This paper present a simulation study of an evolutionary algorithms, Particle Swarm Optimization PSO algorithm to optimize likelihood function of ARMA（1, 1） model, where maximizing likelihood function is equivalent ...This paper present a simulation study of an evolutionary algorithms, Particle Swarm Optimization PSO algorithm to optimize likelihood function of ARMA（1, 1） model, where maximizing likelihood function is equivalent to maximizing its logarithm, so the objective function ＇obj.fun＇ is maximizing log-likelihood function. Monte Carlo method adapted for implementing and designing the experiments of this simulation. This study including a comparison among three versions of PSO algorithm “Constriction coefficient CCPSO, Inertia weight IWPSO, and Fully Informed FIPSO”, the experiments designed by setting different values of model parameters al, bs sample size n, moreover the parameters of PSO algorithms. MSE used as test statistic to measure the efficiency PSO to estimate model. The results show the ability of PSO to estimate ARMA＇ s parameters, and the minimum values of MSE getting for COPSO.展开更多
Profile likelihood function is introduced to analyze the uncertainty of hydrometeorological extreme inference and the theory of estimating confidence intervals of the key parameters and quantiles of extreme value dist...Profile likelihood function is introduced to analyze the uncertainty of hydrometeorological extreme inference and the theory of estimating confidence intervals of the key parameters and quantiles of extreme value distribution by profile likelihood function is described.GEV(generalized extreme value)distribution and GP(generalized Pareto)distribution are used respectively to fit the annual maximum daily flood discharge sample of the Yichang station in the Yangtze River and the daily rainfall sample in10 big cities including Guangzhou.The parameters of the models are estimated by maximum likelihood method and the fitting results are tested by probability plot,quantile plot,return level plot and density plot.The return levels and confidence intervals of flood and rainstorm in different return periods are calculated by profile likelihood function.The results show that the asymmetry of the profile likelihood function curve increases with the return period,which can reflect the effect of the length of sample series and return periods on confidence interval.As an effective tool for estimating confidence interval of the key parameters and quantiles of extreme value distribution,profile likelihood function can lead to a more accurate result and help to analyze the uncertainty of extreme values of hydrometeorology.展开更多
The topic of this article is one-sided hypothesis testing for disparity, i.e., the mean of one group is larger than that of another when there is uncertainty as to which group a datum is drawn. For each datum, the unc...The topic of this article is one-sided hypothesis testing for disparity, i.e., the mean of one group is larger than that of another when there is uncertainty as to which group a datum is drawn. For each datum, the uncertainty is captured with a given discrete probability distribution over the groups. Such situations arise, for example, in the use of Bayesian imputation methods to assess race and ethnicity disparities with certain insurance, health, and financial data. A widely used method to implement this assessment is the Bayesian Improved Surname Geocoding (BISG) method which assigns a discrete probability over six race/ethnicity groups to an individual given the individual’s surname and address location. Using a Bayesian framework and Markov Chain Monte Carlo sampling from the joint posterior distribution of the group means, the probability of a disparity hypothesis is estimated. Four methods are developed and compared with an illustrative data set. Three of these methods are implemented in an R-code and one method in WinBUGS. These methods are programed for any number of groups between two and six inclusive. All the codes are provided in the appendices.展开更多
