Monte Carlo Technique Research Articles

Weak convergence of tamed exponential integrators for stochastic differential equations

We prove weak convergence of order one for a class of exponential based integrators for SDEs with non-globally Lipschitz drift. Our analysis covers tamed versions of Geometric Brownian Motion (GBM) based methods as well as the standard exponential schemes. The numerical performance of both the GBM and exponential tamed methods through four different multi-level Monte Carlo techniques are compared. We observe that for linear noise the standard exponential tamed method requires severe restrictions on the step size unlike the GBM tamed method.

Estimation of multi-stress strength reliability under progressive first failure censoring using generalized inverted exponential distribution

We investigate the estimation of multi-stress strength reliability under progressively first failure censoring for the generalized inverted exponential distribution using classical and Bayesian approaches. Classical estimation employs maximum likelihood estimators with the Expectation-Maximization algorithm to handle incomplete data. Bayesian estimation utilizes Markov Chain Monte Carlo (MCMC) techniques and Tierney-Kadane's approximation to approximate the posterior distribution. Furthermore, A generalized entropy loss function is employed to measure estimation accuracy. Finally, Validation is provided through Monte Carlo simulations and real-world applications. Findings highlight the robustness and accuracy of Bayesian methods, particularly with informative priors, and underscore the strengths of MCMC techniques and Bayesian Credible Intervals in specific aspects of estimation.

Inference on Weibull inverted exponential distribution under progressive first-failure censoring with constant-stress partially accelerated life test

Accelerated life tests (ALTs) play a pivotal role in life testing experiments as they significantly reduce costs and testing time. Hence, this paper investigates the statistical inference issue for the Weibull inverted exponential distribution (WIED) under the progressive first-failure censoring (PFFC) data with the constant-stress partially ALT (CSPALT) under progressive first-failure censoring (PFFC) data for Weibull inverted exponential distribution (WIED). For classical inference, maximum likelihood (ML) estimates for both the parameters and the acceleration factor are derived. Making use of the Fisher information matrix (FIM), asymptotic confidence intervals (ACIs) are constructed for all parameters. Besides, two parametric bootstrap techniques are implemented. For Bayesian inference based on a proposed technique for eliciting the hyperparameters, the Markov chain Monte Carlo (MCMC) technique is provided to acquire Bayesian estimates. In this context, the Bayesian estimates are obtained under symmetric and asymmetric loss functions, and the corresponding credible intervals (CRIs) are constructed. A simulation study is carried out to assay the performance of the ML, bootstrap, and Bayesian estimates, as well as to compare the performance of the corresponding confidence intervals (CIs). Finally, real-life engineering data is analyzed for illustrative purposes.

A Bayesian Hierarchical Model to create synthetic Power Distribution Systems

The growing complexity of Power Distribution Systems, driven by distributed generation, renewable energy integration, and increasing demand, has led to restricted access to DS data due to security and privacy concerns. This study addresses limited data accessibility by proposing a hybrid approach for crafting synthetic power distribution systems tailored for power system analysis and control. Synthetic power distribution systems refer to artificially generated models that faithfully replicate real-world DS features while upholding security and privacy constraints. This innovative methodology merges a Bayesian Hierarchical Model with Markov Chain Monte Carlo techniques, utilizing georeferenced data to capture intricate system dependencies, feeder configurations, switch statuses, and load node distributions. Leveraging OpenStreetMaps for DS topology, the approach incorporates expert knowledge and real-world data. Results highlight the methodology’s ability to evaluate credible intervals for parameters, facilitating a probabilistic assessment of uncertainties and enhancing decision support in power system analysis and control. Findings affirm the hybrid approach’s efficacy in generating realistic synthetic DSs, bridging the gap between statistical and georeferenced methodologies for advanced power system analysis and control. The capacity to generate synthetic DSs provides valuable insights into power system dynamics, addressing security, privacy, and data accessibility concerns for a more informed decision-making process.

