This paper transforms fuzzy number into clear number using the centroid method, thus we can research the traditional linear regression model which is transformed from the fuzzy linear regression model. The model’s in...This paper transforms fuzzy number into clear number using the centroid method, thus we can research the traditional linear regression model which is transformed from the fuzzy linear regression model. The model’s input and output are fuzzy numbers, and the regression coefficients are clear numbers. This paper considers the parameter estimation and impact analysis based on data deletion. Through the study of example and comparison with other models, it can be concluded that the model in this paper is applied easily and better.展开更多
According to the appearing of isosbestic point in the absorption spectra of Ho/Y-Tribromoarsenazo (TBA)systems,the complexation reaction is considered to be M+nL=ML_n.A method has been proposed based on it for calcula...According to the appearing of isosbestic point in the absorption spectra of Ho/Y-Tribromoarsenazo (TBA)systems,the complexation reaction is considered to be M+nL=ML_n.A method has been proposed based on it for calculating the mole fraction of free complexing agent in the solutions from spectral data.and two linear regression formula have been introduced to determine the composition,the molar absorptivity,the conditional stability constant of the complex and the concentration of the complexing agent. This method has been used in Ho-TBA and Y-TBA systems.Ho^(3+)and Y^(3+)react with TBA and form 1: 2 complexes in HCl-NaAc buffer solution at pH 3.80.Their molar absorptivities determined are 1.03×10~8 and 1.10×10~8 cm^2·mol^(-1),and the conditional stability constants(logβ_2)are 11.37 and 11.15 respectively.After considering the pH effect in TBA complexing,their stability constants(log β_2^(ahs))are 43.23 and 43.01. respectively.The new method is adaptable to such systems where the accurate concentration of the complexing agent can not be known conveniently.展开更多
A new method,dual-series linear regression method,has been used to study the complexation equilibrium of praseodymium(Pr^(3+))with tribromoarsenazo(TBA)without knowing the accurate concentra- tion of the complexing ag...A new method,dual-series linear regression method,has been used to study the complexation equilibrium of praseodymium(Pr^(3+))with tribromoarsenazo(TBA)without knowing the accurate concentra- tion of the complexing agent TBA.In 1.2 mol/L HCl solution, Pr^(3+)reacts with TBA and forms 1:3 com- plex,the conditional stability constant(lgβ_3)of the complex determined is 15.47,and its molar absorptivity(ε_3^(630))is 1.48×10~5 L·mol^(-1)·cm^(-1).展开更多
The purpose of this study was to examine the burnout levels of research assistants in Ondokuz Mayis University and to examine the results of multiple linear regression model based on the results obtained from Maslach ...The purpose of this study was to examine the burnout levels of research assistants in Ondokuz Mayis University and to examine the results of multiple linear regression model based on the results obtained from Maslach Burnout Scale with Jackknife Method in terms of validity and generalizability. To do this, a questionnaire was given to 11 research assistants working at Ondokuz Mayis University and the burnout scores of this questionnaire were taken as the dependent variable of the multiple linear regression model. The variable of burnout was explained with the variables of age, weekly hours of classes taught, monthly average credit card debt, numbers of published articles and reports, gender, marital status, number of children and the departments of the research assistants. Dummy variables were assigned to the variables of gender, marital status, number of children and the departments of the research assistants and thus, they were made quantitative. The significance of the model as a result of multiple linear regressions was examined through backward elimination method. After this, for the five explanatory variables which influenced the variable of burnout, standardized model coefficients and coefficients of determination, and 95% confidence intervals of these values were estimated through Jackknife Method and the generalizability of the parameter estimation results of these variables on population was researched.展开更多
