]

The prediction of project completion time, which is important in project management, is only based on an estimate of three numbers, namely the fastest, slowest, and presumably time. The common practice of applying normal distribution through Monte Carlo simulation in Program Evaluation and Review Technique (PERT) research often fails to accurately represent project activity durations, leading to potentially biased project completion prediction. Based on these problems, a different method is proposed, namely, Discrete Event Simulation (DES). The research aims to evaluate the effectiveness of the simmer package in R in conducting PERT analysis. Specifically, there are three objectives in the research: 1) develop a simulation model to predict how long a project will take and find the critical path, 2) create an R script to simulate discrete events on a PERT network, and 3) explore the simulation output using the simmer package in the form of summary statistics and estimation of project risk. Then, a library research with a descriptive and exploratory method is used for data collection. The hypothetical network is used to obtain the numerical results, which provide the predicted value of the project completion, the critical path, and the risk level. Simulation, including 100 replications, results in a predicted project completion time and a standard deviation of 20.7 and 2.2 weeks, respectively. The DES method has been proven highly effective in predicting the completion time of a project described by the PERT network. In addition, it offers increased flexibility. [ABSTRACT FROM AUTHOR]

Sample selection is one of the most important factors in estimating the unknown parameters of distributions, as it saves time, saves effort, and gives the best results. One of the challenges is deciding on a suitable distribution estimate technique and adequate sample selection to provide the best results in comparison with earlier research. The method of moments (MOM) was decided on to estimate the unknown parameters of the Gumbel distribution, but with four changes in the sample selection, which were simple random sample (SRS), ranked set sampling (RSS), maximum ranked set sampling (MRSS), and ordered maximum ranked set sampling (OMRSS) techniques, due to small sample sizes. The MOM is a traditional method for estimation, but it is difficult to use when dealing with RSS modification. RSS modification techniques were used to improve the efficiency of the estimators based on a small sample size compared with the usual SRS estimator. A Monte Carlo simulation study was carried out to compare the estimates based on different sampling. Finally, two datasets were used to demonstrate the adaptability of the Gumbel distribution based on the different sampling techniques. [ABSTRACT FROM AUTHOR]

The arctan uniform distribution (AUD) is a brand-new bounded distribution that may be used for modeling a variety of existing bounded real-world datasets. Ranked set sampling (RSS) is a useful technique for parameter estimation when accurate measurement of the observation is challenging and/or expensive. In the current study, the parameter estimator of the AUD is addressed based on RSS and simple random sampling (SRS) techniques. Some of the popular conventional estimating techniques are considered. The efficiency of the produced estimates is compared using a Monte Carlo simulation. It appears that the maximum product spacing method has an advantage in assessing the quality of proposed estimates based on the outcomes of our simulations for both the SRS and RSS datasets. In comparison to estimates produced from the SRS datasets, it can be seen that those from the RSS datasets are more reliable. This implies that RSS is a more effective sampling technique in terms of generating estimates with a smaller mean squared error. The benefit of the RSS design over the SRS design is further supported by real data results. [ABSTRACT FROM AUTHOR]

This work utilizes generalized order statistics (GOSs) to study the q-Weibull distribution from several statistical perspectives. First, we explain how to obtain the maximum likelihood estimates (MLEs) and utilize Bayesian techniques to estimate the parameters of the model. The Fisher information matrix (FIM) required for asymptotic confidence intervals (CIs) is generated by obtaining explicit expressions. A Monte Carlo simulation study is conducted to compare the performances of these estimates based on type II censored samples. Two well-established measures of information are presented, namely extropy and weighted extropy. In this context, the order statistics (OSs) and sequential OSs (SOSs) for these two measures are studied based on this distribution. A bivariate q-Weibull distribution based on the Farlie-Gumbel-Morgenstern (FGM) family and its relevant concomitants are studied. Finally, two concrete instances of medical real data are ultimately provided. [ABSTRACT FROM AUTHOR]

We provide a formal statistical theory of consistent estimation of the set of all arbitrage portfolios that meet the description of being a stochastic arbitrage opportunity. Two empirical likelihood ratio tests are developed: one for the null that a given arbitrage portfolio is qualified, and another for the alternative that the portfolio is not qualified. Apart from considering generalized concepts and hypotheses based on multiple host portfolios, the statistical assumption framework is also more general than in earlier studies that focused on special cases with a single benchmark portfolio. Various extensions and generalizations of the theory are discussed. A Monte Carlo simulation study shows promising statistical size and power properties for testing the null, for representative data dimensions. The results of an empirical application illustrate the importance of selecting a proper blocking structure and moment estimation method. [ABSTRACT FROM AUTHOR]

In this paper, statistical inferences for the parameters, reliability, and failure rate functions (as parameters) of the exponentiated Kies distribution are accomplished using maximum likelihood and both Lindley and Markov chain Monte Carlo techniques, under adaptive Type-II progressive censoring. Depending on the Fisher information matrix and the delta method, we find the approximate confidence intervals for the parameters and the reliability and failure rate functions, respectively. Furthermore, the samples generated from Markov chains Monte Carlo are used to generate credible intervals for the parameters, reliability, and failure rates functions. Symmetric and asymmetric loss functions are also used to find Bayes estimators using Markov chain Monte Carlo and Lindley techniques. Comparisons between the two techniques of evaluation for different estimators under different sizes of data sets are conducted. Finally, a real-life example is applied to clarify the results of the used techniques. [ABSTRACT FROM AUTHOR]

