Monte Carlo Procedure Research Articles

Improved Drought Characteristics in the Pearl River Basin Based on Reconstructed GRACE Solution with Enhanced Temporal Resolution

As global warming intensifies, the damage caused by drought cannot be disregarded. Traditional drought monitoring is often carried out with monthly resolution, which fails to monitor the sub-monthly climatic event. The GRACE-based drought severity index (DSI) is a drought index based on terrestrial water storage anomalies (TWSA) observed by the gravity recovery and climate experiment (GRACE) satellite. DSI has the ability to monitor drought effectively, and it is in good consistency with other drought monitoring methods. However, the temporal resolution of DSI is limited by that of GRACE observations, so it is necessary to obtain TWSA with a higher temporal resolution to calculate DSI. We use a statistical method to reconstruct the TWSA, which adopts precipitation and temperature to obtain TWSA on a daily resolution. This statistical method needs to be combined with the time series decomposition method, and then the parameters are simulated by the Markov chain Monte Carlo (MCMC) procedure. In this study, we use this TWSA reconstruction method to obtain high-quality TWSA at daily time resolution. The correlation coefficient between CSR–TWSA and the reconstructed TWSA is 0.97, the Nash–Sutcliffe efficiency is 0.93, and the root mean square error is 16.57. The quality of the reconstructed daily TWSA is evaluated, and the DSI on a daily resolution is calculated to analyze the drought phenomenon in the Pearl River basin (PRB). The results show that the TWSA reconstructed by this method has high consistency with other daily publicly available TWSA products and TWSA provided by the Center for Space Research (CSR), which proves the feasibility of this method. The correlation between DSI based on reconstructed daily TWSA, SPI, and SPEI is greater than 0.65, which is feasible for drought monitoring. From 2003 to 2021, the DSI recorded six drought events in the PRB, and the recorded drought is more consistent with SPI-6 and SPEI-6. There was a drought event from 27 May 2011 to 12 October 2011, and this drought event had the lowest DSI minimum (minimum DSI = −1.76) recorded among the six drought events. The drought monitored by the DSI is in line with government announcements. This study provides a method to analyze drought events at a higher temporal resolution, and this method is also applicable in other areas.

Regression in extremes using the four-parameter Kappa distribution

The four-parameter Kappa distribution (4KD) is known to be flexible and has been used for extreme value analysis, especially in hydrological sciences. This distribution has the great advantage of encompassing the two main distributions of extreme values used in the literature: the Generalized Pareto Distribution (GPD) and the Generalized Extreme Value (GEV) distribution. However, the analyses made in previous works for 4KD in the context of extreme values are based only on models with static parameters, not allowing the capture of covariate effects such as seasonality and location variables in a specific dataset. This study proposes that the inference about the 4KD can be made under the Bayesian paradigm by inserting a regression structure on the parameters to assess possible effects of covariates under the model. This proposal allows us to interpret the parameters and predict extreme events when there are covariates. The estimation of the parameters is performed using Markov Chain Monte Carlo (MCMC) procedures. The model was applied with both approaches in extremes: maximum and exceedance data. In this analysis, the proposed model was compared with models that use a regression structure in the usual extreme values distribution (GEV and GPD), and it presented better results in fit measures.

Two super-Earths at the edge of the habitable zone of the nearby M dwarf TOI-2095

