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Journal articles on the topic 'Monte Carlo sampling and estimation'

Author: Grafiati

Published: 21 December 2024

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1

Liao, Meihao, Rong-Hua Li, Qiangqiang Dai, Hongyang Chen, Hongchao Qin, and Guoren Wang. "Efficient Personalized PageRank Computation: The Power of Variance-Reduced Monte Carlo Approaches." Proceedings of the ACM on Management of Data 1, no. 2 (June 13, 2023): 1–26. http://dx.doi.org/10.1145/3589305.

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Personalized PageRank (PPR) computation is a fundamental problem in graph analysis. The state-of-the-art algorithms for PPR computation are based on a bidirectional framework which include a deterministic forward push and a Monte Carlo sampling procedure. The Monte Carlo sampling procedure, however, often has a relatively-large variance, thus reducing the performance of the PPR computation algorithms. To overcome this issue, we develop two novel variance-reduced Monte Carlo techniques for PPR computation. Our first technique is to apply power iterations to reduce the variance of the Monte Carlo sampling procedure. We prove that conducting few power iterations can significantly reduce the variance of existing Monte Carlo estimators, only with few additional costs. Moreover, we show that such a simple and novel variance-reduced Monte Carlo technique can achieve comparable estimation accuracy and the same time complexity as the state-of-the-art bidirectional algorithms. Our second technique is a novel progressive sampling method which uses the historical information of former samples to reduce the variance of the Monte Carlo estimator. We develop several novel PPR computation algorithms by integrating both of these variance reduction techniques with two existing Monte Carlo sampling approaches, including random walk sampling and spanning forests sampling. Finally, we conduct extensive experiments on 5 real-life large graphs to evaluate our solutions. The results show that our algorithms can achieve much higher PPR estimation accuracy by using much less time, compared to the state-of-the-art bidirectional algorithms.

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Wolf, A. T., T. E. Burk, and J. G. Isebrands. "Estimation of daily and seasonal whole-tree photosynthesis using Monte Carlo integration techniques." Canadian Journal of Forest Research 25, no. 2 (February 1, 1995): 253–60. http://dx.doi.org/10.1139/x95-030.

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Monte Carlo estimation is explored as an alternative to traditional survey sampling techniques to estimate both daily and seasonal whole-tree photosynthesis of first-year Populus clones. Several methods, known in the literature as variance-reduction techniques, are applied to the problem of estimation and compared on the basis of relative root mean squared error. Also of interest is gain in precision over the simple expansion estimator (Monte Carlo estimation in its simplest form). Variance reduction is achieved by approximating the photosynthesis curve by some known, easily integrated function. The estimators retain their unbiasedness regardless of the appropriateness of this function. The authors show how these variance reduction techniques can be used to achieve greater precision when estimating both daily and seasonal whole-tree photosynthesis. These methods may be useful alternatives to current purposive sampling methods that have the potential for bias and high error.

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Morio, Jérôme, Baptiste Levasseur, and Sylvain Bertrand. "Drone Ground Impact Footprints with Importance Sampling: Estimation and Sensitivity Analysis." Applied Sciences 11, no. 9 (April 25, 2021): 3871. http://dx.doi.org/10.3390/app11093871.

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This paper addresses the estimation of accurate extreme ground impact footprints and probabilistic maps due to a total loss of control of fixed-wing unmanned aerial vehicles after a main engine failure. In this paper, we focus on the ground impact footprints that contains 95%, 99% and 99.9% of the drone impacts. These regions are defined here with density minimum volume sets and may be estimated by Monte Carlo methods. As Monte Carlo approaches lead to an underestimation of extreme ground impact footprints, we consider in this article multiple importance sampling to evaluate them. Then, we perform a reliability oriented sensitivity analysis, to estimate the most influential uncertain parameters on the ground impact position. We show the results of these estimations on a realistic drone flight scenario.

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4

Nawajah, Inad, Hassan Kanj, Yehia Kotb, Julian Hoxha, Mouhammad Alakkoumi, and Kamel Jebreen. "Bayesian Regression Analysis using Median Rank Set Sampling." European Journal of Pure and Applied Mathematics 17, no. 1 (January 31, 2024): 180–200. http://dx.doi.org/10.29020/nybg.ejpam.v17i1.5015.

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Bayesian estimation of the linear regression parameter system is considered by deploying Median Rank Set Sampling (MRSS). The full conditional distributions and the associated posterior distribution are obtained. Therefore, based on Markov Chain Monte Carlo simulation, the Bayesian point estimates and credible intervals for the regression parameters are determined. To measure the efficiency of the obtained Bayesian estimates concerning the frequentist estimates we compute the asymptotic relative efficiency of the obtained Bayesian estimates using Markov Chain Monte Carlo simulation.

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5

Baker, Matthew J. "Adaptive Markov Chain Monte Carlo Sampling and Estimation in Mata." Stata Journal: Promoting communications on statistics and Stata 14, no. 3 (September 2014): 623–61. http://dx.doi.org/10.1177/1536867x1401400309.

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6

Thom, H., W. Fang, Z. Wang, NJ Welton, T. Goda, and M. Giles. "Advanced Monte-Carlo Sampling Schemes for Value of Information Estimation." Value in Health 20, no. 9 (October 2017): A772. http://dx.doi.org/10.1016/j.jval.2017.08.2219.