The development of prediction supports is a critical step in information systems engineering in this era defined by the knowledge economy, the hub of which is big data. Currently, the lack of a predictive model, wheth...The development of prediction supports is a critical step in information systems engineering in this era defined by the knowledge economy, the hub of which is big data. Currently, the lack of a predictive model, whether qualitative or quantitative, depending on a company’s areas of intervention can handicap or weaken its competitive capacities, endangering its survival. In terms of quantitative prediction, depending on the efficacy criteria, a variety of methods and/or tools are available. The multiple linear regression method is one of the methods used for this purpose. A linear regression model is a regression model of an explained variable on one or more explanatory variables in which the function that links the explanatory variables to the explained variable has linear parameters. The purpose of this work is to demonstrate how to use multiple linear regressions, which is one aspect of decisional mathematics. The use of multiple linear regressions on random data, which can be replaced by real data collected by or from organizations, provides decision makers with reliable data knowledge. As a result, machine learning methods can provide decision makers with relevant and trustworthy data. The main goal of this article is therefore to define the objective function on which the influencing factors for its optimization will be defined using the linear regression method.展开更多
Due to the heterogeneity of rock masses and the variability of in situ stress,the traditional linear inversion method is insufficiently accurate to achieve high accuracy of the in situ stress field.To address this cha...Due to the heterogeneity of rock masses and the variability of in situ stress,the traditional linear inversion method is insufficiently accurate to achieve high accuracy of the in situ stress field.To address this challenge,nonlinear stress boundaries for a numerical model are determined through regression analysis of a series of nonlinear coefficient matrices,which are derived from the bubbling method.Considering the randomness and flexibility of the bubbling method,a parametric study is conducted to determine recommended ranges for these parameters,including the standard deviation(σb)of bubble radii,the non-uniform coefficient matrix number(λ)for nonlinear stress boundaries,and the number(m)and positions of in situ stress measurement points.A model case study provides a reference for the selection of these parameters.Additionally,when the nonlinear in situ stress inversion method is employed,stress distortion inevitably occurs near model boundaries,aligning with the Saint Venant's principle.Two strategies are proposed accordingly:employing a systematic reduction of nonlinear coefficients to achieve high inversion accuracy while minimizing significant stress distortion,and excluding regions with severe stress distortion near the model edges while utilizing the central part of the model for subsequent simulations.These two strategies have been successfully implemented in the nonlinear in situ stress inversion of the Xincheng Gold Mine and have achieved higher inversion accuracy than the linear method.Specifically,the linear and nonlinear inversion methods yield root mean square errors(RMSE)of 4.15 and 3.2,and inversion relative errors(δAve)of 22.08%and 17.55%,respectively.Therefore,the nonlinear inversion method outperforms the traditional multiple linear regression method,even in the presence of a systematic reduction in the nonlinear stress boundaries.展开更多
The concept of missing data is important to apply statistical methods on the dataset. Statisticians and researchers may end up to an inaccurate illation about the data if the missing data are not handled properly. Of ...The concept of missing data is important to apply statistical methods on the dataset. Statisticians and researchers may end up to an inaccurate illation about the data if the missing data are not handled properly. Of late, Python and R provide diverse packages for handling missing data. In this study, an imputation algorithm, cumulative linear regression, is proposed. The proposed algorithm depends on the linear regression technique. It differs from the existing methods, in that it cumulates the imputed variables;those variables will be incorporated in the linear regression equation to filling in the missing values in the next incomplete variable. The author performed a comparative study of the proposed method and those packages. The performance was measured in terms of imputation time, root-mean-square error, mean absolute error, and coefficient of determination (R^2). On analysing on five datasets with different missing values generated from different mechanisms, it was observed that the performances vary depending on the size, missing percentage, and the missingness mechanism. The results showed that the performance of the proposed method is slightly better.展开更多
In the network technology era, the collected data are growing more and more complex, and become larger than before. In this article, we focus on estimates of the linear regression parameters for symbolic interval data...In the network technology era, the collected data are growing more and more complex, and become larger than before. In this article, we focus on estimates of the linear regression parameters for symbolic interval data. We propose two approaches to estimate regression parameters for symbolic interval data under two different data models and compare our proposed approaches with the existing methods via simulations. Finally, we analyze two real datasets with the proposed methods for illustrations.展开更多