The main scientific goal of TESS is to find planets smaller than Neptune around stars that are bright enough to allow for further characterization studies. Given our current instrumentation and detection biases, M dwarfs are prime targets in the search for small planets that are in (or near) the habitable zone of their host star. In this work, we use photometric observations and CARMENES radial velocity (RV) measurements to validate a pair of transiting planet candidates found by TESS. The data were fitted simultaneously, using a Bayesian Markov chain Monte Carlo (MCMC) procedure and taking into account the stellar variability present in the photometric and spectroscopic time series. We confirm the planetary origin of the two transiting candidates orbiting around TOI-2095 (LSPM J1902+7525). The star is a nearby M dwarf (d = 41.90 ± 0.03 pc, Teff = 3759 ± 87 K, V = 12.6 mag), with a stellar mass and radius of M* = 0.44 ± 0.02 M⊙ and R* = 0.44 ± 0.02 R⊙, respectively. The planetary system is composed of two transiting planets: TOI-2095b, with an orbital period of Pb = 17.66484 ± (7 × 10−5) days, and TOI-2095c, with Pc = 28.17232 ± (14 × 10−5) days. Both planets have similar sizes with Rb = 1.25 ± 0.07 R⊕ and Rc = 1.33 ± 0.08 R⊕ for planet b and planet c, respectively. Although we did not detect the induced RV variations of any planet with significance, our CARMENES data allow us to set stringent upper limits on the masses of these objects. We find Mb < 4.1 M⊕ for the inner and Mc < 7.4 M⊕ for the outer planet (95% confidence level). These two planets present equilibrium temperatures in the range of 300–350 K and are close to the inner edge of the habitable zone of their star.

A sensitivity analysis framework for SMA-based self-centering systems considering uncertainty in hysteretic material parameters

Shape memory alloys (SMAs) are widely utilized as the core component to develop self-centering (SC) structures owing to their excellent super-elasticity. Seismic performance of SMA-based structures is significantly influenced by the hysteretic parameters of the exploited SMAs. Uncertainties in the hysteretic parameters of SMAs could cause variation in seismic performance however have not received sufficient attentions. This paper proposes a sensitivity analysis framework to realistically and efficiently quantify the sensitivity of SMA-based structures to hysteretic model parameters. The experimental data from SMA bars are analyzed through the Markov chain Monte Carlo (MCMC) procedure. The probabilistic distributions of SMA hysteretic parameters are then sampled using the linear moment theory. Polynomial chaos expansions (PCE) based surrogate model is then used to evaluate sensitivity of response to different parametric uncertainties through the Sobol indices. The proposed framework is then applied to a total of 120 single-degree-of-freedom (SDOF) systems to demonstrate its efficacy to generalize observations and findings. The results show that the proposed framework provided more effective and realistic sensitivity analysis of seismic responses of SMA-based SDOF systems to account for uncertainty in the hysteretic model parameters. The Sobol indices also indicate that the sensitivity of different seismic response quantities varies for different hysteretic model parameters of SMAs.

Stochastic modeling and statistical calibration with model error and scarce data

This paper introduces a procedure to assess the predictive accuracy of stochastic models subject to model error and sparse data. Model error is introduced as uncertainty on the coefficients of appropriate polynomial chaos expansions (PCE). The error associated with finite sample size allows us to conceive of these coefficients as statistics of the data that we describe as random variables whose influence on output quantities of interest is evaluated through the extended polynomial chaos expansion (EPCE). A Bayesian data assimilation scheme is introduced to update these expansions by considering the resulting nested chaos expansion as a hierarchical probabilistic model. Stochastic models of quantities of interest (QoI) are thus constructed and efficiently evaluated. The Metropolis–Hastings Markov chain Monte Carlo procedure is used to sample the posterior. Two illustrative analytical and numerical problems are used to demonstrate the proposed approach.

QSPR and Nano-QSPR: Which One Is Common? The Case of Fullerenes Solubility

Background: The system of self-consistent models is an attempt to develop a tool to assess the predictive potential of various approaches by considering a group of random distributions of available data into training and validation sets. Considering many different splits is more informative than considering a single model. Methods: Models studied here build up for solubility of fullerenes C60 and C70 in different organic solvents using so-called quasi-SMILES, which contain traditional simplified molecular input-line entry systems (SMILES) incorporated with codes that reflect the presence of C60 and C70. In addition, the fragments of local symmetry (FLS) in quasi-SMILES are applied to improve the solubility’s predictive potential (expressed via mole fraction at 298’K) models. Results: Several versions of the Monte Carlo procedure are studied. The use of the fragments of local symmetry along with a special vector of the ideality of correlation improves the predictive potential of the models. The average value of the determination coefficient on the validation sets is equal to 0.9255 ± 0.0163. Conclusions: The comparison of different manners of the Monte Carlo optimization of the correlation weights has shown that the best predictive potential was observed for models where both fragments of local symmetry and the vector of the ideality of correlation were applied.