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7

Taverniers, Søren, and Daniel M. Tartakovsky. "Estimation of distributions via multilevel Monte Carlo with stratified sampling." Journal of Computational Physics 419 (October 2020): 109572. http://dx.doi.org/10.1016/j.jcp.2020.109572.

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8

Lang, Lixin, Wen-shiang Chen, Bhavik R. Bakshi, Prem K. Goel, and Sridhar Ungarala. "Bayesian estimation via sequential Monte Carlo sampling—Constrained dynamic systems." Automatica 43, no. 9 (September 2007): 1615–22. http://dx.doi.org/10.1016/j.automatica.2007.02.012.

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9

Magnussen, S., R. E. McRoberts, and E. O. Tomppo. "A resampling variance estimator for the k nearest neighbours technique." Canadian Journal of Forest Research 40, no. 4 (April 2010): 648–58. http://dx.doi.org/10.1139/x10-020.

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Current estimators of variance for the k nearest neighbours (kNN) technique are designed for estimates of population totals. Their efficiency in small-area estimation problems can be poor. In this study, we propose a modified balanced repeated replication estimator of variance (BRR) of a kNN total that performs well in small-area estimation problems and under both simple random and cluster sampling. The BRR estimate of variance is the sum of variances and covariances of unit-level kNN estimates in the area of interest. In Monte Carlo simulations of simple random and cluster sampling from seven artificial populations with real and simulated forest inventory data, the agreement between averages of BRR estimates of variance and Monte Carlo sampling variances was good both for population and for small-area totals. The modified BRR estimator is currently limited to sample sizes no larger than 1984. An accurate approximation to the proposed BRR estimator allows significant savings in computing time.

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10

Rulaningtyas, Riries, Yusrinourdi Muhammad Zuchruf, Akif Rahmatillah, Khusnul Ain, Alfian Pramudita Putra, Osmalina Nur Rahma, Limpat Salamat, and Rifai Chai. "ELBOW ANGLE ESTIMATION FROM EMG SIGNALS BASED ON MONTE CARLO SIMULATION." Jurnal Teknologi 84, no. 4 (May 30, 2022): 79–90. http://dx.doi.org/10.11113/jurnalteknologi.v84.17683.

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Monte Carlo simulation is defined as statistical sampling techniques which is used to estimate the solutions of quantitative problems. The aim of this study is to develop Monte Carlo algorithm for elbow angle estimation from EMG signal as preliminary study for further research in rehabilitation tool to make a breakthrough rehabilitation tool for post-stroke patients based on muscle signals to carry out rehabilitation independently and consistently. The Monte Carlo simulation is performed to approach the model’s angle from subject who takes 20 seconds lifting barbell repeatedly for 52 times. Monte Carlo simulations were carried out as many as 10,000 times because it was considered ideal testing for a model. In doing the estimation, the angle will be divided into four ranges, which are determined from the model’s trend value, the estimation of the previous angle, the estimated error angle, and the previous measured angle. Then an average calculation is performed on the Monte Carlo simulation, which enters the angle range to determine the estimated value of the angle. The most optimal estimation is obtained from this study with RMSE (root mean square error) was 8.96°, and the correlation coefficient between estimate angle and the measured angle was 0.96.

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11

Obeidat, Mohammed, Amjad Al-Nasser, and Amer I. Al-Omari. "Estimation of Generalized Gompertz Distribution Parameters under Ranked-Set Sampling." Journal of Probability and Statistics 2020 (September 7, 2020): 1–14. http://dx.doi.org/10.1155/2020/7362657.

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This paper studies estimation of the parameters of the generalized Gompertz distribution based on ranked-set sample (RSS). Maximum likelihood (ML) and Bayesian approaches are considered. Approximate confidence intervals for the unknown parameters are constructed using both the normal approximation to the asymptotic distribution of the ML estimators and bootstrapping methods. Bayes estimates and credible intervals of the unknown parameters are obtained using differential evolution Markov chain Monte Carlo and Lindley’s methods. The proposed methods are compared via Monte Carlo simulations studies and an example employing real data. The performance of both ML and Bayes estimates is improved under RSS compared with simple random sample (SRS) regardless of the sample size. Bayes estimates outperform the ML estimates for small samples, while it is the other way around for moderate and large samples.

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12

McDowell, Allen, and Jeff Pitblado. "From the Help Desk: It's all about the Sampling." Stata Journal: Promoting communications on statistics and Stata 2, no. 2 (June 2002): 190–201. http://dx.doi.org/10.1177/1536867x0200200207.

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Effective estimation and inference, when the data are collected using complex survey designs, requires estimators that fully account for the sampling design. This article explores, by means of Monte Carlo simulations of the power of simple hypothesis tests, the consequences of parameter estimation and inference when naive estimators are employed with survey data.

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13

Chen, Wen-shiang, Bhavik R. Bakshi, Prem K. Goel, and Sridhar Ungarala. "Bayesian Estimation via Sequential Monte Carlo Sampling: Unconstrained Nonlinear Dynamic Systems." Industrial & Engineering Chemistry Research 43, no. 14 (July 2004): 4012–25. http://dx.doi.org/10.1021/ie034010v.