A Mobile Ad-hoc NETwork(MANET)contains numerous mobile nodes,and it forms a structure-less network associated with wireless links.But,the node movement is the key feature of MANETs;hence,the quick action of the nodes ...A Mobile Ad-hoc NETwork(MANET)contains numerous mobile nodes,and it forms a structure-less network associated with wireless links.But,the node movement is the key feature of MANETs;hence,the quick action of the nodes guides a link failure.This link failure creates more data packet drops that can cause a long time delay.As a result,measuring accurate link failure time is the key factor in the MANET.This paper presents a Fuzzy Linear Regression Method to measure Link Failure(FLRLF)and provide an optimal route in the MANET-Internet of Things(IoT).This work aims to predict link failure and improve routing efficiency in MANET.The Fuzzy Linear Regression Method(FLRM)measures the long lifespan link based on the link failure.The mobile node group is built by the Received Signal Strength(RSS).The Hill Climbing(HC)method selects the Group Leader(GL)based on node mobility,node degree and node energy.Additionally,it uses a Data Gathering node forward the infor-mation from GL to the sink node through multiple GL.The GL is identified by linking lifespan and energy using the Particle Swarm Optimization(PSO)algo-rithm.The simulation results demonstrate that the FLRLF approach increases the GL lifespan and minimizes the link failure time in the MANET.展开更多
In this paper, we study some robustness aspects of linear regression models of the presence of outliers or discordant observations considering the use of stable distributions for the response in place of the usual nor...In this paper, we study some robustness aspects of linear regression models of the presence of outliers or discordant observations considering the use of stable distributions for the response in place of the usual normality assumption. It is well known that, in general, there is no closed form for the probability density function of stable distributions. However, under a Bayesian approach, the use of a latent or auxiliary random variable gives some simplification to obtain any posterior distribution when related to stable distributions. To show the usefulness of the computational aspects, the methodology is applied to two examples: one is related to a standard linear regression model with an explanatory variable and the other is related to a simulated data set assuming a 23 factorial experiment. Posterior summaries of interest are obtained using MCMC (Markov Chain Monte Carlo) methods and the OpenBugs software.展开更多
In this article,a procedure for estimating the coefficient functions on the functional-coefficient regression models with different smoothing variables in different coefficient functions is defined.First step,by the l...In this article,a procedure for estimating the coefficient functions on the functional-coefficient regression models with different smoothing variables in different coefficient functions is defined.First step,by the local linear technique and the averaged method,the initial estimates of the coefficient functions are given.Second step,based on the initial estimates,the efficient estimates of the coefficient functions are proposed by a one-step back-fitting procedure.The efficient estimators share the same asymptotic normalities as the local linear estimators for the functional-coefficient models with a single smoothing variable in different functions.Two simulated examples show that the procedure is effective.展开更多
芥菜作为我国特色蔬菜之一,是研究盐胁迫这种关键非生物胁迫因子对植物幼苗时期成长影响的优质实验材料。评估了132份芥菜种质资源在正常条件与从构建的适用于芥菜萌发成苗期的耐盐性鉴定体系所得的最适盐胁迫(1.0%NaCl)下的萌发表现及...芥菜作为我国特色蔬菜之一,是研究盐胁迫这种关键非生物胁迫因子对植物幼苗时期成长影响的优质实验材料。评估了132份芥菜种质资源在正常条件与从构建的适用于芥菜萌发成苗期的耐盐性鉴定体系所得的最适盐胁迫(1.0%NaCl)下的萌发表现及幼苗根系形态。根据生长状况以及各根系性状的耐盐指数并采用隶属函数法进行综合分析,得到耐盐性综合评价决策值(decision value,D值)。最终从132份芥菜分类出38份盐敏感型,鉴定出3份强耐盐种质(D>0.6)、22份耐盐种质(0.3<D<0.6)和69份不耐盐种质(D<0.3)。其中,对根部耐盐系数进行主成分分析,所得的综合指标1(composite index 1,CI_(1))与CI_(2)贡献率分别为66.886%和26.835%,证明在CI_(2)占比较高ST-AD独立性更强,其他根部系数与D值存在线性关系并可构建回归方程。综上,芥菜的根系系数可用于更便捷地综合评估其耐盐性,为评价芥菜的耐盐性提供了新方法。展开更多
