Photovoltaic(PV)systems are widely spread across MV and LV distribution systems and the penetration of PV generation is solidly growing.Because of the uncertain nature of the solar energy resource,PV power forecasting...Photovoltaic(PV)systems are widely spread across MV and LV distribution systems and the penetration of PV generation is solidly growing.Because of the uncertain nature of the solar energy resource,PV power forecasting models are crucial in any energy management system for smart distribution networks.Although point forecasts can suit many scopes,probabilistic forecasts add further flexibility to an energy management system and are recommended to enable a wider range of decision making and optimization strategies.This paper proposes methodology towards probabilistic PV power forecasting based on a Bayesian bootstrap quantile regression model,in which a Bayesian bootstrap is applied to estimate the parameters of a quantile regression model.A novel procedure is presented to optimize the extraction of the predictive quantiles from the bootstrapped estimation of the related coefficients,raising the predictive ability of the final forecasts.Numerical experiments based on actual data quantify an enhancement of the performance of up to 2.2%when compared to relevant benchmarks.展开更多
Hydrological risk is highly dependent on the occurrence of extreme rainfalls.This fact has led to a wide range of studies on the estimation and uncertainty analysis of the extremes.In most cases,confidence intervals(C...Hydrological risk is highly dependent on the occurrence of extreme rainfalls.This fact has led to a wide range of studies on the estimation and uncertainty analysis of the extremes.In most cases,confidence intervals(CIs)are constructed to represent the uncertainty of the estimates.Since the accuracy of CIs depends on the asymptotic normality of the data and is questionable with limited observations in practice,a Bayesian highest posterior density(HPD)interval,bootstrap percentile interval,and profile likelihood(PL)interval have been introduced to analyze the uncertainty that does not depend on the normality assumption.However,comparison studies to investigate their performances in terms of the accuracy and uncertainty of the estimates are scarce.In addition,the strengths,weakness,and conditions necessary for performing each method also must be investigated.Accordingly,in this study,test experiments with simulations from varying parent distributions and different sample sizes were conducted.Then,applications to the annual maximum rainfall(AMR)time series data in South Korea were performed.Five districts with 38-year(1973–2010)AMR observations were fitted by the three aforementioned methods in the application.From both the experimental and application results,the Bayesian method is found to provide the lowest uncertainty of the design level while the PL estimates generally have the highest accuracy but also the largest uncertainty.The bootstrap estimates are usually inferior to the other two methods,but can perform adequately when the distribution model is not heavy-tailed and the sample size is large.The distribution tail behavior and the sample size are clearly found to affect the estimation accuracy and uncertainty.This study presents a comparative result,which can help researchers make decisions in the context of assessing extreme rainfall uncertainties.展开更多
In this paper we propose a consistent and asymptotically normal estimator (CAN) of intensities ρ1 , ρ2 for a queueing network with feedback (in which a job may return to previously visited nodes) with distribution-f...In this paper we propose a consistent and asymptotically normal estimator (CAN) of intensities ρ1 , ρ2 for a queueing network with feedback (in which a job may return to previously visited nodes) with distribution-free inter-arrival and service times. Using this estimator and its estimated variance, some 100(1-α)% asymptotic confidence intervals of intensities are constructed. Also bootstrap approaches such as Standard bootstrap, Bayesian bootstrap, Percentile bootstrap and Bias-corrected and accelerated bootstrap are also applied to develop the confidence intervals of intensities. A comparative analysis is conducted to demonstrate performances of the confidence intervals of intensities for a queueing network with short run data.展开更多
In the Fay–Herriot model,we consider estimators of the linking variance obtained using different types of resampling schemes.The usefulness of this approach is that even when the estimator from the original data fall...In the Fay–Herriot model,we consider estimators of the linking variance obtained using different types of resampling schemes.The usefulness of this approach is that even when the estimator from the original data falls below zero or any other specified threshold,several of the resamples can potentially yield values above the threshold.We establish asymptotic consistency of the resampling-based estimator of the linking variance for a wide variety of resampling schemes and show the efficacy of using the proposed approach in numeric examples.展开更多
This study aims to solve a typical long-term strategic decision problem on supply chain network design with consideration to uncertain demands. Existing methods for these problems are either deterministic or limited i...This study aims to solve a typical long-term strategic decision problem on supply chain network design with consideration to uncertain demands. Existing methods for these problems are either deterministic or limited in scale. We analyze the impact of uncertainty on demand based on actual large data from industrial companies.Deterministic equivalent model with nonanticipativity constraints, branch-and-fix coordination, sample average approximation(SAA) with Bayesian bootstrap, and Latin hypercube sampling were adopted to analyze stochastic demands. A computational study of supply chain network with front-ends in Europe and back-ends in Asia is presented to highlight the importance of stochastic factors in these problems and the efficiency of our proposed solution approach.展开更多
Recently, Kundu and Gupta （Metrika, 48：83 C 97, 1998） established the asymptotic normality of the least squares estimators in the two dimensional cosine model. In this paper, we give the approximation to the genera...Recently, Kundu and Gupta （Metrika, 48：83 C 97, 1998） established the asymptotic normality of the least squares estimators in the two dimensional cosine model. In this paper, we give the approximation to the general least squares estimators by using random weights which is called the Bayesian bootstrap or the random weighting method by Rubin （Annals of Statistics, 9：130 C 134, 1981） and Zheng （Acta Math. Appl. Sinica （in Chinese）, 10（2）： 247 C 253, 1987）. A simulation study shows that this approximation works very well.展开更多
基金supported by the Swiss Federal Office of Energy(SFOE)and by the Italian Ministry of Education,University and Research(MIUR),through the ERA-NET Smart Energy Systems RegSys joint call 2018 project“DiGRiFlex-Real time Distribution GRid control and Flexibility provision under uncertainties.”。
文摘Photovoltaic(PV)systems are widely spread across MV and LV distribution systems and the penetration of PV generation is solidly growing.Because of the uncertain nature of the solar energy resource,PV power forecasting models are crucial in any energy management system for smart distribution networks.Although point forecasts can suit many scopes,probabilistic forecasts add further flexibility to an energy management system and are recommended to enable a wider range of decision making and optimization strategies.This paper proposes methodology towards probabilistic PV power forecasting based on a Bayesian bootstrap quantile regression model,in which a Bayesian bootstrap is applied to estimate the parameters of a quantile regression model.A novel procedure is presented to optimize the extraction of the predictive quantiles from the bootstrapped estimation of the related coefficients,raising the predictive ability of the final forecasts.Numerical experiments based on actual data quantify an enhancement of the performance of up to 2.2%when compared to relevant benchmarks.