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14

Greselin, Francesca, Fabio Piacenza, and Ričardas Zitikis. "Practice Oriented and Monte Carlo Based Estimation of the Value-at-Risk for Operational Risk Measurement." Risks 7, no. 2 (May 1, 2019): 50. http://dx.doi.org/10.3390/risks7020050.

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We explore the Monte Carlo steps required to reduce the sampling error of the estimated 99.9% quantile within an acceptable threshold. Our research is of primary interest to practitioners working in the area of operational risk measurement, where the annual loss distribution cannot be analytically determined in advance. Usually, the frequency and the severity distributions should be adequately combined and elaborated with Monte Carlo methods, in order to estimate the loss distributions and risk measures. Naturally, financial analysts and regulators are interested in mitigating sampling errors, as prescribed in EU Regulation 2018/959. In particular, the sampling error of the 99.9% quantile is of paramount importance, along the lines of EU Regulation 575/2013. The Monte Carlo error for the operational risk measure is here assessed on the basis of the binomial distribution. Our approach is then applied to realistic simulated data, yielding a comparable precision of the estimate with a much lower computational effort, when compared to bootstrap, Monte Carlo repetition, and two other methods based on numerical optimization.

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15

Patel, Jigna, and P. A. Patel. "On non-negative and improved variance estimation for the ratio estimator under the Midzuno-Sen sampling scheme." Statistics in Transition new series 10, no. 3 (December 1, 2009): 371–85. http://dx.doi.org/10.59170/stattrans-2009-028.

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Various studies on variance estimation showed that it is hard to single out a best and non-negative variance estimator in finite population. This paper attempts to find improved variance estimators for the ordinary ratio estimator under the Midzuno-Sen sampling scheme. A Monte Carlo comparison has been carried out. The suggested estimator has performed well and has taken non-negative values with probability 1.

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16

Morio, J., and R. Pastel. "Plug-in estimation of d-dimensional density minimum volume set of a rare event in a complex system." Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability 226, no. 3 (November 21, 2011): 337–45. http://dx.doi.org/10.1177/1748006x11426973.

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Various reliability or hedging problems boil down to quantile estimation. However, real-life systems are usually multidimensional and thus often imply multidimensional density minimum volume set estimation which is usually done with Monte Carlo simulations. Increasing safety standards create a need for density minimum volume set estimation with low probability that crude Monte Carlo cannot fulfil. This paper proposes a new importance sampling algorithm that estimates efficiently multidimensional density minimum volume sets for extreme probability. It also presents some numerical results on a simple bidimensional Gaussian case and on a realistic launcher impact safety zone estimation.

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17

Liu, Jiacheng, Haiyun Liu, Cong Zhang, Jiyin Cao, Aibo Xu, and Jiwei Hu. "Derivative-Variance Hybrid Global Sensitivity Measure with Optimal Sampling Method Selection." Mathematics 12, no. 3 (January 26, 2024): 396. http://dx.doi.org/10.3390/math12030396.

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This paper proposes a derivative-variance hybrid global sensitivity measure with optimal sampling method selection. The proposed sensitivity measure is as computationally efficient as the derivative-based global sensitivity measure, which also serves as the conservative estimation of the corresponding variance-based global sensitivity measure. Moreover, the optimal sampling method for the proposed sensitivity measure is studied. In search of the optimal sampling method, we investigated the performances of six widely used sampling methods, namely Monte Carlo sampling, Latin hypercube sampling, stratified sampling, Latinized stratified sampling, and quasi-Monte Carlo sampling using the Sobol and Halton sequences. In addition, the proposed sensitivity measure is validated through its application to a rural bridge.

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18

Hasibuan, Lilis Harianti, and Rani Kurnia Putri. "Ekspektasi Maksimum Percentage Drawdown pada data Saham PT. Mayora Tbk dengan simulasi Monte Carlo." JOSTECH: Journal of Science and Technology 1, no. 1 (March 31, 2021): 91–104. http://dx.doi.org/10.15548/jostech.v1i1.2440.

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A drawdown is a tool for defining trading strategies for commodities, stocks, and investments. This analysis is one way of monitoring the decline in asset value over a certain period of time. This journal will discuss PT.MayoraTbk stock trading strategy. By analyzing the observed drawdown in the specified time period. The drawdown analysis here uses the feedback control on PT.MayoraTbk stock trading is assumed to follow the geometric Brownian motion. The data obtained is tested whether the data meets Brown's motion assumptions. Then the maximum drawdown expectation is determined at the selected time interval. An estimate is carried out for the maximum expected drawdown percentage of the share value. To test the validity of the estimation results, a Monte Carlo simulation is carried out. Monte Carlo simulation with the term Sampling Simulation or Monte Carlo Sampling Technique. This simulation sampling illustrates the possible use of sample data using the Monte Carlo method and also the distribution can be known or estimated. This simulation uses existing data (historical data) that is actually used in a simulation that includes inventory or sampling with a known and determined probability distribution, so this Monte Carlo simulation can be used. The basic idea of this Monte Carlo simulation is to generate or generate a value to form a model of the variables and study it.

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19

Bucklew, James A., Peter Ney, and John S. Sadowsky. "Monte Carlo simulation and large deviations theory for uniformly recurrent Markov chains." Journal of Applied Probability 27, no. 1 (March 1990): 44–59. http://dx.doi.org/10.2307/3214594.