某一特定场地的岩土力学参数在地质作用下普遍呈现固有的不确定性,融合现场观测数据进行概率反分析可有效缩减这一不确定性。虽然基于子集模拟的贝叶斯更新(Bayesian Updating with Subset simulation,简称BUS)方法可以将等量场地信息...某一特定场地的岩土力学参数在地质作用下普遍呈现固有的不确定性,融合现场观测数据进行概率反分析可有效缩减这一不确定性。虽然基于子集模拟的贝叶斯更新(Bayesian Updating with Subset simulation,简称BUS)方法可以将等量场地信息的高维概率反分析问题转化为等效的结构可靠度问题,但是当现场观测数据增多时,构建的似然函数值会变得非常小,甚至低于计算机浮点运算精度,会严重影响概率反分析计算效率与精度。为此,提出了一种基于并联系统可靠度分析的改进BUS方法,从基于乔列斯基分解的中点法出发,将接受率低的总失效区域分解为多个接受率高的子失效区域,从而避免因融合大量现场观测数据引起的“维度灾难”问题,实现对边坡岩土力学参数的准确概率反分析。最后,通过一不排水饱和黏土边坡案例验证了提出方法的有效性,结果表明提出的方法能够融合大量钻孔数据和边坡服役状态等观测信息高效进行岩土力学参数概率反分析及边坡可靠度评估,为高维空间变异参数概率反分析和边坡可靠度评估提供了一种有效的工具。展开更多
The likelihood function plays a central role in statistical analysis in relation to information, from both frequentist and Bayesian perspectives. In large samples several new properties of the likelihood in relation t...The likelihood function plays a central role in statistical analysis in relation to information, from both frequentist and Bayesian perspectives. In large samples several new properties of the likelihood in relation to information are developed here. The Arrow-Pratt absolute risk aversion measure is shown to be related to the Cramer-Rao Information bound. The derivative of the log-likelihood function is seen to provide a measure of information related stability for the Bayesian posterior density. As well, information similar prior densities can be defined reflecting the central role of likelihood in the Bayes learning paradigm.展开更多
目的:通过分析针刺干预卒中后运动障碍的功能性磁共振(fMRI)临床研究结果,筛选针刺阳明经穴干预该病的中枢核心、稳定核团,为针刺治疗本病的中枢作用机制提供可靠证据。方法:检索PubMed、Web of Science、中国知网、万方和维普文献数据...目的:通过分析针刺干预卒中后运动障碍的功能性磁共振(fMRI)临床研究结果,筛选针刺阳明经穴干预该病的中枢核心、稳定核团,为针刺治疗本病的中枢作用机制提供可靠证据。方法:检索PubMed、Web of Science、中国知网、万方和维普文献数据库,收集从建库—2022年12月使用fMRI观察针刺阳明经穴治疗卒中后脑区变化情况的研究。使用Ginger-ALE 3.0.2软件计算脑区激活似然评估(ALE)分布,最后使用DPABI软件进行图像整合。结果:共有20篇文献纳入研究,包括356名患者和144名健康人。结果显示,与健康人比较,缺血性卒中患者存在异常的大脑功能活动模式,异常的脑区主要与额叶、颞叶、边缘系统以及小脑有关;针刺阳明经穴对缺血性卒中后运动障碍患者左侧顶叶和小脑后叶(具体包括:顶下小叶、缘上回、中央后回以及下半月小叶、蚓锥体和小脑扁桃体)功能活动有稳定的调制作用。结论:卒中发生后相关运动支配脑区存在损伤与功能重塑;针刺阳明经穴可以稳定调节缺血性卒中后运动障碍患者优势侧运动-感觉系统功能活动。展开更多
针对传统高斯正态似然函数(Gaussian likelihood function,GLF)在观测数据存在测量误差和模型算法结构复杂时无法描述模型残差异方差特点,造成马尔科夫链蒙特卡洛(Markov chain Monte Carlo,MCMC)算法进行模型参数校正时结果存在偏差的...针对传统高斯正态似然函数(Gaussian likelihood function,GLF)在观测数据存在测量误差和模型算法结构复杂时无法描述模型残差异方差特点,造成马尔科夫链蒙特卡洛(Markov chain Monte Carlo,MCMC)算法进行模型参数校正时结果存在偏差的问题,通过引入变异系数(coefficient of variation,CV)变换的高斯似然函数(GLF with CV transformation,GLF-CV)和BC(Box-Cox)变换的高斯似然函数(GLF with BC transformation,GLF-BC)对观测数据和模型结构造成的异方差进行特征描述,并比较了参数校正效果及模型不确定度(uncertainty ratio,UR)。以2004—2009年高要雪花粘(早熟)、2001—2004年兴化武育粳3号(中熟)、1991—2004年六安汕优63号(晚熟)3个生态点的田间栽培试验数据为基础,RiceGrow和Oryza2000物候期模型为对象,利用仿射不变马尔科夫链蒙特卡洛集成采样(ensemble sampling for affine-invariant MCMC,EMCEE)算法实现模型参数校正,并比较了GLF-CV、GLF-BC、GLF对校正结果的影响。研究表明:1)3种似然函数下,RiceGrow和Oryza2000物候期模型预测均方根误差(root mean square error,RMSE)范围分别2.66~4.54d、2.30~4.41 d,表明3种似然函数用于参数校正均有效果。2)在RiceGrow物候期模型中,3个水稻品种参数相对均方根偏差(relative root mean square deviation,RRMSD)和模型预测RMSE均是GLF-BC最小,在GLF-BC下模型预测RMSE比GLF-CV小0.09、0.07、0.80 d,比GLF小1.21、0.20、0.07 d,表明GLF-BC对RiceGrow物候期模型具有良好的适应性。3)在Oryza2000物候期模型中,雪花粘、武育粳3号、汕优63号3个水稻品种的模型预测RMSE最小的是GLF、GLF-BC和GLF-CV,分别为2.30、4.17、3.50 d。可以看出LF的选择与模型残差异方差的主要来源有关,当主要来源为观测数据时,GLF-CV好于其他;当主要来源为模型结构本身时,GLF-BC好于其他;当模型残差的异方差性较小时,可使用GLF。展开更多