Testing for the Pareto type I distribution: a comparative study

AbstractPareto distributions are widely used models in economics, finance and actuarial sciences. As a result, a number of goodness-of-fit tests have been proposed for these distributions in the literature. We provide an overview of the existing tests for the Pareto distribution, focussing specifically on the Pareto type I distribution. To date, only a single overview paper on goodness-of-fit testing for Pareto distributions has been published. However, the mentioned paper has a much wider scope than is the case for the current paper as it covers multiple types of Pareto distributions. The current paper differs in a number of respects. First, the narrower focus on the Pareto type I distribution allows a larger number of tests to be included. Second, the current paper is concerned with composite hypotheses compared to the simple hypotheses (specifying the parameters of the Pareto distribution in question) considered in the mentioned overview. Third, the sample sizes considered in the two papers differ substantially. In addition, we consider two different methods of fitting the Pareto Type I distribution; the method of maximum likelihood and a method closely related to moment matching. It is demonstrated that the method of estimation has a profound effect, not only on the powers achieved by the various tests, but also on the way in which numerical critical values are calculated. We show that, when using maximum likelihood, the resulting critical values are shape invariant and can be obtained using a Monte Carlo procedure. This is not the case when moment matching is employed. The paper includes an extensive Monte Carlo power study. Based on the results obtained, we recommend the use of a test based on the phi divergence together with maximum likelihood estimation.

Are historical stage records useful to decrease the uncertainty of flood frequency analysis ? A 200-year long case study

Flood frequency analysis (FFA), a widely used method to estimate flood hazard, is affected by several sources of uncertainty. Extending flood samples by reanalyzing historical systematic stage records has the potential to reduce sampling uncertainty, but the historical flood discharges derived from this reanalysis are generally affected by large uncertainties. This paper explores whether historical stage records improve design flood estimates through a chain of uncertainty estimation methods for FFA. Uncertainties are estimated and propagated from stage and rating curves to design flood estimates using Monte Carlo procedures. The role of both streamflow and sampling uncertainties in design flood estimation is examined. This procedure is applied to the 205-year long stage series of the Rhône River at Beaucaire, France (95 590 km2). The estimated streamflow 95% uncertainty varies from 30% (XIXth Century) to 5% (1967–2020). The total uncertainty of design flood is significantly reduced when the length of the series increases from 20 to 100 years due to sampling uncertainty reduction. However, the total uncertainty remains stable beyond this sample size: this is because large uncertainties affecting the XIXth Century flood discharges compensate for the reduction in sampling uncertainty. Enlarging the sample size to two centuries leads to including the two largest known floods in 1840 and 1856. In turn, this induces a 15% increase of the 1000-year flood estimates.

Bias of the independently based gain and offset error in ADC testing using the histogram method

When normally distributed additive noise is present on the test setup, it leads to a bias on the values of estimated gain and offset error of analog-to-digital converters when estimated using the Histogram Test Method. It is shown that the offset estimation is unbiased while the gain estimation can have up to 5% bias for values of signal-to-noise ratio as low as 10 dB. It is also shown that this bias is not dependent on the number of samples acquired. An approximate analytical expression, in closed form, is proposed for rapid estimation of gain error. It considers the signal-to-noise ratio as well as the amount of overdrive used. The analytical derivations made are validated using simulated data using a Monte Carlo procedure. The same procedure is used with experimental data obtained with a real data acquisition system to validate the results obtained.