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Importance sampling is a Monte Carlo simulation technique in which the simulation distribution is different from the true underlying distribution. In order to obtain an unbiased Monte Carlo estimate of the desired parameter, simulated events are weighted to reflect their true relative frequency. In this paper, we consider the estimation via simulation of certain large deviations probabilities for time-homogeneous Markov chains. We first demonstrate that when the simulation distribution is also a homogeneous Markov chain, the estimator variance will vanish exponentially as the sample size n tends to∞. We then prove that the estimator variance is asymptotically minimized by the same exponentially twisted Markov chain which arises in large deviation theory, and furthermore, this optimization is unique among uniformly recurrent homogeneous Markov chain simulation distributions.

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20

Bucklew, James A., Peter Ney, and John S. Sadowsky. "Monte Carlo simulation and large deviations theory for uniformly recurrent Markov chains." Journal of Applied Probability 27, no. 01 (March 1990): 44–59. http://dx.doi.org/10.1017/s0021900200038419.

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Importance sampling is a Monte Carlo simulation technique in which the simulation distribution is different from the true underlying distribution. In order to obtain an unbiased Monte Carlo estimate of the desired parameter, simulated events are weighted to reflect their true relative frequency. In this paper, we consider the estimation via simulation of certain large deviations probabilities for time-homogeneous Markov chains. We first demonstrate that when the simulation distribution is also a homogeneous Markov chain, the estimator variance will vanish exponentially as the sample size n tends to∞. We then prove that the estimator variance is asymptotically minimized by the same exponentially twisted Markov chain which arises in large deviation theory, and furthermore, this optimization is unique among uniformly recurrent homogeneous Markov chain simulation distributions.

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21

Li, Shaowei, and Wenhao Gui. "Bayesian Survival Analysis for Generalized Pareto Distribution Under Progressively Type II Censored Data." International Journal of Reliability, Quality and Safety Engineering 27, no. 01 (August 8, 2019): 2050001. http://dx.doi.org/10.1142/s0218539320500011.

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In this paper, based on the progressively type II censoring data of generalized Pareto distribution, we consider the maximum likelihood estimation and asymptotic interval estimations of survival function and hazard function by using the Fisher information matrix and delta method. Also, we present a nonparametric Bootstrap-p method to generate the bootstrap samples and derive confidence interval estimation. In addition, we propose the Bayes estimator of Adaptive Rejection Metropolis Sampling algorithm to derive the point estimate and credible intervals. Finally, Monte Carlo simulation study is carried out to compare the performances of the three proposed methods based on different data schemes. An illustrative example is presented.

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22

Zakrad, Az-eddine, and Abdelaziz Nasroallah. "Estimation of steady-state quantities of an HMM with some rarely generated emissions." Monte Carlo Methods and Applications 28, no. 1 (February 15, 2022): 27–44. http://dx.doi.org/10.1515/mcma-2022-2103.

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Abstract 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.

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23

Ben Zaabza, H., E. A. Mäntysaari, and I. Strandén. "Estimation of individual animal SNP-BLUP reliability using full Monte Carlo sampling." JDS Communications 2, no. 3 (May 2021): 137–41. http://dx.doi.org/10.3168/jdsc.2020-0058.

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24

Saha, S., and S. M. Kay. "Maximum likelihood parameter estimation of superimposed chirps using Monte Carlo importance sampling." IEEE Transactions on Signal Processing 50, no. 2 (2002): 224–30. http://dx.doi.org/10.1109/78.978378.

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25

Guha, Subharup, and Steven N. MacEachern. "Generalized Poststratification and Importance Sampling for Subsampled Markov Chain Monte Carlo Estimation." Journal of the American Statistical Association 101, no. 475 (September 2006): 1175–84. http://dx.doi.org/10.1198/016214506000000474.

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26

Müller, Christoph, T. Rütting, J. Kattge, R. J. Laughlin, and R. J. Stevens. "Estimation of parameters in complex 15N tracing models by Monte Carlo sampling." Soil Biology and Biochemistry 39, no. 3 (March 2007): 715–26. http://dx.doi.org/10.1016/j.soilbio.2006.09.021.

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27

Xu, Yuanwei, and P. Mark Rodger. "Improved Estimation of Density of States for Monte Carlo Sampling via MBAR." Journal of Chemical Theory and Computation 11, no. 10 (September 2015): 4565–72. http://dx.doi.org/10.1021/acs.jctc.5b00189.

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28

Blasone, Roberta-Serena, Jasper A. Vrugt, Henrik Madsen, Dan Rosbjerg, Bruce A. Robinson, and George A. Zyvoloski. "Generalized likelihood uncertainty estimation (GLUE) using adaptive Markov Chain Monte Carlo sampling." Advances in Water Resources 31, no. 4 (April 2008): 630–48. http://dx.doi.org/10.1016/j.advwatres.2007.12.003.

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29

Swain, J. J., and B. W. Schmeiser. "Monte carlo estimation of the sampling distribution of nonlinear model parameter estimators." Annals of Operations Research 8, no. 1 (December 1987): 243–56. http://dx.doi.org/10.1007/bf02187095.

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30

Huang, S. R. "Effectiveness of optimum stratified sampling and estimation in Monte Carlo production simulation." IEEE Transactions on Power Systems 12, no. 2 (May 1997): 566–72. http://dx.doi.org/10.1109/59.589605.

