Prediction intervals(PIs)for industrial time series can provide useful guidance for workers.Given that the failure of industrial sensors may cause the missing point in inputs,the existing kernel dynamic Bayesian netwo...Prediction intervals(PIs)for industrial time series can provide useful guidance for workers.Given that the failure of industrial sensors may cause the missing point in inputs,the existing kernel dynamic Bayesian networks(KDBN),serving as an effective method for PIs construction,suffer from high computational load using the stochastic algorithm for inference.This study proposes a variational inference method for the KDBN for the purpose of fast inference,which avoids the timeconsuming stochastic sampling.The proposed algorithm contains two stages.The first stage involves the inference of the missing inputs by using a local linearization based variational inference,and based on the computed posterior distributions over the missing inputs the second stage sees a Gaussian approximation for probability over the nodes in future time slices.To verify the effectiveness of the proposed method,a synthetic dataset and a practical dataset of generation flow of blast furnace gas(BFG)are employed with different ratios of missing inputs.The experimental results indicate that the proposed method can provide reliable PIs for the generation flow of BFG and it exhibits shorter computing time than the stochastic based one.展开更多
In this article, analytical results are obtained apparently for the first time in the literature, for the lower and upper bounds of the roots of quadratic equations when two or all three coefficients a, b, c constitut...In this article, analytical results are obtained apparently for the first time in the literature, for the lower and upper bounds of the roots of quadratic equations when two or all three coefficients a, b, c constitute an interval, with a method called the sign-variation analysis. The results are compared with the parametrization technique offered by Elishakoff and Miglis, and with the solution yielded by minimization and maximization commands of the Maple software. Solutions for some interval word problems are also provided to edulcorate the methodology. This article only focuses on the real roots of those quadratic equations, complex solutions being beyond this investigation.展开更多
In data envelopment analysis (DEA), input and output values are subject to change for several reasons. Such variations differ in their input/output items and their decision-making units (DMUs). Hence, DEA efficiency s...In data envelopment analysis (DEA), input and output values are subject to change for several reasons. Such variations differ in their input/output items and their decision-making units (DMUs). Hence, DEA efficiency scores need to be examined by considering these factors. In this paper, we propose new resampling models based on these variations for gauging the confidence intervals of DEA scores. The first model utilizes past-present data for estimating data variations imposing chronological order weights which are supplied by Lucas series (a variant of Fibonacci series). The second model deals with future prospects. This model aims at forecasting the future efficiency score and its confidence interval for each DMU. We applied our models to a dataset composed of Japanese municipal hospitals.展开更多
Accurately forecasting gasoline volatility is significant for risk management,economic analysis,and option pricing formulas for future contracts.This study proposes a novel interval-valued hierarchical decomposition a...Accurately forecasting gasoline volatility is significant for risk management,economic analysis,and option pricing formulas for future contracts.This study proposes a novel interval-valued hierarchical decomposition and ensemble(IHDE)approach to investigate gasoline price volatility.Our interval-based IHDE method can decompose the complex price process into different components to capture the distinct features of each component,which is helpful for forecasting and analyzing complex price processes.By using interval-valued data,the dynamics of gasoline prices in terms of levels and variations can be fully utilized in this study.Fully utilizing the informational gain of interval-valued data improves forecasting performance.In forecasting weekly gasoline volatility,we document that the proposed IHDE approach outperforms the GARCH,EGARCH,CARR,and ACI models,indicating the importance of capturing features of different frequency components and utilizing the informational gain of interval-valued data for gasoline volatility forecasts.展开更多
Although there are many measures of variability for qualitative variables, they are little used in social research, nor are they included in statistical software. The aim of this article is to present six measures of ...Although there are many measures of variability for qualitative variables, they are little used in social research, nor are they included in statistical software. The aim of this article is to present six measures of variation for qualitative variables of simple calculation, as well as to facilitate their use by means of the R software. The measures considered are, on the one hand, Freemans variation ratio, Morals universal variation ratio, Kvalseths standard deviation from the mode, and Wilcoxs variation ratio which are most affected by proximity to a constant random variable, where the measures of variability for qualitative variables reach their minimum value of 0. On the other hand, the Gibbs-Poston index of qualitative variation and Shannons relative entropy are included, which are more affected by the proximity to a uniform distribution, where the measures of variability for qualitative variables reach their maximum value of 1. Point and interval estimation are addressed. Bootstrap by the percentile and bias-corrected and accelerated percentile methods are used to obtain confidence intervals. Two calculation situations are presented: with a sample mode and with two or more modes. The standard deviation from the mode among the six considered measures, and the universal variation ratio among the three variation ratios, are particularly recommended for use.展开更多