A comprehensive assessment of a prototype high ratio antiscatter grid in interventional cardiology using experimental measurements and Monte Carlo simulations

Objective. To assess the performance of a new antiscatter grid design in interventional cardiology for image quality improvement and dose reduction using experimental measurements and Monte Carlo (MC) simulation. Approach. Experimental measurements were performed on an angiography system, using a multi-layered tissue simulating composite phantom made from of poly(methyl methacrylate), aluminium and expanded polystyrene (2/0.2/0.7 cm). The total phantom thickness ranged from 20.3 cm to 40.6 cm. Four conditions were compared; (A) 105 cm source-image receptor distance (SID) without grid, (B i) 105 cm SID with grid ratio (r) and strip density (N) (r15N80), (B ii) 120 cm SID without grid, and (Biii) 120 cm SID with high ratio grid (r29N80). The system efficiency (η), defined by the signal-to-noise ratio, was compared from the B conditions against case A. These conditions were also simulated with MC techniques, allowing additional phantom compositions to be explored. Weighted image quality improvement factor (ηw (u)) was studied experimentally at a specific spatial frequency due to the SID change. Images were simulated with an anthropomorphic chest phantom for the different conditions, and the system efficiency was compared for the different anatomical regions. Main results. Good agreement was found between the η and ηw (u) methods using both measured and simulated data, with average relative differences between 2%–11%. Case B iii provided higher η values compared to A, and B i for thicknesses larger than 20.3 cm. In addition, case B iii also provided higher η values for high attenuating areas in the anthropomorphic phantom, such as behind the spine. Significance. The new antiscatter grid design provided higher system efficiency compared to the standard grid for the parameters explored in this work.

Research on three-dimensional wake model of horizontal axis wind turbine based on Weibull function

In wind turbine wake models, Gaussian models depend on multidimensional integration to ascertain the distribution of wake velocity deficits. These integrations, which often involve complex boundary conditions, significantly enhance the complexity of mathematical computations. Due to the difficulty of obtaining analytical solutions, numerical integration methods such as Monte Carlo or other numerical integration techniques are commonly employed. This study presents a three-dimensional wake model (3DJW) for horizontal axis wind turbines, utilizing the Weibull function to simplify wake deficit characterization instead of traditional Gaussian distribution methods. The 3DJW model considers wind shear effects and mass conservation laws to enhance predictions of vertical wake velocities. By integrating incoming wind conditions and turbine parameters, the model efficiently computes downstream wake velocities, improving computational efficiency. To enhance predictions in the ultra-far wake region, an improved three-dimensional Weibull wake model is proposed using the exponential fitting method. Validation through wind tunnel experiments and wind farm data demonstrates the model's accuracy in predicting wake deficits at the hub height, with relative errors in horizontal and vertical profiles mostly within 5% and 3%, respectively. The proposed model enables accurate and rapid calculation of wake velocities at any spatial location downstream, facilitating enhanced energy utilization and reduced costs.

Refining Credit Risk Analysis- Integrating Bayesian MCMC with Hamiltonian Monte Carlo

The accurate prediction of loan defaults is paramount for financial institutions to enhance decision-making processes, optimize loan approval rates, and mitigate associated risks. This study develops a predictive model utilizing Bayesian Markov Chain Monte Carlo (MCMC) techniques to forecast potential loan defaults. Employing a comprehensive dataset of 255,000 borrower profiles, which include detailed borrower characteristics and loan information, the model integrates advanced statistical methods to assess and interpret the factors influencing loan defaults. The Bayesian framework allows for robust uncertainty quantification and model complexity management, making it particularly suitable for the nuanced nature of credit risk assessment. Results from the model demonstrate a compelling accuracy rate, substantially aligning with industry benchmarks while providing deeper insights into the probability of default as influenced by various borrower attributes. This research underscores the efficacy of Bayesian MCMC modelling in financial risk management and offers a scalable approach for financial institutions aiming to refine their credit evaluation strategies.

Evidence for Spatially Distinct Galactic Dust Populations

We present an implementation of a Bayesian mixture model using Hamiltonian Monte Carlo techniques to search for the spatial separation of Galactic dust populations. Utilizing intensity measurements from the Planck High Frequency Instrument, we apply this model to high-latitude Galactic dust emission. Our analysis reveals a strong preference for a spatially varying two-population dust model over a one-population dust model, when the latter must capture the total variance in the sky. Each dust population is well characterized by a single-component spectral energy distribution (SED) and accommodates small variations. These populations could signify two distinct components or may originate from a one-component model with different temperatures resulting in different SED scalings. While no spatial information is built into the likelihood, our investigation unveils large-scale spatially coherent structures with high significance, pointing to a physical origin for the observed spatial variation. These results are robust to our choice of likelihood and input data. Furthermore, this spatially varying two-population model is the most favored from Bayesian evidence calculations. Incorporating IRAS 100 μm to constrain the Wein side of the blackbody function, we find the dust populations differ at the 2.5σ level in the spectral index (β d ) versus temperature (T d ) plane. The presence of multiple dust populations has implications for component separation techniques frequently employed in the recovery of the cosmic microwave background.