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31

Talbot, J., P. Bereolos, and K. C. Chao. "Estimation of free energy via single particle sampling in Monte Carlo simulations." Journal of Chemical Physics 98, no. 2 (January 15, 1993): 1531–33. http://dx.doi.org/10.1063/1.464268.

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32

Gu, Minghao, Shiliang Sun, and Yan Liu. "Dynamical Sampling with Langevin Normalization Flows." Entropy 21, no. 11 (November 10, 2019): 1096. http://dx.doi.org/10.3390/e21111096.

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In Bayesian machine learning, sampling methods provide the asymptotically unbiased estimation for the inference of the complex probability distributions, where Markov chain Monte Carlo (MCMC) is one of the most popular sampling methods. However, MCMC can lead to high autocorrelation of samples or poor performances in some complex distributions. In this paper, we introduce Langevin diffusions to normalization flows to construct a brand-new dynamical sampling method. We propose the modified Kullback-Leibler divergence as the loss function to train the sampler, which ensures that the samples generated from the proposed method can converge to the target distribution. Since the gradient function of the target distribution is used during the process of calculating the modified Kullback-Leibler, which makes the integral of the modified Kullback-Leibler intractable. We utilize the Monte Carlo estimator to approximate this integral. We also discuss the situation when the target distribution is unnormalized. We illustrate the properties and performances of the proposed method on varieties of complex distributions and real datasets. The experiments indicate that the proposed method not only takes the advantage of the flexibility of neural networks but also utilizes the property of rapid convergence to the target distribution of the dynamics system and demonstrate superior performances competing with dynamics based MCMC samplers.

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Ross, Keith W., and Jie Wang. "Monte Carlo Summation Applied to Product-Form Loss Networks." Probability in the Engineering and Informational Sciences 6, no. 3 (July 1992): 323–48. http://dx.doi.org/10.1017/s0269964800002576.

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Loss networks with direct routing have a product-form solution for their equilibrium probabilities. The product-form solution typically involves a normalization constant calling for a multidimensional summation over an astronomical number of states. We propose the application of Monte Carlo summation in order to determine the normalization constant, the blocking probabilities, and the revenue sensitivities. We show that if the proper sampling technique is employed, then the computational effort of Monte Carlo summation is independent of link capacities. We also discuss the application of importance sampling, antithetic variates, and indirect estimation via Little's formula. The method is illustrated with a four-leaf star network supporting multirate traffic.

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Bastin, Fabian, Cinzia Cirillo, and Stephane Hess. "Evaluation of Optimization Methods for Estimating Mixed Logit Models." Transportation Research Record: Journal of the Transportation Research Board 1921, no. 1 (January 2005): 35–43. http://dx.doi.org/10.1177/0361198105192100105.

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The performances of different simulation-based estimation techniques for mixed logit modeling are evaluated. A quasi–Monte Carlo method (modified Latin hypercube sampling) is compared with a Monte Carlo algorithm with dynamic accuracy. The classic Broyden–Fletcher–Goldfarb–Shanno (BFGS) optimization algorithm line-search approach and trust region methods, which have proved to be extremely powerful in nonlinear programming, are also compared. Numerical tests are performed on two real data sets: stated preference data for parking type collected in the United Kingdom, and revealed preference data for mode choice collected as part of a German travel diary survey. Several criteria are used to evaluate the approximation quality of the log likelihood function and the accuracy of the results and the associated estimation runtime. Results suggest that the trust region approach outperforms the BFGS approach and that Monte Carlo methods remain competitive with quasi–Monte Carlo methods in high-dimensional problems, especially when an adaptive optimization algorithm is used.

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Laureau, Axel, Vincent Lamirand, Dimitri Rochman, and Andreas Pautz. "Total Monte Carlo acceleration for the PETALE experimental programme in the CROCUS reactor." EPJ Web of Conferences 211 (2019): 03002. http://dx.doi.org/10.1051/epjconf/201921103002.

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The Bayesian Monte Carlo technics requires individual evaluations of random cross section files based on a Total Monte Carlo propagation. This article discusses the use of a Correlated Sampling acceleration applied to TMC calculations for experiments where a brute force technics is too expensive. An e_cient estimation of the reaction rate uncertainties in small dosimeters is obtained, together with the inter-dosimeter correlation associated to the cross section uncertainties.

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Mahdizadeh, M., and Ehsan Zamanzade. "Dynamic reliability estimation in a rank-based design." Probability and Mathematical Statistics 39, no. 1 (June 10, 2019): 1–18. http://dx.doi.org/10.19195/0208-4147.39.1.1.

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Ranked set sampling RSS is a data collection method that allows us to direct attention toward measurements of more representative sample units. This article deals with estimating a time-dependent reliability measure under a generalization of the RSS. Some results concerning optimal properties of the proposed estimator are presented. Monte Carlo simulation is employed to assess performance of the estimator. A sport data set is finally analyzed.

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Jin, Nai Gao, Fei Mo Li, and Zhao Xing Li. "Quasi-Monte Carlo Gaussian Particle Filtering Acceleration Using CUDA." Applied Mechanics and Materials 130-134 (October 2011): 3311–15. http://dx.doi.org/10.4028/www.scientific.net/amm.130-134.3311.