基金supported by the National Key Research andDevelopment Program of China(2017YFA0700300)the National Natural Sciences Foundation of China(61533005,61703071,61603069)。
文摘Prediction intervals(PIs)for industrial time series can provide useful guidance for workers.Given that the failure of industrial sensors may cause the missing point in inputs,the existing kernel dynamic Bayesian networks(KDBN),serving as an effective method for PIs construction,suffer from high computational load using the stochastic algorithm for inference.This study proposes a variational inference method for the KDBN for the purpose of fast inference,which avoids the timeconsuming stochastic sampling.The proposed algorithm contains two stages.The first stage involves the inference of the missing inputs by using a local linearization based variational inference,and based on the computed posterior distributions over the missing inputs the second stage sees a Gaussian approximation for probability over the nodes in future time slices.To verify the effectiveness of the proposed method,a synthetic dataset and a practical dataset of generation flow of blast furnace gas(BFG)are employed with different ratios of missing inputs.The experimental results indicate that the proposed method can provide reliable PIs for the generation flow of BFG and it exhibits shorter computing time than the stochastic based one.
文摘In this article, analytical results are obtained apparently for the first time in the literature, for the lower and upper bounds of the roots of quadratic equations when two or all three coefficients a, b, c constitute an interval, with a method called the sign-variation analysis. The results are compared with the parametrization technique offered by Elishakoff and Miglis, and with the solution yielded by minimization and maximization commands of the Maple software. Solutions for some interval word problems are also provided to edulcorate the methodology. This article only focuses on the real roots of those quadratic equations, complex solutions being beyond this investigation.
文摘In data envelopment analysis (DEA), input and output values are subject to change for several reasons. Such variations differ in their input/output items and their decision-making units (DMUs). Hence, DEA efficiency scores need to be examined by considering these factors. In this paper, we propose new resampling models based on these variations for gauging the confidence intervals of DEA scores. The first model utilizes past-present data for estimating data variations imposing chronological order weights which are supplied by Lucas series (a variant of Fibonacci series). The second model deals with future prospects. This model aims at forecasting the future efficiency score and its confidence interval for each DMU. We applied our models to a dataset composed of Japanese municipal hospitals.
基金Supported by National Natural Science Foundation of China(72322016,72073126,71988101)Beijing Natural Science Foundation(9254024)。
文摘Accurately forecasting gasoline volatility is significant for risk management,economic analysis,and option pricing formulas for future contracts.This study proposes a novel interval-valued hierarchical decomposition and ensemble(IHDE)approach to investigate gasoline price volatility.Our interval-based IHDE method can decompose the complex price process into different components to capture the distinct features of each component,which is helpful for forecasting and analyzing complex price processes.By using interval-valued data,the dynamics of gasoline prices in terms of levels and variations can be fully utilized in this study.Fully utilizing the informational gain of interval-valued data improves forecasting performance.In forecasting weekly gasoline volatility,we document that the proposed IHDE approach outperforms the GARCH,EGARCH,CARR,and ACI models,indicating the importance of capturing features of different frequency components and utilizing the informational gain of interval-valued data for gasoline volatility forecasts.
文摘Although there are many measures of variability for qualitative variables, they are little used in social research, nor are they included in statistical software. The aim of this article is to present six measures of variation for qualitative variables of simple calculation, as well as to facilitate their use by means of the R software. The measures considered are, on the one hand, Freemans variation ratio, Morals universal variation ratio, Kvalseths standard deviation from the mode, and Wilcoxs variation ratio which are most affected by proximity to a constant random variable, where the measures of variability for qualitative variables reach their minimum value of 0. On the other hand, the Gibbs-Poston index of qualitative variation and Shannons relative entropy are included, which are more affected by the proximity to a uniform distribution, where the measures of variability for qualitative variables reach their maximum value of 1. Point and interval estimation are addressed. Bootstrap by the percentile and bias-corrected and accelerated percentile methods are used to obtain confidence intervals. Two calculation situations are presented: with a sample mode and with two or more modes. The standard deviation from the mode among the six considered measures, and the universal variation ratio among the three variation ratios, are particularly recommended for use.