In this paper, we consider a simultaneous modeling of good and bad outputs. We use an input distance function (IDF) with endogenous inputs as well as endogenous bad outputs, which is novel in the literature. Moreover, we model input efficiency to depend on the production of bad outputs which allows us to investigate whether emissions of pollutants (bad outputs) are related to technological performance (technical efficiency). We also model production of each bad output with a spatial structure separately, each depending on production of good outputs, inputs and other exogenous variables. These bad output production functions allow us to estimate both direct and indirect effects of good output on the production of bad outputs, which may be of special interest because they show the cost (to the society) in terms of releasing pollutants to the environment in order to increase production of good outputs. We apply the new technique to a data set on U.S. electric utilities with four bad outputs, three inputs and two good outputs. We used a Bayesian technique to estimate the model which is a system consisting of the input distance function, reduced form equations for each input, dynamics of inefficiency and bad output production technology--separately for each. Empirically, bad outputs are found to affect inefficiency positively. Percentage increases in inefficiency due to a percentage increase in each bad output are found to vary from 0.225% to 0.42%. Energy prices are found to be positively related to inefficiency. From the spatial specifications of bad outputs, we find that the spillover effects of increasing production of good outputs account for the majority of the total effect, indicating that neighborhood effects are more important than own effects. This means, the neighboring utilities played a crucial role indicating "contagion" of practices. [ABSTRACT FROM AUTHOR]

In this paper, we developed a simulator-optimizer model based on risk analysis to determine Waste Load Allocation (WLA). A new Fuzzy index as Fuzzy Risk Index (FRI) was linked with multi-objective optimization to minimize FRI for the environmental stakeholder and the total cost of sewage treatment for the polluting industries as the other collective stakeholder. Afterwards, the conflict was resolved with the help of Nash bargaining and bankruptcy approach (Constrained Equal Awards Rule). The model was run using quantitative/qualitative data for the KhoramAbad River. To check the efficiency of FRI, the process followed for WLA was reimplemented by the Monte Carlo simulation (MCS). A comparison between the two approaches revealed that the outcomes derived from Fuzzy arithmetic across all aspects, encompassing river qualitative simulation, nondominated curve, Nash bargaining's agreed point, and bankruptcy output, closely mirrored the results of MCS. The notable distinction lies in the drastic reduction of the model's execution time by a factor of 450. [ABSTRACT FROM AUTHOR]

Factor analysis is a multivariate statistical analysis technique that has become very popular in recent years. In the factor analysis model, the error covariance matrix is assumed to be the multivariate normal distribution, and outliers are likely to be accounted for. Various estimation methods were compared with Monte Carlo simulation for the factor analysis model. The performances of the estimation methods were evaluated based on the ratio of the total variance explained and the criterion fit values. Considering the MLE, PCA, WLS, and GLS methods for classical factor analysis and the MCD, M, and S methods for robust factor analysis, the ratio of total variance explained, and fit values decreased as the sample size increased. When the number of variables increases, the ratio of total variance explained, and fit values increase at different sample sizes. It can be said that the WLS and GLS methods are better than others for classical factor analysis and the MCD and M methods are better than others for robust factor analysis. [ABSTRACT FROM AUTHOR]

This paper presents new consistent methods for continuous-time Multiple-Input-Single-Output (MISO) Errors-In-Variables (EIV) systems by fractional models. The proposed idea is to use Higher-Order Statistics (HOS), such as fourth-order cumulants (foc), instead of noisy input and output measurements to obtain unbiased estimates. Firstly, all differentiation orders are assumed to be known a priori and linear coefficients are estimated. The developed estimator is based on minimizing the equation error and it is called fractional fourth-order based-least squares estimator ( f r a c - f o c - l s ). Secondly, the global commensurability of the fractional MISO system is considered. The f r a c - f o c - l s is combined with a non linear technique to estimate the global commensurate order along with linear coefficients. The developed algorithm is based on minimizing the output error and called fractional fourth-order cumulants based-least squares combined with global commensurate order optimization ( f r a c - f o c - g c o o l s ). The consistency of the developed estimators, in presence of high levels of noise corrupting both the input and output measurements, is assessed through a numerical example with the help of Monte Carlo simulations. [ABSTRACT FROM AUTHOR]

This paper proposes modified Karhunen–Loeve transform with total least square estimation of signal parameters using rotational in-variance technique (MKLT-TLS-ESPRIT) to approximate the low-frequency oscillatory modes. MKLT decreases the impact of highly correlated additive colored Gaussian noise (ACGN) from the signal by differentiating the correlation matrix w.r.t from the final time instance. A quantitative study of the suggested method with other estimation methods is used to evaluate the effectiveness of the proposed method. Monte Carlo simulations with 50,000 runs are conducted to test the robustness of the estimation scheme for MKLT-TLS-ESPRIT. The evaluation of the efficiency of the proposed method in real-time perspective, the two-area system, and New England sixty-eight bus test system has been considered. The analysis shows that the suggested methodology correctly measures the interarea modes and lowers their mean and standard deviation to a minimum value. [ABSTRACT FROM AUTHOR]

Localization is one of the essential problems in wireless sensor applications (WSNs). Most range‐free localization schemes for mobile WSNs are based on the Sequential Monte Carlo (SMC) algorithm. Multiple iterations, sample impoverishment and less sample diversity, leading to low localizing efficiency, are the most usual problems demanding to be solved in these SMC‐based methods. An improved localization scheme for mobile aquaculture WSNs based on the Improving Dynamic Population Monte Carlo Localization (I‐DPMCL) method is proposed. A population of probability density functions is proposed to approximate the unknown location distribution based on a set of observations through an iterative mixture importance sampling procedure, accompanied by node dynamic behaviours being analysed quantitatively or definitely. Threefold constrain rules are put forward in the I‐DPMCL scheme to decrease the iteration number and trade off iteration number and enough valid samples to obtain the optimum iteration number. Then, these localization behaviours, especial delay, are predicted based on the statistical point of view. Moreover, performance comparisons of I‐DPMCL with other SMC‐based schemes are also proposed. Simulation results show that delay of I‐DPMCL has some superiority to those of other schemes, and accuracy and energy consumption are improved in some cases of lower mobile velocity. [ABSTRACT FROM AUTHOR]