Data analysis with applications in physics and engineering using XLindley model with improved adaptive Type-II progressively censored samples

Recently, a novel improved adaptive Type-II progressive censoring strategy has been suggested in order to obtain adequate data from trials that require a lengthy amount of time. Considering this scheme, this paper focuses on various classical and Bayesian estimation challenges for parameter and some reliability metrics for the XLindley distribution. Two classical estimation methods are considered from the classical perspective to get the point and interval estimations of the model parameter as well as reliability and hazard rate functions. In addition to the usual approaches, the Bayesian methodology is looked at by leveraging the squared error loss function and the Markov chain Monte Carlo technique. The Bayes point and credible intervals are obtained based on two forms of the posterior distribution. A simulation examination is implemented adopting multiple circumstances to distinguish between the conventional and Bayesian estimations. The simulation results demonstrate that the Bayesian approach using the likelihood function is superior for estimating the model parameter when compared with the other methods. In contrast, when estimating reliability metrics, it is advisable to utilize the Bayesian method with the spacings function. Two real-world data sets are analyzed to integrate the proposed approaches into practice, and the ideal progressive censoring strategy is chosen using some optimality criteria.

Forecast of Joint Analysis of Cosmic Shear and Supernovae Magnification from the CSST and LSST

Cosmic shear and cosmic magnification reflect the same gravitational lensing field. Each of these two probes are affected by different systematics. We study the auto- and cross-correlations of cosmic shear from the China Space Survey Telescope and cosmic magnification of supernovae from the Large Synoptic Survey Telescope. We want to determine to what extent, by adding the magnification data, we can remove the systematic bias in cosmic shear measurements. We generate mock shear/magnification maps based on the correlation between different tomographic bins. After obtaining the corrected power spectra, we adopt the Markov Chain Monte Carlo technique to fit the theoretical models and investigate the constraints on the cosmological and nuisance parameters. We find that, with only the cosmic shear data, there are 1σ biases in the σ 8 and intrinsic alignment model parameters. By adding the magnification data, we are able to remove these biases perfectly.

The Nonsingular Estimator for Exoplanet Orbits: An Unscented Batch Estimation Method for Direct Imaging Measurements

We present a new method for fitting exoplanet orbits to direct astrometric measurements, using nonlinear batch estimation and nonsingular orbital elements. Our estimation technique is based on the unscented transform, which approximates probability distributions using finite, deterministic sets of weighted sample points. Furthermore, we use Gaussian mixtures to account for the strong nonlinearities in the measurement model. As a fitting basis, we use a set of orbital elements developed specifically for directly observed exoplanets, combining features of the Thiele–Innes constants and the Cohen–Hubbard nonsingular elements. We validate the new method using simulated exoplanet orbits, and we demonstrate its use with real exoplanet data. Compared to state-of-the-art Markov Chain Monte Carlo and Bayesian rejection sampling techniques, the new method is found to give orbit estimates of comparable or higher accuracy but with much faster execution.

Sampling and active learning methods for network reliability estimation using K-terminal spanning tree

Network reliability analysis remains a challenge due to the increasing size and complexity of networks. This paper presents a novel sampling method and an active learning method for efficient and accurate network reliability estimation under node failure and edge failure scenarios. The proposed sampling method adopts Monte Carlo technique to sample component lifetimes and the K-terminal spanning tree algorithm to accelerate structure function computation. Unlike existing methods that compute only one structure function value per sample, our method generates multiple component state vectors and corresponding structure function values from each sample. Network reliability is estimated based on survival signatures derived from these values. A transformation technique extends this method to handle both node failure and edge failure. To enhance efficiency of proposed sampling method and achieve adaptability to network topology changes, we introduce an active learning method utilizing a random forest (RF) classifier. This classifier directly predicts structure function values, integrates network behaviors across diverse topologies, and undergoes iterative refinement to enhance predictive accuracy. Importantly, the trained RF classifier can directly predict reliability for variant networks, a capability beyond the sampling method alone. Through investigating several network examples and two practical applications, the effectiveness of both proposed methods is demonstrated.