In order to solve the problem of chronic heart failure risk prediction in the elderly,a logistic regression modeling framework with Bayesian method was proposed,aiming to solve the problem of insufficient generalizati...In order to solve the problem of chronic heart failure risk prediction in the elderly,a logistic regression modeling framework with Bayesian method was proposed,aiming to solve the problem of insufficient generalization perfor-mance caused by overfitting in small sample data of traditional logistic regres-sion.By including 16 multi-dimensional clinical indicators(age,gender,BMI and alcohol history,etc.)in 20 elderly patients with chronic heart failure,the initial feature set was multicollinearity screened based on the variance infla-tion factor(VIF)test,and the high collinearity variables with VIF value≥10(such as fall risk,frailty assessment,etc.)were retained,so as to reduce the interference of redundant information on the stability of the model.Subse-quently,the entropy weight method was used to weight the filtered variables,and the information contribution of each index was quantified by information entropy,and standardized weighted data was generated,so as to optimize the feature importance allocation and alleviate the residual collinearity.Finally,based on the weighted data,Spearman correlation analysis was used to quan-titatively evaluate the association strength of each variable with heart failure classification,and the core predictors of balance and gait ability(correlation coefficient 0.52)and physical function status were identified.The results show that although the traditional logistic model achieves 100%accuracy on the training set,its parameters are significantly abnormal due to the singularity of the Hasten matrix,indicating that the model has a serious risk of overfitting.To this end,a Bayesian framework was introduced in this study,with a normal prior constraint regression coefficient with a mean of 0 and a standard devia-tion of 10,through the Markov Chain Monte Carlo(MCMC).The posterior distribution of parameters is obtained by sampling,which effectively balances the complexity of the model and the likelihood of the data.The experimental results show that Bayesian logistic regression has a classification accuracy of 85%on the independent test set,and the confusion matrix shows that the mis-judgments are only concentrated in the categories with overlapping features(one case in the second category is misjudged to the first category),and the F1 score is significantly improved(category 1:0.86,category 2:0.80,category 3:1.00),which avoids the singularity of the Haysen matrix.This study confirms that Bayesian logistic regression provides a highly robust solution for model-ing chronic heart failure in small elderly populations through probability reg-ularization and uncertainty quantification.展开更多
There is a need for determinations of soil organic carbon (SOC) and inorganic carbon (SIC) due to increasing interest in soil carbon sequestration. Two sets of soil samples were collected separately from the Yanqi Bas...There is a need for determinations of soil organic carbon (SOC) and inorganic carbon (SIC) due to increasing interest in soil carbon sequestration. Two sets of soil samples were collected separately from the Yanqi Basin of northwest China to evaluate loss-on-ignition (LOI) method for estimating SOC and SIC in arid soils through determining SOC using an element analyzer, a modified Walkley-Black method and a LOI method with combustion at 375℃ for 17 h and determining SIC using a pressure calcimeter method and a LOI procedure estimated by a weight loss between 375 to 800℃. Our results indicated that the Walkley-Black method provided 99%recovery of SOC for the arid soils tested. There were strong linear relationships(r > 0.93, P < 0.001) for both SOC and SIC between the traditional method and the LOI technique. One set of soil samples was used to develop relationships between LOI and SOC(by the Walkley-Black method), and between LOI and SIC(by the pressure calcimeter method), and the other set of soil samples was used to evaluate the derived equations by comparing predicted SOC and SIC with measured values. The mean absolute errors were small for both SOC (1.7 g C kg-1) and SIC(1.22 g C kg-1), demonstrating that the LOI method was reliable and could provide accurate estimates of SOC and SIC for arid soils.展开更多
In recent years,the ecological environment along highways in Tibetan Plateau has been severely affected due to the rapid construction of highways.In order to solve the problems of multiple indicators and inconsistent ...In recent years,the ecological environment along highways in Tibetan Plateau has been severely affected due to the rapid construction of highways.In order to solve the problems of multiple indicators and inconsistent criteria in the ecological impact assessment of highways,and to scientifically screen assessment indicators,the paper proposes a multi-round indicator screening method,which combines literature analysis,expert rating,and statistical analysis.Based on this screening method,normalized difference vegetation index,land surface temperature,elevation,and normalized difference soil index are screened out.Combined with multiple linear regression,an ecological impact assessment model is established and applied to ecological impact assessment of Gonghe-Yushu Expressway.The results show that the expressway construction is the first driving force for the deterioration of the ecological environment along the roadside,and its interference range on the desert grassland ecosystem is greater than that on the agroforestry system.The ecological environment within 150 m on both sides of the expressway should be protected.展开更多