Optical code division multiple access (OCDMA) represents the development of optical communication. The advantages of OCDMA such as, asynchronous multiuser communication transmission, flexibility, ample bandwidth and scalability; have made this technique a better candidate to be proposed for next generation network on chip. In this paper, performance of on-chip OCDMA communication system is analyzed. Analytical techniques for estimating the performance of optical communication systems are difficult, complicated and no complete analytical treatment of the problem has been obtained before. Simulation techniques such as Monte Carlo (MC) are used to obtain reasonable estimates of these systems performance. For optical communications, Monte Carlo require excessively large sample sizes which makes it cumbersome in terms of physical resources, and are not practical for estimating very low values of error probabilities. Modified Monte-Carlo (Importance sampling/IS) method was used to reduce the number of simulation tests for estimating error probabilities for optical communications systems by modifying the probability density function of the on-chip noise process. Simulation results are presented and assessed in term of bit error rate (BER), showing the contribution of IS relatively to MC. [ABSTRACT FROM AUTHOR]

The widely used Prais–Winsten technique for estimating parameters of linear regression model with serial correlation is sensitive to outliers. In this paper, an alternative method based on Gini mean difference (GMD) is proposed. A Monte Carlo simulation is used to show that the Gini estimator is more robust than the general least squares one when the data are contaminated by outliers. [ABSTRACT FROM AUTHOR]

Using the Monte Carlo simulation method, this study analyzes the impacts on fit indices by the degree of nonnormality of variables, the sample size, and the choice of estimation method. To address these issues, we use the causal model of consumer involvement as elaborated by Mittal and Lee. Results of this study show that adjusted goodness of fit index (AGFI) and goodness of fit index (GFI) are subject to variation in sample size, and their use requires a sample size of at least 300 observations to be reliable. Comparative fit index (CFI) and root mean square error of approximation (RSMEA) are more reliable with the generalized least squares (GLS) compared with maximum likelihood estimation (MLE) method under different settings of sample size and degree of nonnormality. Finally, for the standardized root mean square residual (SRMR), it is recommended that it is used with the MLE method. This study provides prescriptions for the choice of fit indices and the requirements of sample size and estimation method to test the causal model of consumer involvement. The method used here can be extended to any model before fitting it to real data. It helps researchers to prevent conflictual results regarding the choice of fit indices. [ABSTRACT FROM AUTHOR]

Gibbs samplings is a Markov Chain Monte Carlo technique for estimating conditional probabilities in Bayesian networks. A major problem of Gibbs sampling is the dependency of the generated chain of samples. Thus the estimates are biased unless the initial value of the chain is drawn from the target distribution. One elegant method to overcome the initial bias is regenerative samplings. We reported elsewhere the "stationary minorization condition" that makes any Markov Chain Monte Carlo technique regenerative. In this paper, we show how this condition can be easily met in the simulations of any Bayesian network. [ABSTRACT FROM AUTHOR]

Nonresponse data are common in achievement tests or questionnaires. Chang et al. (Br J Math Stat Psychol 74:487–512, 2021) proposed an Item Response tree model, namely TR4, for modeling some potential mechanisms underlying nonresponses so that the estimates of parameters of interest would not be biased due to missing not at random (Rubin in Biometrika 63:581–592, 1976). TR4 has two notable degenerate cases, both with insightful practical meanings. When TR4 is fitted to data originated from some degenerate cases, there exist model identifiability issues so that the existing frequentist inference for the TR4 model is not suitable. In the current study, we propose a Bayesian estimation procedure that incorporates the Markov chain Monte Carlo technique for estimating the TR4 model. We conducted simulation studies to demonstrate the effectiveness of the Bayesian estimation procedure in solving the model unidentifiability issue. In addition, the TR4 model is further extended in the present study to effectively accommodate the complexity underlying some real data. The advantage of the extended models over TR4 is demonstrated in the real data analysis where we apply our method to the data of a geography test for college admission in Taiwan. [ABSTRACT FROM AUTHOR]

Sample size estimation is a necessary and crucial step in clinical trial research. Statistical requirements, limited patient availability and high financial risk of a clinical trial necessitate the proper calculation of this measure. The aim of this paper is to discuss the reasons why the estimation of the sample size is important and, based on the obtained results, to show how this process may be completed in selected cases. Stochastic simulations based on the Monte Carlo methods approach are applied. Therefore, new challenges facing this area of research are mentioned. [ABSTRACT FROM AUTHOR]

Offshore Probabilistic Tsunami Hazard Assessments (offshore PTHAs) provide large-scale analyses of earthquake-tsunami frequencies and uncertainties in the deep ocean, but do not provide high-resolution onshore tsunami hazard information as required for many risk-management applications. To understand the implications of an offshore PTHA for the onshore hazard at any site, in principle the tsunami inundation should be simulated locally for every earthquake scenario in the offshore PTHA. In practice this is rarely feasible due to the computational expense of inundation models, and the large number of scenarios in offshore PTHAs. Monte Carlo methods offer a practical and rigorous alternative for approximating the onshore hazard, using a random subset of scenarios. The resulting Monte Carlo errors can be quantified and controlled, enabling high-resolution onshore PTHAs to be implemented at a fraction of the computational cost. This study develops efficient Monte Carlo approaches for offshore-to-onshore PTHA. Modelled offshore PTHA wave heights are used to preferentially sample scenarios that have large offshore waves near an onshore site of interest. By appropriately weighting the scenarios, the Monte Carlo errors are reduced without introducing bias. The techniques are demonstrated in a high-resolution onshore PTHA for the island of Tongatapu in Tonga, using the 2018 Australian PTHA as the offshore PTHA, while considering only thrust earthquake sources on the Kermadec-Tonga trench. The efficiency improvements are equivalent to using 4–18 times more random scenarios, as compared with stratified-sampling by magnitude, which is commonly used for onshore PTHA. The greatest efficiency improvements are for rare, large tsunamis, and for calculations that represent epistemic uncertainties in the tsunami hazard. To facilitate the control of Monte Carlo errors in practical applications, this study also provides analytical techniques for estimating the errors both before and after inundation simulations are conducted. Before inundation simulation, this enables a proposed Monte Carlo sampling scheme to be checked, and potentially improved, at minimal computational cost. After inundation simulation, it enables the remaining Monte Carlo errors to be quantified at onshore sites, without additional inundation simulations. In combination these techniques enable offshore PTHAs to be rigorously transformed into onshore PTHAs, with quantification of epistemic uncertainties, while controlling Monte Carlo errors. [ABSTRACT FROM AUTHOR]