Selection of the Lateral Distance for the Assessment Area in a Monte Carlo Procedure Under Indirect Lightning for Overhead Distribution Lines

Monte Carlo procedures are commonly adopted to evaluate the lightning flashover rate on overhead lines due to indirect lightning. This letter presents a discussion on selecting a lateral distance of the assessment area, in which a lightning stroke would cause a flashover. An inappropriate choice would either cause unexpected assessment errors or incur an extra computational burden. Unfortunately, in the literature, there is no systematic discussion on this issue. In this letter, the influence of this lateral distance on the flashover rate evaluation is discussed. The utmost lateral distance is introduced, beyond which indirect lightning events would not cause a flashover. A general procedure is provided to determine this utmost lateral distance. With this selected utmost lateral distance, the computational burden could be relieved while the assessment accuracy preserved.

A Measurement of the Kuiper Belt’s Mean Plane From Objects Classified By Machine Learning

Mean plane measurements of the Kuiper Belt from observational data are of interest for their potential to test dynamical models of the solar system. Recent measurements have yielded inconsistent results. Here we report a measurement of the Kuiper Belt’s mean plane with a sample size more than twice as large as in previous measurements. The sample of interest is the nonresonant Kuiper Belt objects, which we identify by using machine learning on the observed Kuiper Belt population whose orbits are well determined. We estimate the measurement error with a Monte Carlo procedure. We find that the overall mean plane of the nonresonant Kuiper Belt (semimajor axis range of 35–150 au) and also that of the classical Kuiper Belt (semimajor axis range of 42–48 au) are both close to (within ∼0.°7) but distinguishable from the invariable plane of the solar system to greater than 99.7% confidence. When binning the sample into smaller semimajor axis bins, we find the measured mean plane is mostly consistent with both the invariable plane and the theoretically expected Laplace surface forced by the known planets. Statistically significant discrepancies are found only in the semimajor axis ranges 40.3–42 au and 45–50 au; these ranges are in proximity to the ν 8 secular resonance and Neptune’s 2:1 mean motion resonance where the theory for the Laplace surface is likely to be inaccurate. These results do not support a previously reported anomalous warp at semimajor axes above 50 au.

Stochastic EM Algorithm for Joint Model of Logistic Regression and Mechanistic Nonlinear Model in Longitudinal Studies

We study a joint model where logistic regression is applied to binary longitudinal data with a mismeasured time-varying covariate that is modeled using a mechanistic nonlinear model. Multiple random effects are necessary to characterize the trajectories of the covariate and the response variable, leading to a high dimensional integral in the likelihood. To account for the computational challenge, we propose a stochastic expectation-maximization (StEM) algorithm with a Gibbs sampler coupled with Metropolis–Hastings sampling for the inference. In contrast with previous developments, this algorithm uses single imputation of the missing data during the Monte Carlo procedure, substantially increasing the computing speed. Through simulation, we assess the algorithm’s convergence and compare the algorithm with more classical approaches for handling measurement errors. We also conduct a real-world data analysis to gain insights into the association between CD4 count and viral load during HIV treatment.

Flexible Bayesian quantile regression for nonlinear mixed effects models based on the generalized asymmetric Laplace distribution

We propose flexible Bayesian quantile regression for a class of parametric nonlinear mixed effects models for longitudinal data based on the generalized asymmetric Laplace distribution, which exhibits more flexibility in skewness, mode and tail behaviour than the frequently used asymmetric Laplace distribution in quantile regression. An efficient Markov chain Monte Carlo procedure based on the adaptive random walk Metropolis-within-Gibbs sampling algorithm is derived for posterior inference. We demonstrate through simulation studies and empirical analysis that the proposed method could provide more accurate parameter estimation and better model fit than the existing methods.