Power flow(PF)is one of the most important calculations in power systems.The widely-used PF methods are the Newton-Raphson PF(NRPF)method and the fast-decoupled PF(FDPF)method.In smart grids,power generations and load...Power flow(PF)is one of the most important calculations in power systems.The widely-used PF methods are the Newton-Raphson PF(NRPF)method and the fast-decoupled PF(FDPF)method.In smart grids,power generations and loads become intermittent and much more uncertain,and the topology also changes more frequently,which may result in significant state shifts and further make NRPF or FDPF difficult to converge.To address this problem,we propose a data-driven PF(DDPF)method based on historical/simulated data that includes an offline learning stage and an online computing stage.In the offline learning stage,a learning model is constructed based on the proposed exact linear regression equations,and then the proposed learning model is solved by the ridge regression(RR)method to suppress the effect of data collinearity.In online computing stage,the nonlinear iterative calculation is not needed.Simulation results demonstrate that the proposed DDPF method has no convergence problem and has much higher calculation efficiency than NRPF or FDPF while ensuring similar calculation accuracy.展开更多
文摘This paper transforms fuzzy number into clear number using the centroid method, thus we can research the traditional linear regression model which is transformed from the fuzzy linear regression model. The model’s input and output are fuzzy numbers, and the regression coefficients are clear numbers. This paper considers the parameter estimation and impact analysis based on data deletion. Through the study of example and comparison with other models, it can be concluded that the model in this paper is applied easily and better.
文摘According to the appearing of isosbestic point in the absorption spectra of Ho/Y-Tribromoarsenazo (TBA)systems,the complexation reaction is considered to be M+nL=ML_n.A method has been proposed based on it for calculating the mole fraction of free complexing agent in the solutions from spectral data.and two linear regression formula have been introduced to determine the composition,the molar absorptivity,the conditional stability constant of the complex and the concentration of the complexing agent. This method has been used in Ho-TBA and Y-TBA systems.Ho^(3+)and Y^(3+)react with TBA and form 1: 2 complexes in HCl-NaAc buffer solution at pH 3.80.Their molar absorptivities determined are 1.03×10~8 and 1.10×10~8 cm^2·mol^(-1),and the conditional stability constants(logβ_2)are 11.37 and 11.15 respectively.After considering the pH effect in TBA complexing,their stability constants(log β_2^(ahs))are 43.23 and 43.01. respectively.The new method is adaptable to such systems where the accurate concentration of the complexing agent can not be known conveniently.
文摘A new method,dual-series linear regression method,has been used to study the complexation equilibrium of praseodymium(Pr^(3+))with tribromoarsenazo(TBA)without knowing the accurate concentra- tion of the complexing agent TBA.In 1.2 mol/L HCl solution, Pr^(3+)reacts with TBA and forms 1:3 com- plex,the conditional stability constant(lgβ_3)of the complex determined is 15.47,and its molar absorptivity(ε_3^(630))is 1.48×10~5 L·mol^(-1)·cm^(-1).
文摘The purpose of this study was to examine the burnout levels of research assistants in Ondokuz Mayis University and to examine the results of multiple linear regression model based on the results obtained from Maslach Burnout Scale with Jackknife Method in terms of validity and generalizability. To do this, a questionnaire was given to 11 research assistants working at Ondokuz Mayis University and the burnout scores of this questionnaire were taken as the dependent variable of the multiple linear regression model. The variable of burnout was explained with the variables of age, weekly hours of classes taught, monthly average credit card debt, numbers of published articles and reports, gender, marital status, number of children and the departments of the research assistants. Dummy variables were assigned to the variables of gender, marital status, number of children and the departments of the research assistants and thus, they were made quantitative. The significance of the model as a result of multiple linear regressions was examined through backward elimination method. After this, for the five explanatory variables which influenced the variable of burnout, standardized model coefficients and coefficients of determination, and 95% confidence intervals of these values were estimated through Jackknife Method and the generalizability of the parameter estimation results of these variables on population was researched.