This paper studies profile estimation of a road. The prediction has been achieved using the Independent Component Analysis Method (ICA). The vehicle dynamic responses were calculated for different road profiles which were defined using an ISO norm. The robustness of this method was proven by implementing the stochastic Monte Carlo (MC) technique in the presence of inevitable uncertainty parameters simultaneously associated with the vehicle mass, spring stiffness and damping for different vehicle speeds and wind values. Convergence was assessed when comparing real profiles to simulated ones. The obtained results prove the efficiency of the ICA in estimating the profile variabilities under uncertainties [ABSTRACT FROM AUTHOR]

The susceptibility of masonry walls to out-of-plane failure under seismic loading presents a significant engineering concern. In adherence to contemporary limit state design philosophy and as mandated by performance-based design guidelines, it is crucial to accurately estimate statistics parameters such as the mean and variance of out-of-plane resistance. To achieve this, two deterministic models are often considered within the Monte Carlo simulation framework: design-code models, known for their computational efficiency but potential for significant model error, and mechanics-based finite element models, noted for their accuracy but computational intensity. Relying solely on either model for statistics estimation presents challenges due to their respective inherent limitations. This study introduces an improved strategy that synergizes the strengths of both models, resulting in enhanced statistics estimators for the out-of-plane resistance of masonry walls. The proposed methodology involves the use of the control variate method by integrating numerous design-code model evaluations to boost computational efficiency while incorporating a limited number of finite element model evaluations to ensure accuracy. The constructions of the proposed estimators follow rigorous optimization procedures to minimize associated errors and variances. Theoretical derivations are provided for essential elements in the estimator constructions, such as model evaluation numbers for finite element and design-code models and control variate coefficients. Moreover, the accuracy of the proposed estimators is compared with that of the crude Monte Carlo estimator. A key benefit of the proposed estimators is their unbiased nature, and their accuracy is not compromised by the discrepancies between the finite element model and the design-code model. To demonstrate the practicality of these estimators, two case studies are illustrated: one focusing on unreinforced masonry walls and the other on reinforced masonry walls. The results indicate that design-code model-based estimators exhibit large bias, and compared to the estimators that solely rely on the finite element model, the proposed estimators achieve higher accuracy given the same computational budget. • An improved strategy is proposed for estimating statistics of the OOP resistance of masonry walls. • The proposed methodology leverages a limited number of expensive finite element models and a large number of efficient design-code models. • The proposed mean and variance estimators are unbiased. • Two case studies are presented to show the performance of the proposed estimators. [ABSTRACT FROM AUTHOR]

The lightning performance of transmission lines is a criterion of utmost importance to be evaluated in transmission system reliability. In order to accurately estimate the expected number of shutdowns, it is imperative to account for the stochastic nature of the lightning phenomenon. In this sense, the most widely used technique to estimate these shutdowns is the Monte Carlo method (MCM). Although the MCM is a trustful method, it has a huge drawback in terms of computational burden. Therefore, this paper proposes the use of an alternative statistical technique, the Unscented Transform method (UTM). This method achieves an approximate non-linear mapping by employing a set of points (associated with input statistical data), which are deterministically selected and weighted. The set of these points and weights is then used to estimate the lightning overvoltage across insulator strings, which represents a significant reduction in the number of samples evaluated in the process in relation to the application from MCM. In this paper, the MCM and UTM methods are applied and compared in the lightning overvoltage evaluation, which is carried out with the help of the Alternative Transient Program (ATP). From the studies conducted, it was found that the application of UTM in place of MCM allowed for significant computational gains while maintaining satisfactory levels of accuracy in the estimation of indicators. • Unscented Transform applied to transmission line lightning performance estimation. • Monte Carlo applied to transmission line lightning performance estimation. • Accelerating the assessment process of transmission line lightning performance. • Monte Carlo and Unscented Transform performance in lightning-related study. [ABSTRACT FROM AUTHOR]

This paper revisits classical work of Rauch et al. (1965) and develops a novel statistical method for maximum likelihood (ML) recursive state estimation in general state–space models. The new method is based on statistical estimation theory for incomplete information, which has been well developed primarily for ML parameter estimation (Dempster et al., 1977). Distributional identities for the posterior score function and information matrix of state are established. Using these identities, a fast convergent EM-gradient algorithm is proposed, extending the Lange (1995) algorithm for ML recursive state estimation. It revisits and provides an improvement to the EM-algorithm of Ramadan and Bitmead (2022). An explicit form of the information matrix is developed to provide empirical estimates of the standard errors. Sequential Monte Carlo method is used for the valuation of the score function, information and posterior covariance matrices. Some numerical examples are discussed to exemplify the main results. [ABSTRACT FROM AUTHOR]

We propose to apply the importance sampling and the antithetic variates statistical techniques to estimate steady-state quantities of an Hidden Markov chain (HMM) of which certain emissions are rarely generated. Compared to standard Monte Carlo simulation, the use of these techniques, allow a significant reduction in simulation time. Numerical Monte Carlo examples are studied to show the usefulness and efficiency of the proposed approach. [ABSTRACT FROM AUTHOR]