Stochastic modelling of material variability in structural dynamics: A threefold comparison of Monte Carlo, polynomial chaos, and random sampling techniques

This article investigates the influence of random elastic modulus on beam eigenfrequencies using multiple simulation techniques: Monte Carlo simulations (employing Cholesky decomposition (MCS-CD) and Kosambi-Karhunen-Loève expansion (MCS-KKL)), Polynomial Chaos expansion (PCE), and a proposed Random Sampling method (RSM). Anomalies in Monte Carlo simulations, where normally distributed elastic modulus led to negative values and imaginary eigenfrequencies, were effectively addressed by adopting a log-normal distribution. Comparative analyses focused on covariance variation of the first three eigenfrequencies with correlation length and standard deviation of the random field, highlighting nuanced differences between normal and log-normal distributions. PCE exhibited distinct responses, showcasing variations in covariance with different distributions. The study culminates in eigenfrequency estimation using the proposed RSM, wherein the beam is discretised into n elements with randomly assigned elastic moduli. The mean and variance of eigenfrequencies are compared with existing methods, which represent an alternative method for achieving similar outcomes.These comparative studies provide a comprehensive understanding of how different statistical treatments and simulation methods impact the reliability and accuracy of eigenfrequency predictions in beams with random elastic properties, thus contributing valuable insights for structural analysis and design under uncertainty.

Mathematical Evaluation of Direct and Inverse Problem Applied in Breakthrough Models of Metal Adsorption

The treatment of industrial effluents has great environmental and human health importance. The purification of water from polluting components, such as metals and organic compounds, can be considered one of the main applications in this field, with adsorption being one of the main treatment methods. Therefore, with the objective of describing the dynamics of the process in an adsorption column and estimating the parameters involved, in this work, an algorithm for the Method of Lines (MOL) was used in order to numerically solve the model formed by the mass balance in liquid phase, the linear driving force equation (LDF), and the Langmuir isotherm for equilibrium. In addition, a sensitivity analysis of the phenomenon was carried out in relation to the parameters and a subsequent estimation of these was made through the Monte Carlo technique via the Markov chain (MCMC). The validation algorithm was created using data from actual breakthrough curves found in the literature. The experimental data were obtained from the literature for the adsorption of Cadmium (Cd), Copper (Cu), Nickel (Ni), Zinc (Zn), and Chrome (Cr) ions. Among all the estimates, the one that had the lowest adjustment to the data was that related to zinc metal, which had an R2 equal to 0.8984. For the other metals, the correlation coefficient had a value closer to unity. This demonstrates that, in general, the estimates were good enough to represent the dynamics of adsorption.

Accurate Surge Arrester Modeling for Optimal Risk-Aware Lightning Protection Utilizing a Hybrid Monte Carlo–Particle Swarm Optimization Algorithm

The application of arresters is critical for the safe operation of electric grids against lightning. Arresters limit the consequences of lightning-induced over-voltages. However, surge arrester protection in electric grids is challenging due to the intrinsic complexities of distribution grids, including overhead lines and power components such as transformers. In this paper, an optimal arrester placement technique is developed by proposing a multi-objective function that includes technical, safety and risk, and economic indices. However, an effective placement model demands a comprehensive and accurate modeling of an electric grid’s components. In this light, appropriate models of a grid’s components including an arrester, the earth, an oil-immersed transformer, overhead lines, and lightning-induced voltage are developed. To achieve accurate models, high-frequency transient mathematical models are developed for the grid’s components. Notably, to have an accurate model of the arrester, which critically impacts the performance of the arrester placement technique, a new arrester model is developed and evaluated based on real technical data from manufacturers such as Pars, Tridelta, and Siemens. Then, the proposed model is compared with the IEEE, Fernandez, and Pinceti models. The arrester model is incorporated in an optimization problem considering the performance of the over-voltage protection and the risk, technical, and economic indices, and it is solved using the particle swarm optimization (PSO) and Monte Carlo (MC) techniques. To validate the proposed arrester model and the placement technique, real data from the Chopoghloo feeder in Bahar, Hamedan, Iran, are simulated. The feeder is expanded over three different geographical areas, including rural, agricultural plain, and mountainous areas.