In this article, we propose a generalized empirical likelihood inference for the parametric component in semiparametric generalized partially linear models with longitudinal data. Based on the extended score vector, a...In this article, we propose a generalized empirical likelihood inference for the parametric component in semiparametric generalized partially linear models with longitudinal data. Based on the extended score vector, a generalized empirical likelihood ratios function is defined, which integrates the within-cluster?correlation meanwhile avoids direct estimating the nuisance parameters in the correlation matrix. We show that the proposed statistics are asymptotically?Chi-squared under some suitable conditions, and hence it can be used to construct the confidence region of parameters. In addition, the maximum empirical likelihood estimates of parameters and the corresponding asymptotic normality are obtained. Simulation studies demonstrate the performance of the proposed method.展开更多
文摘This paper present a simulation study of an evolutionary algorithms, Particle Swarm Optimization PSO algorithm to optimize likelihood function of ARMA（1, 1） model, where maximizing likelihood function is equivalent to maximizing its logarithm, so the objective function ＇obj.fun＇ is maximizing log-likelihood function. Monte Carlo method adapted for implementing and designing the experiments of this simulation. This study including a comparison among three versions of PSO algorithm “Constriction coefficient CCPSO, Inertia weight IWPSO, and Fully Informed FIPSO”, the experiments designed by setting different values of model parameters al, bs sample size n, moreover the parameters of PSO algorithms. MSE used as test statistic to measure the efficiency PSO to estimate model. The results show the ability of PSO to estimate ARMA＇ s parameters, and the minimum values of MSE getting for COPSO.
基金supported by the National Basic Research Program of China("973" Program)(Grant Nos.2013CB036406,2010CB951102)the National Natural Science Foundation of China(Grant No.51109224)
文摘Profile likelihood function is introduced to analyze the uncertainty of hydrometeorological extreme inference and the theory of estimating confidence intervals of the key parameters and quantiles of extreme value distribution by profile likelihood function is described.GEV(generalized extreme value)distribution and GP(generalized Pareto)distribution are used respectively to fit the annual maximum daily flood discharge sample of the Yichang station in the Yangtze River and the daily rainfall sample in10 big cities including Guangzhou.The parameters of the models are estimated by maximum likelihood method and the fitting results are tested by probability plot,quantile plot,return level plot and density plot.The return levels and confidence intervals of flood and rainstorm in different return periods are calculated by profile likelihood function.The results show that the asymmetry of the profile likelihood function curve increases with the return period,which can reflect the effect of the length of sample series and return periods on confidence interval.As an effective tool for estimating confidence interval of the key parameters and quantiles of extreme value distribution,profile likelihood function can lead to a more accurate result and help to analyze the uncertainty of extreme values of hydrometeorology.