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A CUDA accelerated Quasi-Monte Carlo Gaussian particle filter (QMC-GPF) is proposed to deal with real-time non-linear non-Gaussian problems. GPF is especially suitable for parallel implementation as a result of the elimination of resampling step. QMC-GPF is an efficient counterpart of GPF using QMC sampling method instead of MC. Since particles generated by QMC method provides the best-possible distribution in the sampling space, QMC-GPF can make more accurate estimation with the same number of particles compared with traditional particle filter. Experimental results show that our GPU implementation of QMC-GPF can achieve the maximum speedup ratio of 95 on NVIDIA GeForce GTX 460.

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Asmussen, Søren, and Dirk P. Kroese. "Improved algorithms for rare event simulation with heavy tails." Advances in Applied Probability 38, no. 2 (June 2006): 545–58. http://dx.doi.org/10.1239/aap/1151337084.

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The estimation of P(Sn>u) by simulation, where Sn is the sum of independent, identically distributed random varibles Y1,…,Yn, is of importance in many applications. We propose two simulation estimators based upon the identity P(Sn>u)=nP(Sn>u, Mn=Yn), where Mn=max(Y1,…,Yn). One estimator uses importance sampling (for Yn only), and the other uses conditional Monte Carlo conditioning upon Y1,…,Yn−1. Properties of the relative error of the estimators are derived and a numerical study given in terms of the M/G/1 queue in which n is replaced by an independent geometric random variable N. The conclusion is that the new estimators compare extremely favorably with previous ones. In particular, the conditional Monte Carlo estimator is the first heavy-tailed example of an estimator with bounded relative error. Further improvements are obtained in the random-N case, by incorporating control variates and stratification techniques into the new estimation procedures.

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Krauße, T., and J. Cullmann. "Identification of hydrological model parameters for flood forecasting using data depth measures." Hydrology and Earth System Sciences Discussions 8, no. 2 (March 7, 2011): 2423–76. http://dx.doi.org/10.5194/hessd-8-2423-2011.

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Abstract. The development of methods for estimating the parameters of hydrological models considering uncertainties has been of high interest in hydrological research over the last years. Besides the very popular Markov Chain Monte Carlo (MCMC) methods which estimate the uncertainty of model parameters in the settings of a Bayesian framework, the development of depth based sampling methods, also entitled robust parameter estimation (ROPE), have attracted an increasing research interest. These methods understand the estimation of model parameters as a geometric search of a set of robust performing parameter vectors by application of the concept of data depth. Recent studies showed that the parameter vectors estimated by depth based sampling perform more robust in validation. One major advantage of this kind of approach over the MCMC methods is that the formulation of a likelihood function within a Bayesian uncertainty framework gets obsolete and arbitrary purpose-oriented performance criteria defined by the user can be integrated without any further complications. In this paper we present an advanced ROPE method entitled the Advanced Robust Parameter Estimation by Monte Carlo algorithm (AROPEMC). The AROPEMC algorithm is a modified version of the original robust parameter estimation algorithm ROPEMC developed by Bárdossy and Singh (2008). AROPEMC performs by merging iterative Monte Carlo simulations, identifying well performing parameter vectors, the sampling of robust parameter vectors according to the principle of data depth and the application of a well-founded stopping criterion applied in supervised machine learning. The principals of the algorithm are illustrated by means of the Rosenbrock's and Rastrigin's function, two well known performance benchmarks for optimisation algorithms. Two case studies demonstrate the advantage of AROPEMC compared to state of the art global optimisation algorithms. A distributed process-oriented hydrological model is calibrated and validated for flood forecasting in a small catchment characterised by extreme process dynamics.

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Cronin, Beau, Ian H. Stevenson, Mriganka Sur, and Konrad P. Körding. "Hierarchical Bayesian Modeling and Markov Chain Monte Carlo Sampling for Tuning-Curve Analysis." Journal of Neurophysiology 103, no. 1 (January 2010): 591–602. http://dx.doi.org/10.1152/jn.00379.2009.

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A central theme of systems neuroscience is to characterize the tuning of neural responses to sensory stimuli or the production of movement. Statistically, we often want to estimate the parameters of the tuning curve, such as preferred direction, as well as the associated degree of uncertainty, characterized by error bars. Here we present a new sampling-based, Bayesian method that allows the estimation of tuning-curve parameters, the estimation of error bars, and hypothesis testing. This method also provides a useful way of visualizing which tuning curves are compatible with the recorded data. We demonstrate the utility of this approach using recordings of orientation and direction tuning in primary visual cortex, direction of motion tuning in primary motor cortex, and simulated data.

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Zhao, Lei, Bing Li, and Peng Xiang Diwu. "Reservoir Volume Estimation in Exploration Phase by Monte Carlo Simulation." Advanced Materials Research 859 (December 2013): 248–52. http://dx.doi.org/10.4028/www.scientific.net/amr.859.248.

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The STOIIP determines the scale of civil engineering in the oilfield, so the accurate calculation STOIIP has a very important significance on civil engineering, especially in the exploration phase few data are available in oilfield, traditional volume calculation method is hardly to provide a reasonable result. The mathematical statistics method, namely Monte Carlo simulation is introduced to calculate reservoir volumes for hydrocarbons in place (STOIIP or GIIP). This method can provide several volume results by monte carlo sampling. making the resource assessment results a probability distribution rather than a single valuation, which greatly improve the credibility and usefulness of evaluation results. The S oilfield in Malaysia are evaluated and the results show the P50 STOIIP is 4.82 MMbbl.