We consider batch size selection for a general class of multivariate batch means variance estimators, which are computationally viable for high-dimensional Markov chain Monte Carlo simulations. We derive the asymptotic mean squared error for this class of estimators. Further, we propose a parametric technique for estimating optimal batch sizes and discuss practical issues regarding the estimating process. Vector auto-regressive, Bayesian logistic regression, and Bayesian dynamic space-time examples illustrate the quality of the estimation procedure where the proposed optimal batch sizes outperform current batch size selection methods. [ABSTRACT FROM AUTHOR]

In Statistics of Extremes, the estimation of the extreme value index is an essential requirement for further tail inference. In this work, we deal with the estimation of a strictly positive extreme value index from a model with a Pareto‐type right tail. Under this framework, we propose a new class of weighted Hill estimators, parameterized with a tuning parameter a. We derive their non‐degenerate asymptotic behavior and analyze the influence of the tuning parameter in such result. Their finite sample performance is analyzed through a Monte Carlo simulation study. A comparison with other important extreme value index estimators from the literature is also provided. [ABSTRACT FROM AUTHOR]

Monte Carlo integration is a technique for numerically estimating a definite integral by stochastically sampling its integrand. These samples can be averaged to make an improved estimate, and the progressive estimates form a sequence that converges to the integral value on the limit. Unfortunately, the sequence of Monte Carlo estimates converges at a rate of O(), where n denotes the sample count, effectively slowing down as more samples are drawn. To overcome this, we can apply sequence transformation, which transforms one converging sequence into another with the goal of accelerating the rate of convergence. However, analytically finding such a transformation for Monte Carlo estimates can be challenging, due to both the stochastic nature of the sequence, and the complexity of the integrand. In this paper, we propose to leverage neural networks to learn sequence transformations that improve the convergence of the progressive estimates of Monte Carlo integration. We demonstrate the effectiveness of our method on several canonical 1D integration problems as well as applications in light transport simulation. [ABSTRACT FROM AUTHOR]

Evaluating the response statistics of nonlinear structures constitutes a key issue in engineering design. Hereby, the Monte Carlo method has proven useful, although the computational cost turns out to be considerably high. In particular, around the design point of the system near structural failure, a reliable estimation of the statistics is unfeasible for complex high‐dimensional systems. Thus, in this paper, we develop a machine‐learning‐enhanced Monte Carlo simulation strategy for nonlinear behaving engineering structures. A neural network learns the response behavior of the structure subjected to an initial nonstationary ground excitation subset, which is generated based on the spectral properties of a chosen ground acceleration record. Then using the superior computational efficiency of the neural network, it is possible to predict the response statistics of the full sample set, which is considerably larger than the initial training sample set. To ensure a reliable neural network response prediction in case of rare events near structural failure, we propose to extend the initial training sample set increasing the variance of the intensity. We show that using this extended initial sample set enables a reliable prediction of the response statistics, even in the tail end of the distribution. HIGHLIGHTS A new Monte Carlo method is developed that provides the response statistics of a nonlinear system in the tail end of the distribution.A nonstationary filter is applied to a Gaussian white noise to generate realistic artificial earthquake records.An extended training strategy using neural networks is proposed to improve the reliability of the method in the tail end of the distribution.The new strategy reveals a significant speedup as well as a prediction of the response statistics in the tail end with high confidence. [ABSTRACT FROM AUTHOR]

In this article, we propose Liu-type shrinkage estimators for the zero-inflated Poisson regression (ZIPR) model in the presence of multicollinearity. Our new approach is a remedy to the problem of inflated variances for the ML estimation technique—which is a standard approach to estimate these types of count data models. When the data are in the form of non-negative integers with a surplus of zeros it induces overdispersion in the dependent variable. Considerable multicollinearity is frequently observed, but usually disregarded, for these types of data sets. Based on a Monte Carlo study we illustrate that our proposed estimators exhibit better MSE and MAE than the usual ML estimator and some other Liu estimators in the presence of multicollinearity. To demonstrate the advantages and the empirical relevance of our improved estimators, maternal death data are analyzed and the results illustrate similar benefits as is demonstrated in our simulation study. [ABSTRACT FROM AUTHOR]

Cyclones endanger life and cause great financial impact on interior and coastal regions through the destruction of buildings and land. Governments need to have a way of estimating the chance of different regions being impacted by a cyclone. The goal of this paper is to use big data to better predict future cyclone impacts. Large cyclone data sets from the CMA Tropical Cyclone Data Center are used in the analysis. By using big data analysis techniques, long-term patterns in cyclone locations and size can be revealed. The Hausdorff distance is used to determine overall changes in cyclone positions decade by decade. Monte Carlo techniques estimate the probability of a region being impacted by a cyclone any given year. This is done by creating random data sets that mimic long-term patterns in cyclone position and radii. It will be shown that any region can be assigned a probability of cyclone impact purely on large historical data sets. [ABSTRACT FROM AUTHOR]

The second virial coefficient, A2, for trivial-ring polymers in dilute condition was estimated from a Metropolis Monte Carlo (MC) simulation, and the temperature dependence of A2 has been discussed with their Flory's scaling exponent, v, in Rg ∝ Nv, where Rg is radius of gyration of a polymer molecule. A limited but not too small number of polymer molecules were employed in the simulation, and the A2 values at various temperatures were calculated from the molecular density fluctuation in the solution. In the simulation, the topology of ring polymers was kept, since chain crossing was prohibited. The excluded volume effects can be screened by the attractive force between segments, which depends on the temperature, Tα, defined in the Metropolis MC method. Linear and trivial-ring polymers have the v value of 1/2 at Tα = 10.605 and 10.504. At Tα = 10.504, the excluded volume effects are screened by the attractive force generated between segments in a ring polymer, but the A2 value for ring polymers is positive. Thus, the temperature at A2 = 0 for a ring polymer is lower than that at v = 1/2, and this fact can be explained with the following two reasons. (a) Rg value for a ring polymer is much smaller than that for a linear polymer at the same temperature and molecular weight, where interpenetration of a ring polymer chain into neighboring chains is apparently less than a linear chain. (b) The conformation of trivial rings can be statistically described as a closed random walk at v = 1/2, but their topologies are kept, being produced topological constraints, which strongly relate not only to the long-distance interaction between segments in a molecule but also the inter-molecular interaction. [ABSTRACT FROM AUTHOR]