文摘The development of prediction supports is a critical step in information systems engineering in this era defined by the knowledge economy, the hub of which is big data. Currently, the lack of a predictive model, whether qualitative or quantitative, depending on a company’s areas of intervention can handicap or weaken its competitive capacities, endangering its survival. In terms of quantitative prediction, depending on the efficacy criteria, a variety of methods and/or tools are available. The multiple linear regression method is one of the methods used for this purpose. A linear regression model is a regression model of an explained variable on one or more explanatory variables in which the function that links the explanatory variables to the explained variable has linear parameters. The purpose of this work is to demonstrate how to use multiple linear regressions, which is one aspect of decisional mathematics. The use of multiple linear regressions on random data, which can be replaced by real data collected by or from organizations, provides decision makers with reliable data knowledge. As a result, machine learning methods can provide decision makers with relevant and trustworthy data. The main goal of this article is therefore to define the objective function on which the influencing factors for its optimization will be defined using the linear regression method.
基金funded by the National Key R&D Program of China(Grant No.2022YFC2903904)the National Natural Science Foundation of China(Grant Nos.51904057 and U1906208).
文摘Due to the heterogeneity of rock masses and the variability of in situ stress,the traditional linear inversion method is insufficiently accurate to achieve high accuracy of the in situ stress field.To address this challenge,nonlinear stress boundaries for a numerical model are determined through regression analysis of a series of nonlinear coefficient matrices,which are derived from the bubbling method.Considering the randomness and flexibility of the bubbling method,a parametric study is conducted to determine recommended ranges for these parameters,including the standard deviation(σb)of bubble radii,the non-uniform coefficient matrix number(λ)for nonlinear stress boundaries,and the number(m)and positions of in situ stress measurement points.A model case study provides a reference for the selection of these parameters.Additionally,when the nonlinear in situ stress inversion method is employed,stress distortion inevitably occurs near model boundaries,aligning with the Saint Venant's principle.Two strategies are proposed accordingly:employing a systematic reduction of nonlinear coefficients to achieve high inversion accuracy while minimizing significant stress distortion,and excluding regions with severe stress distortion near the model edges while utilizing the central part of the model for subsequent simulations.These two strategies have been successfully implemented in the nonlinear in situ stress inversion of the Xincheng Gold Mine and have achieved higher inversion accuracy than the linear method.Specifically,the linear and nonlinear inversion methods yield root mean square errors(RMSE)of 4.15 and 3.2,and inversion relative errors(δAve)of 22.08%and 17.55%,respectively.Therefore,the nonlinear inversion method outperforms the traditional multiple linear regression method,even in the presence of a systematic reduction in the nonlinear stress boundaries.
文摘The concept of missing data is important to apply statistical methods on the dataset. Statisticians and researchers may end up to an inaccurate illation about the data if the missing data are not handled properly. Of late, Python and R provide diverse packages for handling missing data. In this study, an imputation algorithm, cumulative linear regression, is proposed. The proposed algorithm depends on the linear regression technique. It differs from the existing methods, in that it cumulates the imputed variables;those variables will be incorporated in the linear regression equation to filling in the missing values in the next incomplete variable. The author performed a comparative study of the proposed method and those packages. The performance was measured in terms of imputation time, root-mean-square error, mean absolute error, and coefficient of determination (R^2). On analysing on five datasets with different missing values generated from different mechanisms, it was observed that the performances vary depending on the size, missing percentage, and the missingness mechanism. The results showed that the performance of the proposed method is slightly better.
文摘In the network technology era, the collected data are growing more and more complex, and become larger than before. In this article, we focus on estimates of the linear regression parameters for symbolic interval data. We propose two approaches to estimate regression parameters for symbolic interval data under two different data models and compare our proposed approaches with the existing methods via simulations. Finally, we analyze two real datasets with the proposed methods for illustrations.