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Graf, Peter, Katherine Dykes, Rick Damiani, Jason Jonkman, and Paul Veers. "Adaptive stratified importance sampling: hybridization of extrapolation and importance sampling Monte Carlo methods for estimation of wind turbine extreme loads." Wind Energy Science 3, no. 2 (July 11, 2018): 475–87. http://dx.doi.org/10.5194/wes-3-475-2018.

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Abstract. Wind turbine extreme load estimation is especially difficult because turbulent inflow drives nonlinear turbine physics and control strategies; thus there can be huge differences in turbine response to essentially equivalent environmental conditions. The two main current approaches, extrapolation and Monte Carlo sampling, are both unsatisfying: extrapolation-based methods are dangerous because by definition they make predictions outside the range of available data, but Monte Carlo methods converge too slowly to routinely reach the desired 50-year return period estimates. Thus a search for a better method is warranted. Here we introduce an adaptive stratified importance sampling approach that allows for treating the choice of environmental conditions at which to run simulations as a stochastic optimization problem that minimizes the variance of unbiased estimates of extreme loads. Furthermore, the framework, built on the traditional bin-based approach used in extrapolation methods, provides a close connection between sampling and extrapolation, and thus allows the solution of the stochastic optimization (i.e., the optimal distribution of simulations in different wind speed bins) to guide and recalibrate the extrapolation. Results show that indeed this is a promising approach, as the variance of both the Monte Carlo and extrapolation estimates are reduced quickly by the adaptive procedure. We conclude, however, that due to the extreme response variability in turbine loads to the same environmental conditions, our method and any similar method quickly reaches its fundamental limits, and that therefore our efforts going forward are best spent elucidating the underlying causes of the response variability.

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Martinásková, Magdalena, and Miroslav Vořechovský. "Failure Probability Estimation Using Asymptotic Sampling and Its Dependence upon the Selected Sampling Scheme." Transactions of the VŠB – Technical University of Ostrava, Civil Engineering Series. 17, no. 2 (December 1, 2017): 65–72. http://dx.doi.org/10.1515/tvsb-2017-0029.

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Abstract The article examines the use of Asymptotic Sampling (AS) for the estimation of failure probability. The AS algorithm requires samples of multidimensional Gaussian random vectors, which may be obtained by many alternative means that influence the performance of the AS method. Several reliability problems (test functions) have been selected in order to test AS with various sampling schemes: (i) Monte Carlo designs; (ii) LHS designs optimized using the Periodic Audze-Eglājs (PAE) criterion; (iii) designs prepared using Sobol’ sequences. All results are compared with the exact failure probability value.

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Li, Cheng, Sanvesh Srivastava, and David B. Dunson. "Simple, scalable and accurate posterior interval estimation." Biometrika 104, no. 3 (June 25, 2017): 665–80. http://dx.doi.org/10.1093/biomet/asx033.

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Summary Standard posterior sampling algorithms, such as Markov chain Monte Carlo procedures, face major challenges in scaling up to massive datasets. We propose a simple and general posterior interval estimation algorithm to rapidly and accurately estimate quantiles of the posterior distributions for one-dimensional functionals. Our algorithm runs Markov chain Monte Carlo in parallel for subsets of the data, and then averages quantiles estimated from each subset. We provide strong theoretical guarantees and show that the credible intervals from our algorithm asymptotically approximate those from the full posterior in the leading parametric order. Our algorithm has a better balance of accuracy and efficiency than its competitors across a variety of simulations and a real-data example.

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Hassan, Marwa K. H., and Abdisalam Hassan Muse. "Fuzzy Stress-Strength Model and Mean Remaining Strength for Lindley Distribution: Estimation and Application in Cancer of Benign Endocrine." Computational and Mathematical Methods in Medicine 2023 (November 2, 2023): 1–14. http://dx.doi.org/10.1155/2023/8952946.

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This paper is interested in the Bayesian and non-Bayesian estimation of the stress-strength model and the mean remaining strength when there is fuzziness for stress and strength random variables having Lindley’s distribution with different parameters. A fuzzy is defined as a function of the difference between stress and strength variables. In the context of Bayesian estimation, two approximate algorithms are used importance sampling algorithm and the Monte Carlo Markov chain algorithm. For non-Bayesian estimation, maximum likelihood estimation and maximum product of spacing method are used. The Monte Carlo simulation study is performed to compare between different estimators for our proposed models using statistical criteria. Finally, to show the ability of our proposed models in real life, real medical application is introduced.

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Sabry, Mohamed Abd Elhamed, Hiba Zeyada Muhammed, Mostafa Shaaban, and Abd El Hady Nabih. "Parameter Estimation Based on Double Ranked Set Samples with Applications to Weibull Distribution." Journal of Modern Applied Statistical Methods 19, no. 1 (January 6, 2022): 2–24. http://dx.doi.org/10.22237/jmasm/1619482260.