基金supported by Hanyang University(Grant No.HY-2014)
文摘Hydrological risk is highly dependent on the occurrence of extreme rainfalls.This fact has led to a wide range of studies on the estimation and uncertainty analysis of the extremes.In most cases,confidence intervals(CIs)are constructed to represent the uncertainty of the estimates.Since the accuracy of CIs depends on the asymptotic normality of the data and is questionable with limited observations in practice,a Bayesian highest posterior density(HPD)interval,bootstrap percentile interval,and profile likelihood(PL)interval have been introduced to analyze the uncertainty that does not depend on the normality assumption.However,comparison studies to investigate their performances in terms of the accuracy and uncertainty of the estimates are scarce.In addition,the strengths,weakness,and conditions necessary for performing each method also must be investigated.Accordingly,in this study,test experiments with simulations from varying parent distributions and different sample sizes were conducted.Then,applications to the annual maximum rainfall(AMR)time series data in South Korea were performed.Five districts with 38-year(1973–2010)AMR observations were fitted by the three aforementioned methods in the application.From both the experimental and application results,the Bayesian method is found to provide the lowest uncertainty of the design level while the PL estimates generally have the highest accuracy but also the largest uncertainty.The bootstrap estimates are usually inferior to the other two methods,but can perform adequately when the distribution model is not heavy-tailed and the sample size is large.The distribution tail behavior and the sample size are clearly found to affect the estimation accuracy and uncertainty.This study presents a comparative result,which can help researchers make decisions in the context of assessing extreme rainfall uncertainties.
文摘In this paper we propose a consistent and asymptotically normal estimator (CAN) of intensities ρ1 , ρ2 for a queueing network with feedback (in which a job may return to previously visited nodes) with distribution-free inter-arrival and service times. Using this estimator and its estimated variance, some 100(1-α)% asymptotic confidence intervals of intensities are constructed. Also bootstrap approaches such as Standard bootstrap, Bayesian bootstrap, Percentile bootstrap and Bias-corrected and accelerated bootstrap are also applied to develop the confidence intervals of intensities. A comparative analysis is conducted to demonstrate performances of the confidence intervals of intensities for a queueing network with short run data.
基金This research is partially supported by the National Science Foundation(NSF)[grant numbers#DMS-1622483 and#DMS-1737918].
文摘In the Fay–Herriot model,we consider estimators of the linking variance obtained using different types of resampling schemes.The usefulness of this approach is that even when the estimator from the original data falls below zero or any other specified threshold,several of the resamples can potentially yield values above the threshold.We establish asymptotic consistency of the resampling-based estimator of the linking variance for a wide variety of resampling schemes and show the efficacy of using the proposed approach in numeric examples.
文摘This study aims to solve a typical long-term strategic decision problem on supply chain network design with consideration to uncertain demands. Existing methods for these problems are either deterministic or limited in scale. We analyze the impact of uncertainty on demand based on actual large data from industrial companies.Deterministic equivalent model with nonanticipativity constraints, branch-and-fix coordination, sample average approximation(SAA) with Bayesian bootstrap, and Latin hypercube sampling were adopted to analyze stochastic demands. A computational study of supply chain network with front-ends in Europe and back-ends in Asia is presented to highlight the importance of stochastic factors in these problems and the efficiency of our proposed solution approach.
基金Supported by the National Natural Science Foundations of China(No.11271193)Humanities and Social Sciences Planning Foundation of Chinese Ministry of Education(11YJA910004)+1 种基金Natural Science Foundation of the Jiangsu Higher Education Institutions of China(11KJB110005)Key Research Base for Humanities and Social Sciences of Zhejiang Provincial High Education Talents(Statistics of Zhejiang Gongshang University)
文摘Recently, Kundu and Gupta （Metrika, 48：83 C 97, 1998） established the asymptotic normality of the least squares estimators in the two dimensional cosine model. In this paper, we give the approximation to the general least squares estimators by using random weights which is called the Bayesian bootstrap or the random weighting method by Rubin （Annals of Statistics, 9：130 C 134, 1981） and Zheng （Acta Math. Appl. Sinica （in Chinese）, 10（2）： 247 C 253, 1987）. A simulation study shows that this approximation works very well.