文摘A Mobile Ad-hoc NETwork(MANET)contains numerous mobile nodes,and it forms a structure-less network associated with wireless links.But,the node movement is the key feature of MANETs;hence,the quick action of the nodes guides a link failure.This link failure creates more data packet drops that can cause a long time delay.As a result,measuring accurate link failure time is the key factor in the MANET.This paper presents a Fuzzy Linear Regression Method to measure Link Failure(FLRLF)and provide an optimal route in the MANET-Internet of Things(IoT).This work aims to predict link failure and improve routing efficiency in MANET.The Fuzzy Linear Regression Method(FLRM)measures the long lifespan link based on the link failure.The mobile node group is built by the Received Signal Strength(RSS).The Hill Climbing(HC)method selects the Group Leader(GL)based on node mobility,node degree and node energy.Additionally,it uses a Data Gathering node forward the infor-mation from GL to the sink node through multiple GL.The GL is identified by linking lifespan and energy using the Particle Swarm Optimization(PSO)algo-rithm.The simulation results demonstrate that the FLRLF approach increases the GL lifespan and minimizes the link failure time in the MANET.
基金financial support from the Brazilian Institution Conselho Nacional de Desenvolvimento Cientifico e Tecnologico(CNPq).
文摘In this paper, we study some robustness aspects of linear regression models of the presence of outliers or discordant observations considering the use of stable distributions for the response in place of the usual normality assumption. It is well known that, in general, there is no closed form for the probability density function of stable distributions. However, under a Bayesian approach, the use of a latent or auxiliary random variable gives some simplification to obtain any posterior distribution when related to stable distributions. To show the usefulness of the computational aspects, the methodology is applied to two examples: one is related to a standard linear regression model with an explanatory variable and the other is related to a simulated data set assuming a 23 factorial experiment. Posterior summaries of interest are obtained using MCMC (Markov Chain Monte Carlo) methods and the OpenBugs software.
文摘In this article,a procedure for estimating the coefficient functions on the functional-coefficient regression models with different smoothing variables in different coefficient functions is defined.First step,by the local linear technique and the averaged method,the initial estimates of the coefficient functions are given.Second step,based on the initial estimates,the efficient estimates of the coefficient functions are proposed by a one-step back-fitting procedure.The efficient estimators share the same asymptotic normalities as the local linear estimators for the functional-coefficient models with a single smoothing variable in different functions.Two simulated examples show that the procedure is effective.
文摘芥菜作为我国特色蔬菜之一,是研究盐胁迫这种关键非生物胁迫因子对植物幼苗时期成长影响的优质实验材料。评估了132份芥菜种质资源在正常条件与从构建的适用于芥菜萌发成苗期的耐盐性鉴定体系所得的最适盐胁迫(1.0%NaCl)下的萌发表现及幼苗根系形态。根据生长状况以及各根系性状的耐盐指数并采用隶属函数法进行综合分析,得到耐盐性综合评价决策值(decision value,D值)。最终从132份芥菜分类出38份盐敏感型,鉴定出3份强耐盐种质(D>0.6)、22份耐盐种质(0.3<D<0.6)和69份不耐盐种质(D<0.3)。其中,对根部耐盐系数进行主成分分析,所得的综合指标1(composite index 1,CI_(1))与CI_(2)贡献率分别为66.886%和26.835%,证明在CI_(2)占比较高ST-AD独立性更强,其他根部系数与D值存在线性关系并可构建回归方程。综上,芥菜的根系系数可用于更便捷地综合评估其耐盐性,为评价芥菜的耐盐性提供了新方法。
文摘In order to solve the problem of chronic heart failure risk prediction in the elderly,a logistic regression modeling framework with Bayesian method was proposed,aiming to solve the problem of insufficient generalization perfor-mance caused by overfitting in small sample data of traditional logistic regres-sion.By including 16 multi-dimensional clinical indicators(age,gender,BMI and alcohol history,etc.)in 20 elderly patients with chronic heart failure,the initial feature set was multicollinearity screened based on the variance infla-tion factor(VIF)test,and the high collinearity variables with VIF value≥10(such as fall risk,frailty assessment,etc.)were retained,so as to reduce the interference of redundant information on the stability of the model.Subse-quently,the entropy weight method was used to weight the filtered variables,and the information contribution of each index was quantified by information entropy,and standardized weighted data was generated,so as to optimize the feature importance allocation and alleviate the residual collinearity.Finally,based on the weighted data,Spearman correlation analysis was used to quan-titatively evaluate the association strength of each variable with heart failure classification,and the core predictors of balance and gait ability(correlation coefficient 0.52)and physical function status were identified.The results show that although the traditional logistic model achieves 100%accuracy on the training set,its parameters are significantly abnormal due to the singularity of the Hasten matrix,indicating that the model has a serious risk of overfitting.To this end,a Bayesian framework was introduced in this study,with a normal prior constraint regression coefficient with a mean of 0 and a standard devia-tion of 10,through the Markov Chain Monte Carlo(MCMC).The posterior distribution of parameters is obtained by sampling,which effectively balances the complexity of the model and the likelihood of the data.The experimental results show that Bayesian logistic regression has a classification accuracy of 85%on the independent test set,and the confusion matrix shows that the mis-judgments are only concentrated in the categories with overlapping features(one case in the second category is misjudged to the first category),and the F1 score is significantly improved(category 1:0.86,category 2:0.80,category 3:1.00),which avoids the singularity of the Haysen matrix.This study confirms that Bayesian logistic regression provides a highly robust solution for model-ing chronic heart failure in small elderly populations through probability reg-ularization and uncertainty quantification.