We present high-sensitivity, wide-band observations (704–4032 MHz) of the young to middle-aged radio pulsar J1452–6036, taken at multiple epochs before and, serendipitously, shortly after a glitch occurred on 2019 April 27. We obtained the data using the new ultra-wide-bandwidth low-frequency (UWL) receiver at the Parkes radio telescope, and we used Markov chain Monte Carlo techniques to estimate the glitch parameters robustly. The data from our third observing session began 3 h after the best-fitting glitch epoch, which we constrained to within ∼4 min. The glitch was of intermediate size, with a fractional change in spin frequency of 270.52(3) × 10−9. We measured no significant change in spin-down rate and found no evidence for rapidly decaying glitch components. We systematically investigated whether the glitch affected any radiative parameters of the pulsar and found that its spectral index, spectral shape, polarization fractions, and rotation measure stayed constant within the uncertainties across the glitch epoch. However, its pulse-averaged flux density increased significantly by about 10 per cent in the post-glitch epoch and decayed slightly before our fourth observation a day later. We show that the increase was unlikely caused by calibration issues. While we cannot exclude that it was due to refractive interstellar scintillation, it is hard to reconcile with refractive effects. The chance coincidence probability of the flux density increase and the glitch event is low. Finally, we present the evolution of the pulsar's pulse profile across the band. The morphology of its polarimetric pulse profile stayed unaffected to a precision of better than 2 per cent. [ABSTRACT FROM AUTHOR]

Turning movements are one of the key inputs required for several traffic studies. Several methods have been developed to measure them. However, present techniques have high operational or capital costs, which motivate researchers to develop new techniques to estimate turning movements. However, there is neither a flexible technique available to make best use of different available information types, nor a framework that supports deciding additional data to achieve a target accuracy. This paper proposes a new methodology using all available data to identify the subspace containing all solutions and determine its centroid; thus, providing the most realistic and non-extreme solution. In addition, a framework, including scenarios with different data combinations, is developed with capability to evaluate the proposed solution and then locate further measurements to achieve the target accuracy. The framework is validated using a considerable set of intersections at Edmonton city, Canada. The results show that the proposed framework can achieve the target accuracy with minimum field measurements saving time, effort and cost. [ABSTRACT FROM AUTHOR]

Few studies have been conducted on the precision estimation of weighted total least squares (WTLS) by using the approximate function probability distribution method. And the existing Monte Carlo method needs to simulate a lot, the amount of calculation is large and the results obtained are uncertain. In order to further improve the total least squares precision estimation theory, this paper introduces the Jackknife method into Geomatics data processing. Combining the Jackknife method and WTLS method, the delete-1 Jackknife method and delete-d Jackknife method are proposed. The biases and standard deviations or covariance of parameter estimations are calculated by these proposed methods. And the specific steps of the precision estimation of these two methods are given. Applying these methods to the linear regression model and the coordinate transformation model, and comparing with the approximate function method and the Monte Carlo method, we can see that the Jackknife methods for precision estimation can obtain more stable and reasonable precision results and are very adaptive. In order to get more reasonable precision results, the Jackknife method does spend much more time over total least squares when the amount of the observed data is large. But compared with Monte Carlo method, it can reduce the amount of calculation and improve the computational efficiency. The method in this paper could provide an idea for further study on the precision estimation for total least squares. [ABSTRACT FROM AUTHOR]

Consider a fractional Brownian motion (fBM) B H = { B H (t) : t ∈ [ 0 , 1 ] } with Hurst index H ∈ (0 , 1) . We construct a probability space supporting both BH and a fully simulatable process B ^ ∈ H such that sup t ∈ [ 0 , 1 ] | B H (t) − B ^ ∈ H (t) | ≤ ∈ with probability one for any user-specified error bound ∈ > 0. When H > 1 / 2 , we further enhance our error guarantee to the α-Hölder norm for any α ∈ (1 / 2 , H) . This enables us to extend our algorithm to the simulation of fBM-driven stochastic differential equations Y = { Y (t) : t ∈ [ 0 , 1 ] } . Under mild regularity conditions on the drift and diffusion coefficients of Y, we construct a probability space supporting both Y and a fully simulatable process Y ^ ∈ such that sup t ∈ [ 0 , 1 ] | Y (t) − Y ^ ∈ (t) | ≤ ∈ with probability one. Our algorithms enjoy the tolerance-enforcement feature, under which the error bounds can be updated sequentially in an efficient way. Thus, the algorithms can be readily combined with other advanced simulation techniques to estimate the expectations of functionals of fBMs efficiently. [ABSTRACT FROM AUTHOR]