Statistical Analysis of Inverse Lindley Data Using Adaptive Type-II Progressively Hybrid Censoring with Applications

This paper deals with the statistical inference of the unknown parameter and some life parameters of inverse Lindley distribution under the assumption that the data are adaptive Type-II progressively censored. The maximum likelihood method is considered to acquire the point and interval estimates of the distribution parameter, reliability, and hazard rate functions. The approximate confidence intervals are also addressed. The delta method is taken into consideration to approximate the variances of the estimators of the reliability and hazard rate functions to get the required intervals. Based on the assumption of gamma prior, we further consider Bayesian estimation of the different parameters. The Bayes estimates are obtained by considering squared error and general entropy loss functions. The Bayes estimates and highest posterior density credible intervals are obtained by employing the Markov chain Monte Carlo procedure. An exhaustive numerical study is conducted to compare the offered estimates with regard to their root means squared error, relative absolute biases, confidence lengths, and coverage probabilities. To explain the suggested methods, two applications are investigated. The numerical findings show that the Bayes estimates perform better than those obtained based on the maximum likelihood method. The Bayesian estimations using the asymmetric loss function give more efficient estimates than the symmetric loss. Finally, the inverse Lindley distribution is recommended to be used as a suitable model to fit airborne communication transceiver and wooden toys data sets when compared with some competitive models including inverse Weibull, inverse gamma and alpha power inverted exponential.

Bayesian inversion of log-normal eikonal equations

We study the Bayesian inverse problem for inferring the log-normal slowness function of the eikonal equation, given noisy observation data on its solution at a set of spatial points. We contribute rigorous proofs on the existence and well-posedness of the problem. We then study approximation of the posterior probability measure by solving the truncated eikonal equation, which contains only a finite number of terms in the Karhunen–Loeve expansion of the slowness function, by the fast marching method (FMM). The error of this approximation in the Hellinger metric is deduced in terms of the truncation level of the slowness and the grid size in the FMM resolution. It is well known that the plain Markov chain Monte Carlo (MCMC) procedure for sampling the posterior probability is highly expensive. We develop and justify the convergence of a multilevel MCMC method. Using the heap sort procedure in solving the forward eikonal equation by the FMM, our multilevel MCMC method achieves a prescribed level of accuracy for approximating the posterior expectation of quantities of interest, requiring only an essentially optimal level of complexity. Numerical examples confirm the theoretical results.

Reliability Estimation under Normal Operating Conditions for Progressively Type-II XLindley Censored Data

This paper assumes constant-stress accelerated life tests when the lifespan of the test units follows the XLindley distribution. In addition to the maximum likelihood estimation, the Bayesian estimation of the model parameters is acquired based on progressively Type-II censored samples. The point and interval estimations of the model parameters and some reliability indices under normal operating conditions at mission time are derived using both estimation methods. Using the Markov chain Monte Carlo algorithm, the Bayes estimates are calculated using the squared error loss function. Simulating the performances of the different estimation methods is performed to illustrate the proposed methodology. As an example of how the proposed methods can be applied, we look at two real-life accelerated life test cases. According to the numerical outcomes and based on some criteria, including the root of the mean square error and interval length, we can conclude that the Bayesian estimation method based on the Markov chain Monte Carlo procedure performs better than the classical methods in evaluating the XLindley parameters and some of its reliability measures when a constant-stress accelerated life test is applied with progressively Type-II censoring.

Probabilistic analysis of composite stiffened panels including random AFP-produced defects towards enhanced design allowables

Automated fiber placement introduces defects such as gaps and overlaps during production, which add uncertainty to the mechanical behavior of composite parts. This study describes a probabilistic methodology which allows the direct introduction of random defects to the composite part and the calculation of the allowable design values through probabilistic virtual testing. The method is applied on a stiffened panel and is based on measurements regarding the random defect magnitude. An offline database of knock-down factors for stiffness and strength properties is first generated via detailed defected FE models. The factors are then assigned to the panel FE model accordingly, and via a Monte Carlo procedure the statistical response sample of the part is calculated. The process is further accelerated by a machine learning technique able to emulate the relationship between the random input and the selected responses. Several parametric analyses reveal that the number of defects on the panel is often more sensitive than the defect size, while the intensity of the defect at the through-the-thickness direction and the affected plies have a rather strong effect. Moreover, the conservatism of the deterministic design approach based on safety factors is proven by a direct comparison to the described probabilistic approach.