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In this paper, the likelihood function for parameter estimation based on double ranked set sampling (DRSS) schemes is introduced. The proposed likelihood function is used for the estimation of the Weibull distribution parameters. The maximum likelihood estimators (MLEs) are investigated and compared to the corresponding ones based on simple random sampling (SRS) and ranked set sampling (RSS) schemes. A Monte Carlo simulation is conducted and the absolute relative biases, mean square errors, and efficiencies are compared for the different schemes. It is found that, the MLEs based on DRSS is more efficient than MLE using SRS and RSS for estimating the two parameters of the Weibull distribution (WD).

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XU, QING, WEI WANG, and SHIQIANG BAO. "A NEW COMPUTATIONAL WAY TO MONTE CARLO GLOBAL ILLUMINATION." International Journal of Image and Graphics 06, no. 01 (January 2006): 23–34. http://dx.doi.org/10.1142/s0219467806002057.

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In this paper, we present a new Monte Carlo computational way for solving the global illumination problem whereby plenty of unbiased estimators can be employed to enrich the solutions leading to simple error control and faster estimation. Especially so, the zero variance importance sampling procedure can be exploited to calculate the global illumination optimally. Based on the new scheme, a new Monte Carlo global illumination algorithm and its importance driven version have been developed and carried out. Results, which have been obtained by rendering test scenes, show that this new framework is promising.

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Bin, Li, Rashana Abbas, Muhammad Shahzad, and Nouman Safdar. "Probabilistic Load Flow Analysis Using Nonparametric Distribution." Sustainability 16, no. 1 (December 27, 2023): 240. http://dx.doi.org/10.3390/su16010240.

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In the pursuit of sustainable energy solutions, this research addresses the critical need for accurate probabilistic load flow (PLF) analysis in power systems. PLF analysis is an essential tool for estimating the statistical behavior of power systems under uncertainty. It plays a vital part in power system planning, operation, and dependability studies. To perform accurate PLF analysis, this article proposes a Kernel density estimation with adaptive bandwidth for probability density function (PDF) estimation of power injections from sustainable energy sources like solar and wind, reducing errors in PDF estimation. To reduce the computational burden, a Latin hypercube sampling approach was incorporated. Input random variables are modeled using kernel density estimation (KDE) in conjunction with Latin hypercube sampling (LHS) for probabilistic load flow (PLF) analysis. To test the proposed techniques, IEEE 14 and IEEE 118 bus systems are used. Two benchmark techniques, the Monte Carlo Simulation (MCS) method and Hamiltonian Monte Carlo (HMC), were set side by side for validation of results. The results illustrate that an adaptive bandwidth kernel density estimation with the Latin hypercube sampling (AKDE-LHS) method provides better performance in terms of precision and computational efficiency. The results also show that the suggested technique is more feasible in reducing errors, uncertainties, and computational time while depicting arbitrary distributions of photovoltaic and wind farms for probabilistic load flow analysis. It can be a potential solution to tackle challenges posed by sustainable energy sources in power systems.

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Gent, David H., William W. Turechek, and Walter F. Mahaffee. "Sequential Sampling for Estimation and Classification of the Incidence of Hop Powdery Mildew I: Leaf Sampling." Plant Disease 91, no. 8 (August 2007): 1002–12. http://dx.doi.org/10.1094/pdis-91-8-1002.

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Hop powdery mildew (caused by Podosphaera macularis) is an important disease of hops (Humulus lupulus) in the Pacific Northwest. Sequential sampling models for estimation and classification of the incidence of powdery mildew on leaves of hop were developed based on the beta-binomial distribution, using parameter estimates of the binary power law determined in previous studies. Stop lines, models that indicate that enough information has been collected to estimate disease incidence and cease sampling, for sequential estimation were validated by bootstrap simulations of a select group of 18 data sets (out of a total of 198 data sets) from the model-construction data, and through simulated sampling of 104 data sets collected independently (i.e., validation data sets). The achieved coefficient of variation (C) approached prespecified C values as the achieved disease incidence ([Formula: see text]) increased. Achieving a C of 0.1 was not possible for data sets in which [Formula: see text] < 0.10. The 95% confidence interval of the median difference between the true p and [Formula: see text] included zero for 16 of 18 data sets evaluated at C = 0.2 and all data sets when C = 0.1. For sequential classification, Monte-Carlo simulations were used to determine the probability of classifying mean disease incidence as less than a threshold incidence, pt (operating characteristic [OC]), and average sample number (ASN) curves for 16 combinations of candidate stop lines and error levels (α and β). Four pairs of stop lines were selected for further evaluation based on the results of the Monte-Carlo simulations. Bootstrap simulations of the 18 selected data sets indicated that the OC and ASN curves of the sequential sampling plans for each of the four sets of stop lines were similar to OC and ASN values determined by Monte Carlo simulation. Correct classification of disease incidence as being above or below preselected thresholds was 2.0 to 7.7% higher when stop lines were determined by the beta-binomial approximation than when stop lines were calculated using the binomial distribution. Correct decision rates differed depending on the location where sampling was initiated in the hop yard; however, in all instances were greater than 86% when stop lines were determined using the beta-binomial approximation. The sequential sampling plans evaluated in this study should allow for rapid and accurate estimation and classification of the incidence of hop leaves with powdery mildew, and aid in sampling for pest management decision making.

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Fishman, George S. "A Monte Carlo Sampling Plan for Estimating Network Reliability." Operations Research 34, no. 4 (August 1986): 581–94. http://dx.doi.org/10.1287/opre.34.4.581.

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