基金Supported by the "Hundred Talents Program" of the Chinese Academy of Sciences
文摘There is a need for determinations of soil organic carbon (SOC) and inorganic carbon (SIC) due to increasing interest in soil carbon sequestration. Two sets of soil samples were collected separately from the Yanqi Basin of northwest China to evaluate loss-on-ignition (LOI) method for estimating SOC and SIC in arid soils through determining SOC using an element analyzer, a modified Walkley-Black method and a LOI method with combustion at 375℃ for 17 h and determining SIC using a pressure calcimeter method and a LOI procedure estimated by a weight loss between 375 to 800℃. Our results indicated that the Walkley-Black method provided 99%recovery of SOC for the arid soils tested. There were strong linear relationships(r > 0.93, P < 0.001) for both SOC and SIC between the traditional method and the LOI technique. One set of soil samples was used to develop relationships between LOI and SOC(by the Walkley-Black method), and between LOI and SIC(by the pressure calcimeter method), and the other set of soil samples was used to evaluate the derived equations by comparing predicted SOC and SIC with measured values. The mean absolute errors were small for both SOC (1.7 g C kg-1) and SIC(1.22 g C kg-1), demonstrating that the LOI method was reliable and could provide accurate estimates of SOC and SIC for arid soils.
基金supported by the National Natural Science Foundation of China(NSFC)(No.41801387)。
文摘In recent years,the ecological environment along highways in Tibetan Plateau has been severely affected due to the rapid construction of highways.In order to solve the problems of multiple indicators and inconsistent criteria in the ecological impact assessment of highways,and to scientifically screen assessment indicators,the paper proposes a multi-round indicator screening method,which combines literature analysis,expert rating,and statistical analysis.Based on this screening method,normalized difference vegetation index,land surface temperature,elevation,and normalized difference soil index are screened out.Combined with multiple linear regression,an ecological impact assessment model is established and applied to ecological impact assessment of Gonghe-Yushu Expressway.The results show that the expressway construction is the first driving force for the deterioration of the ecological environment along the roadside,and its interference range on the desert grassland ecosystem is greater than that on the agroforestry system.The ecological environment within 150 m on both sides of the expressway should be protected.
基金supported in part by National Natural Science Foundation of China(No.52077076)in part by the State Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources(No.LAPS202118)。
文摘Power flow(PF)is one of the most important calculations in power systems.The widely-used PF methods are the Newton-Raphson PF(NRPF)method and the fast-decoupled PF(FDPF)method.In smart grids,power generations and loads become intermittent and much more uncertain,and the topology also changes more frequently,which may result in significant state shifts and further make NRPF or FDPF difficult to converge.To address this problem,we propose a data-driven PF(DDPF)method based on historical/simulated data that includes an offline learning stage and an online computing stage.In the offline learning stage,a learning model is constructed based on the proposed exact linear regression equations,and then the proposed learning model is solved by the ridge regression(RR)method to suppress the effect of data collinearity.In online computing stage,the nonlinear iterative calculation is not needed.Simulation results demonstrate that the proposed DDPF method has no convergence problem and has much higher calculation efficiency than NRPF or FDPF while ensuring similar calculation accuracy.