Testing independence of bivariate censored data using random walk on restricted permutation graph

In this paper, we propose a procedure to test the independence of bivariate censored data, which is generic and applicable to any censoring types in the literature. To test the hypothesis, we consider a rank-based statistic, Kendall’s tau statistic. The censored data defines a restricted permutation space of all possible ranks of the observations. We propose the statistic, the average of Kendall’s tau over the ranks in the restricted permutation space. To evaluate the statistic and its reference distribution, we develop a Markov chain Monte Carlo (MCMC) procedure to obtain uniform samples on the restricted permutation space and numerically approximate the null distribution of the averaged Kendall’s tau. We numerically compare the power of our procedure to existing state of the art procedures in the literature under various censoring types. We apply the procedure to three real data examples with different censoring types, and compare the results with those by existing methods.

Grand canonical Brownian dynamics simulations of adsorption and self-assembly of SAS-6 rings on a surface.

The Spindle Assembly Abnormal Protein 6 (SAS-6) forms dimers, which then self-assemble into rings that are critical for the nine-fold symmetry of the centriole organelle. It has recently been shown experimentally that the self-assembly of SAS-6 rings is strongly facilitated on a surface, shifting the reaction equilibrium by four orders of magnitude compared to the bulk. Moreover, a fraction of non-canonical symmetries (i.e., different from nine) was observed. In order to understand which aspects of the system are relevant to ensure efficient self-assembly and selection of the nine-fold symmetry, we have performed Brownian dynamics computer simulation with patchy particles and then compared our results with the experimental ones. Adsorption onto the surface was simulated by a grand canonical Monte Carlo procedure and random sequential adsorption kinetics. Furthermore, self-assembly was described by Langevin equations with hydrodynamic mobility matrices. We find that as long as the interaction energies are weak, the assembly kinetics can be described well by coagulation-fragmentation equations in the reaction-limited approximation. By contrast, larger interaction energies lead to kinetic trapping and diffusion-limited assembly. We find that the selection of nine-fold symmetry requires a small value for the angular interaction range. These predictions are confirmed by the experimentally observed reaction constant and angle fluctuations. Overall, our simulations suggest that the SAS-6 system works at the crossover between a relatively weak binding energy that avoids kinetic trapping and a small angular range that favors the nine-fold symmetry.

Using Source Fingerprinting Techniques to Investigate Sediment Sources during Snowmelt and Rainfall Erosion Events in a Small Catchment in the Black Soil Region of Northeast China

Concern for the offsite impact of eroded sediment and the need to develop effective catchment sediment management strategies has directed attention to the need for an improved understanding of the primary sediment sources within catchments and the potential of sediment source fingerprinting techniques to provide such information. The study reported here was undertaken in the black soil region of Northeast China, where soil erosion is seen as a serious threat to the sustainable use of soil resources and offsite impacts of eroded soil are also concerned. The study applies source fingerprinting techniques to the evaluation of sediment sources in a small (3.46 km2) agricultural catchment. Sediment sources from five snowmelt and five rainfall events of varying magnitude were contrasted. Three key potential sediment sources were identified within the study catchment: gullies, cultivated topsoil and uncultivated topsoil. Geochemical properties of the source materials (Ti, Ga, Br and Ba) were used as composite fingerprints capable of discriminating between the three potential sources. A mixing model, optimized using a genetic algorithm and coupled with a Monte Carlo procedure to quantify the uncertainty associated with the resulting estimates, was used for source apportionment. The results indicated mean source contributions for the set of 10 events for cultivated topsoil, uncultivated topsoil and the gullies of ~30%, ~10% and ~60%, respectively. In general, snowmelt and rainfall events were characterized by increased contributions from gully sources and cultivated topsoil, respectively. The study is seen as demonstrating the potential for using source tracing techniques to investigate sediment sources in environments where strong seasonal contrasts between snowmelt and rainfall events exist.