Computational investigation of transport parameters of ions in gas-filled radiation detectors

In this study, a novel computational method was developed to investigate the transport characteristics of ions in gas-filled radiation detectors, which are closely linked to the behavior of ions in gaseous detectors. Parameters such as polarizability, mean free path, collision frequency, and mean free time, which directly impact ion mobility, were physically manipulated using the Monte Carlo technique, and the results were validated against fundamental physical principles. As an initial scenario, computations were performed on the mobility of Ar+ ions in an argon environment as a carrier gas. The distribution of the radial velocity components of the ion following an ion-gas collision was represented as a two-dimensional histogram with a disc-shaped pattern, and this result was elucidated utilizing the Maxwell-Boltzmann distribution. The findings regarding the mean free time and mean free path of an Ar+ ion in an argon carrier gas align with the results derived from Skullerud's methodologies. These findings hold promise for Garfield++ simulations, enabling the computation of ion mobility and even cluster ions in the mixture, thereby considering their impact on the detector's gain parameters. The results of this investigation offer novel insights into the behavior of ions within detector settings, significantly enhancing our comprehension of the mobility of ions and its effects on radiation detection efficiency.

Monte Carlo simulation of the effect of melanin concentration on light-tissue interactions for transmittance pulse oximetry measurement.

Questions about the accuracy of pulse oximeters in measuring arterial oxygen saturation ( ) in individuals with darker skin pigmentation have resurfaced since the COVID-19 pandemic. This requires investigation to improve patient safety, clinical decision making, and research. We aim to use computational modeling to identify the potential causes of inaccuracy in measurement in individuals with dark skin and suggest practical solutions to minimize bias. An in silico model of the human finger was developed to explore how changing melanin concentration and arterial oxygen saturation ( ) affect pulse oximeter calibration algorithms using the Monte Carlo (MC) technique. The model generates calibration curves for Fitzpatrick skin types I, IV, and VI and an range between 70% and 100% in transmittance mode. was derived by inputting the computed ratio of ratios for light and dark skin into a widely used calibration algorithm equation to calculate bias ( ). These were validated against an experimental study to suggest the validity of the Monte Carlo model. Further work included applying different multiplication factors to adjust the moderate and dark skin calibration curves relative to light skin. Moderate and dark skin calibration curve equations were different from light skin, suggesting that a single algorithm may not be suitable for all skin types due to the varying behavior of light in different epidermal melanin concentrations, especially at 660nm. The ratio between the mean bias in White and Black subjects in the cohort study was 6.6 and 5.47 for light and dark skin, respectively, from the Monte Carlo model. A linear multiplication factor of 1.23 and exponential factor of 1.8 were applied to moderate and dark skin calibration curves, resulting in similar alignment. This study underpins the careful re-assessment of pulse oximeter designs to minimize bias in measurements across diverse populations.

Automated Bayesian variable selection methods for binary regression models with missing covariate data

Data collection and the availability of large data sets has increased over the last decades. In both statistical and machine learning frameworks, two methodological issues typically arise when performing regression analysis on large data sets. First, variable selection is crucial in regression modeling, as it helps to identify an appropriate model with respect to the considered set of conditioning variables. Second, especially in the context of survey data, handling of missing values is important for estimation, which occur even with state-of-the-art data collection and processing methods. Within this paper, we provide an Bayesian approach based on a spike-and-slab prior for the regression coefficients, which allows for simultaneous handling of variable selection and estimation in combination with handling of missing values in covariate data. The paper also discusses the implementation of the approach using Markov chain Monte Carlo techniques and provides results for simulated data sets and an empirical illustration based on data from the German National Educational Panel Study. The suggested Bayesian approach is compared to other statistical and machine learning frameworks such as Lasso, ridge regression, and Elastic net, and is shown to perform well in terms of estimation performance and variable selection accuracy. The simulation results demonstrate that ignoring the handling of missing values in data sets can lead to the generation of biased selection results. Overall, the proposed Bayesian method offers a holistic, flexible, and powerful framework for variable selection in the presence of missing covariate data.