With small to modest sample sizes and complex models, maximum likelihood (ML) estimation of confirmatory factor analysis (CFA) models can show serious estimation problems such as non-convergence or parameter estimates outside the admissible parameter space. In this article, we distinguish different Bayesian estimators that can be used to stabilize the parameter estimates of a CFA: the mode of the joint posterior distribution that is obtained from penalized maximum likelihood (PML) estimation, and the mean (EAP), median (Med), or mode (MAP) of the marginal posterior distribution that are calculated by using Markov Chain Monte Carlo (MCMC) methods. In two simulation studies, we evaluated the performance of the Bayesian estimators from a frequentist point of view. The results show that the EAP produced more accurate estimates of the latent correlation in many conditions and outperformed the other Bayesian estimators in terms of root mean squared error (RMSE). We also argue that it is often advantageous to choose a parameterization in which the main parameters of interest are bounded, and we suggest the four-parameter beta distribution as a prior distribution for loadings and correlations. Using simulated data, we show that selecting weakly informative four-parameter beta priors can further stabilize parameter estimates, even in cases when the priors were mildly misspecified. Finally, we derive recommendations and propose directions for further research. [ABSTRACT FROM AUTHOR]

We present entropy balancing – a relatively new technique for estimating treatment effects, which has been under-utilised in the applied biomedical literature. Our objective is to share our experiences learned from using entropy balancing in nonexperimental studies, via Monte Carlo simulations and two empirical examples. We used the inverse probability of treatment weighting method for benchmarking the performance of entropy balancing. Entropy balancing had remarkably superior performance in terms of covariate balance and efficient estimation of treatment effects. Entropy balancing does not require extensive tweaking of the propensity score specification to achieve the optimal covariate balance. Instead, it directly incorporates covariate balance into the weight function that is applied to the sample units. Notably, the excellent performance of entropy balancing is not only on the first moment (mean) but also on higher-order moments. However, we also highlighted the situations where entropy balancing may fail or not have optimal performance. Entropy balancing merits more widespread adoption in biomedical research. [ABSTRACT FROM AUTHOR]

The folding properties of a protein whose native structure contains a 52 knot are investigated by means of extensive Monte Carlo simulations of a simple lattice model and compared with those of a 31 knot. A 52 knot embedded in the native structure enhances the kinetic stability of the carrier lattice protein in a way that is clearly more pronounced than in the case of the 31 knot. However, this happens at the expense of a severe loss in folding efficiency, an observation that is consistent with the relative abundance of 31 and 52 knots in the Protein Data Bank. The folding mechanism of the 52 knot shares with that of the 31 knot the occurrence of a threading movement of the chain terminus that lays closer to the knotted core. However, co-concomitant knotting and folding in the 52 knot occurs with negligible probability, in sharp contrast to what is observed for the 31 knot. The study of several single point mutations highlights the importance in the folding of knotted proteins of the so-called structural mutations (i.e., energetic perturbations of native interactions between residues that are critical for knotting but not for folding). On the other hand, the present study predicts that mutations that perturb the folding transition state may significantly enhance the kinetic stability of knotted proteins provided they involve residues located within the knotted core. [ABSTRACT FROM AUTHOR]

The charge carrier drift mobility in disordered semiconductors is commonly graphically extracted from time-of-flight (TOF) photocurrent transients yielding a single transit time. However, the term transit time is ambiguously defined and fails to deliver a mobility in terms of a statistical average. Here, we introduce an advanced computational procedure to evaluate TOF transients, which allows to extract the whole distribution of transit times and mobilities from the photocurrent transient, instead of a single value. This method, extending the work of Scott et al. (Phys. Rev. B 46, 8603 (1992)), is applicable to disordered systems with a Gaussian density of states and its accuracy is validated using one-dimensional Monte Carlo simulations. We demonstrate the superiority of this new approach by comparing it to the common geometrical analysis of hole TOF transients measured on poly(3-hexyl thiophene-2,5-diyl). The extracted distributions provide access to a very detailed and accurate analysis of the charge carrier transport. For instance, not only the mobility given by the mean transit time but also the mean mobility can be calculated. Whereas the latter determines the macroscopic photocurrent, the former is relevant for an accurate determination of the energetic disorder parameter σ within the Gaussian disorder model. σ derived by using the common geometrical method is, as we show, underestimated instead. [ABSTRACT FROM AUTHOR]

The mutual entropic depletion force felt by two solute "big" hard spheres immersed in a binary mixture solvent of nonadditive "small" hard spheres is calculated as a function of the surface-to-surface distance by means of canonical Monte Carlo simulations and through a recently proposed rational-function approximation [R. Fantoni and A. Santos, Phys. Rev. E 84, 041201 (2011)]. Four representative scenarios are investigated: symmetric solute particles and the limit where one of the two solute spheres becomes a planar hard wall, in both cases with symmetric and asymmetric solvents. In all cases, the influence on the depletion force due to the nonadditivity in the solvent is determined in the mixed state. Comparison between results from the theoretical approximation and from the simulation shows a good agreement for surface-to-surface distances greater than the smallest solvent diameter. [ABSTRACT FROM AUTHOR]

This paper aims at determining sustained reaction fluxes in a nonlinear chemical system driven in a nonequilibrium steady state. The method relies on the computation of cross-correlation functions for the internal fluctuations of chemical species concentrations. By employing Langevin-type equations, we derive approximate analytical formulas for the cross-correlation functions associated with nonlinear dynamics. Kinetic Monte Carlo simulations of the chemical master equation are performed in order to check the validity of the Langevin equations for a bistable chemical system. The two approaches are found in excellent agreement, except for critical parameter values where the bifurcation between monostability and bistability occurs. From the theoretical point of view, the results imply that the behavior of cross-correlation functions cannot be exploited to measure sustained reaction fluxes in a specific nonlinear system without the prior knowledge of the associated chemical mechanism and the rate constants. [ABSTRACT FROM AUTHOR]