Evolution of some flow-related properties of diffusive aerosols along a tube

This is the third of a series of papers dealing with the behavior of Brownian aerosol particles immersed in a laminar fluid flow. The evolution along the tube of the distributions of particle radial positions (RPD), particle residence time (RTD), and particle mean axial velocity (MAVD) were determined by Monte Carlo (MC) simulation of particles trajectories. The RPD and particle penetration was also determined by numerical solution of the advection-diffusion equation (ADE) with negligible particle axial diffusion. The fairly good agreement shown between the results obtained by these two methods justifies our confidence on the use of the MC technique to determine other particle properties, as MAVD and RTD, for which the corresponding differential equation is yet unknown. Flow-related properties of the aerosol, such as penetration and residence time, are mainly determined by its MAVD. The MAVD is intimately related to the RPD; the latter evolves in such a manner that the surviving particles tend to accumulate nearer the tube axis and farther from the wall. When the fluid local velocity depends on the spatial location, the mean particle axial velocity increases as the aerosol flows downstream the tube, and its value can be considerably larger than the mean fluid velocity, in spite that no external force is acting on the particle. A direct consequence of this counterintuitive fact is that the mean aerosol residence time in the tube can be much smaller, by a factor of ∼0.65, than that of the fluid for even moderate values of the particle diffusion coefficient. This asymptotic value of the aerosol mean residence time can be predicted using the ADE in conjunction with a simple estimation model proposed here. If the fluid velocity is constant within the tube (uniform or plug flow), the mean particle axial velocity is everywhere equal to the fluid velocity, and particles and fluid spend the same time to traverse the tube. The larger the departure of the fluid velocity profile from uniformity, the larger the difference of mean axial velocity and mean residence time between particles and fluid.

Mutual Diffusivities of Mixtures of Carbon Dioxide and Hydrogen and Their Solubilities in Brine: Insight from Molecular Simulations.

H2-CO2 mixtures find wide-ranging applications, including their growing significance as synthetic fuels in the transportation industry, relevance in capture technologies for carbon capture and storage, occurrence in subsurface storage of hydrogen, and hydrogenation of carbon dioxide to form hydrocarbons and alcohols. Here, we focus on the thermodynamic properties of H2-CO2 mixtures pertinent to underground hydrogen storage in depleted gas reservoirs. Molecular dynamics simulations are used to compute mutual (Fick) diffusivities for a wide range of pressures (5 to 50 MPa), temperatures (323.15 to 423.15 K), and mixture compositions (hydrogen mole fraction from 0 to 1). At 5 MPa, the computed mutual diffusivities agree within 5% with the kinetic theory of Chapman and Enskog at 423.15 K, albeit exhibiting deviations of up to 25% between 323.15 and 373.15 K. Even at 50 MPa, kinetic theory predictions match computed diffusivities within 15% for mixtures comprising over 80% H2 due to the ideal-gas-like behavior. In mixtures with higher concentrations of CO2, the Moggridge correlation emerges as a dependable substitute for the kinetic theory. Specifically, when the CO2 content reaches 50%, the Moggridge correlation achieves predictions within 10% of the computed Fick diffusivities. Phase equilibria of ternary mixtures involving CO2-H2-NaCl were explored using Gibbs Ensemble (GE) simulations with the Continuous Fractional Component Monte Carlo (CFCMC) technique. The computed solubilities of CO2 and H2 in NaCl brine increased with the fugacity of the respective component but decreased with NaCl concentration (salting out effect). While the solubility of CO2 in NaCl brine decreased in the ternary system compared to the binary CO2-NaCl brine system, the solubility of H2 in NaCl brine increased less in the ternary system compared to the binary H2-NaCl brine system. The cooperative effect of H2-CO2 enhances the H2 solubility while suppressing the CO2 solubility. The water content in the gas phase was found to be intermediate between H2-NaCl brine and CO2-NaCl brine systems. Our findings have implications for hydrogen storage and chemical technologies dealing with CO2-H2 mixtures, particularly where experimental data are lacking, emphasizing the need for reliable thermodynamic data on H2-CO2 mixtures.