In this work, the size-exclusion partitioning of neutral solutes in crosslinked polymer networks has been studied through Monte Carlo simulations. Two models that provide user-friendly expressions to predict the partition coefficient have been tested over a wide range of volume fractions: Ogston's model (especially devised for fibrous media) and the pore model. The effects of crosslinking and bond stiffness have also been analyzed. Our results suggest that the fiber model can acceptably account for size-exclusion effects in crosslinked gels. Its predictions are good for large solutes if the fiber diameter is assumed to be the effective monomer diameter. For solutes sizes comparable to the monomer dimensions, a smaller fiber diameter must be used. Regarding the pore model, the partition coefficient is poorly predicted when the pore diameter is estimated as the distance between adjacent crosslinker molecules. On the other hand, our results prove that the pore sizes obtained from the pore model by fitting partitioning data of swollen gels are overestimated. [ABSTRACT FROM AUTHOR]

We develop statistical mechanical models amenable to analytic treatment for the dissociative adsorption of O2 at hollow sites on fcc(100) metal surfaces. The models incorporate exclusion of nearest-neighbor pairs of adsorbed O. However, corresponding simple site-blocking models, where adsorption requires a large ensemble of available sites, exhibit an anomalously fast initial decrease in sticking. Thus, in addition to blocking, our models also incorporate more facile adsorption via orientational steering and funneling dynamics (features supported by ab initio Molecular Dynamics studies). Behavior for equilibrated adlayers is distinct from those with finite adspecies mobility. We focus on the low-temperature limited-mobility regime where analysis of the associated master equations readily produces exact results for both short- and long-time behavior. Kinetic Monte Carlo simulation is also utilized to provide a more complete picture of behavior. These models capture both the initial decrease and the saturation of the experimentally observed sticking versus coverage, as well as features of non-equilibrium adlayer ordering as assessed by surface-sensitive diffraction. [ABSTRACT FROM AUTHOR]

Accurate values of the free energies of C60 and C70 fullerene crystals are obtained using expanded ensemble method and acceptance ratio method combined with the Einstein-molecule approach. Both simulation methods, when tested for Lennard-Jones crystals, give accurate results of the free energy differing from each other in the fifth significant digit. The solid-solid phase transition temperature of C60 crystal is determined from free energy profiles, and found to be 260 K, which is in good agreement with experiment. For C70 crystal, using the potential model of Sprik et al. [Phys. Rev. Lett. 69, 1660 (1992)], low-temperature solid-solid phase transition temperature is found to be 160K determined from the free energy profiles. Whereas this is somewhat lower than the experimental value, it is in agreement with conventional molecular simulations, which validates the methodological consistency of the present simulation method. From the calculations of the free energies of C60 and C70 crystals, we note the significance of symmetry number for crystal phase needed to properly account for the indistinguishability of orientationally disordered states. [ABSTRACT FROM AUTHOR]

In this contribution, we develop a coarse-graining methodology for mapping specific block copolymer systems to bead-spring particle-based models. We map the constituent Kuhn segments to Lennard-Jones particles, and establish a semi-empirical correlation between the experimentally determined Flory-Huggins parameter χ and the interaction of the model potential. For these purposes, we have performed an extensive set of isobaric-isothermal Monte Carlo simulations of binary mixtures of Lennard-Jones particles with the same size but with asymmetric energetic parameters. The phase behavior of these monomeric mixtures is then extended to chains with finite sizes through theoretical considerations. Such a top-down coarse-graining approach is important from a computational point of view, since many characteristic features of block copolymer systems are on time and length scales which are still inaccessible through fully atomistic simulations. We demonstrate the applicability of our method for generating parameters by reproducing the morphology diagram of a specific diblock copolymer, namely, poly(styrene-b-methyl methacrylate), which has been extensively studied in experiments. [ABSTRACT FROM AUTHOR]

Synchrotron X-ray diffraction measurements have been conducted on liquid phosphorus trichloride, tribromide, and triiodide. Molecular Dynamics simulations for these molecular liquids were performed with a dual purpose: (1) to establish whether existing intermolecular potential functions can provide a picture that is consistent with diffraction data and (2) to generate reliable starting configurations for subsequent Reverse Monte Carlo modelling. Structural models (i.e., sets of coordinates of thousands of atoms) that were fully consistent with experimental diffraction information, within errors, have been prepared by means of the Reverse Monte Carlo method. Comparison with reference systems, generated by hard sphere-like Monte Carlo simulations, was also carried out to demonstrate the extent to which simple space filling effects determine the structure of the liquids (and thus, also estimating the information content of measured data). Total scattering structure factors, partial radial distribution functions and orientational correlations as a function of distances between the molecular centres have been calculated from the models. In general, more or less antiparallel arrangements of the primary molecular axes that are found to be the most favourable orientation of two neighbouring molecules. In liquid PBr3 electrostatic interactions seem to play a more important role in determining intermolecular correlations than in the other two liquids; molecular arrangements in both PCl3 and PI3 are largely driven by steric effects. [ABSTRACT FROM AUTHOR]

Potential energy functions including many-body polarization are in widespread use in simulations of aqueous and biological systems, metal-organics, molecular clusters, and other systems where electronically induced redistribution of charge among local atomic sites is of importance. The polarization interactions, treated here via the methods of Thole and Applequist, while long-ranged, can be computed for moderate-sized periodic systems with extremely high accuracy by extending Ewald summation to the induced fields as demonstrated by Nymand, Sala, and others. These full Ewald polarization calculations, however, are expensive and often limited to very small systems, particularly in Monte Carlo simulations, which may require energy evaluation over several hundred-thousand configurations. For such situations, it shall be shown that sufficiently accurate computation of the polarization energy can be produced in a fraction of the central processing unit (CPU) time by neglecting the long-range extension to the induced fields while applying the long-range treatments of Ewald or Wolf to the static fields; these methods, denoted Ewald E-Static and Wolf E-Static (WES), respectively, provide an effective means to obtain polarization energies for intermediate and large systems including those with several thousand polarizable sites in a fraction of the CPU time. Furthermore, we shall demonstrate a means to optimize the damping for WES calculations via extrapolation from smaller trial systems. [ABSTRACT FROM AUTHOR]