文摘The topic of this article is one-sided hypothesis testing for disparity, i.e., the mean of one group is larger than that of another when there is uncertainty as to which group a datum is drawn. For each datum, the uncertainty is captured with a given discrete probability distribution over the groups. Such situations arise, for example, in the use of Bayesian imputation methods to assess race and ethnicity disparities with certain insurance, health, and financial data. A widely used method to implement this assessment is the Bayesian Improved Surname Geocoding (BISG) method which assigns a discrete probability over six race/ethnicity groups to an individual given the individual’s surname and address location. Using a Bayesian framework and Markov Chain Monte Carlo sampling from the joint posterior distribution of the group means, the probability of a disparity hypothesis is estimated. Four methods are developed and compared with an illustrative data set. Three of these methods are implemented in an R-code and one method in WinBUGS. These methods are programed for any number of groups between two and six inclusive. All the codes are provided in the appendices.
文摘某一特定场地的岩土力学参数在地质作用下普遍呈现固有的不确定性,融合现场观测数据进行概率反分析可有效缩减这一不确定性。虽然基于子集模拟的贝叶斯更新(Bayesian Updating with Subset simulation,简称BUS)方法可以将等量场地信息的高维概率反分析问题转化为等效的结构可靠度问题,但是当现场观测数据增多时,构建的似然函数值会变得非常小,甚至低于计算机浮点运算精度,会严重影响概率反分析计算效率与精度。为此,提出了一种基于并联系统可靠度分析的改进BUS方法,从基于乔列斯基分解的中点法出发,将接受率低的总失效区域分解为多个接受率高的子失效区域,从而避免因融合大量现场观测数据引起的“维度灾难”问题,实现对边坡岩土力学参数的准确概率反分析。最后,通过一不排水饱和黏土边坡案例验证了提出方法的有效性,结果表明提出的方法能够融合大量钻孔数据和边坡服役状态等观测信息高效进行岩土力学参数概率反分析及边坡可靠度评估,为高维空间变异参数概率反分析和边坡可靠度评估提供了一种有效的工具。
文摘The likelihood function plays a central role in statistical analysis in relation to information, from both frequentist and Bayesian perspectives. In large samples several new properties of the likelihood in relation to information are developed here. The Arrow-Pratt absolute risk aversion measure is shown to be related to the Cramer-Rao Information bound. The derivative of the log-likelihood function is seen to provide a measure of information related stability for the Bayesian posterior density. As well, information similar prior densities can be defined reflecting the central role of likelihood in the Bayes learning paradigm.
文摘目的:通过分析针刺干预卒中后运动障碍的功能性磁共振(fMRI)临床研究结果,筛选针刺阳明经穴干预该病的中枢核心、稳定核团,为针刺治疗本病的中枢作用机制提供可靠证据。方法:检索PubMed、Web of Science、中国知网、万方和维普文献数据库,收集从建库—2022年12月使用fMRI观察针刺阳明经穴治疗卒中后脑区变化情况的研究。使用Ginger-ALE 3.0.2软件计算脑区激活似然评估(ALE)分布,最后使用DPABI软件进行图像整合。结果:共有20篇文献纳入研究,包括356名患者和144名健康人。结果显示,与健康人比较,缺血性卒中患者存在异常的大脑功能活动模式,异常的脑区主要与额叶、颞叶、边缘系统以及小脑有关;针刺阳明经穴对缺血性卒中后运动障碍患者左侧顶叶和小脑后叶(具体包括:顶下小叶、缘上回、中央后回以及下半月小叶、蚓锥体和小脑扁桃体)功能活动有稳定的调制作用。结论:卒中发生后相关运动支配脑区存在损伤与功能重塑;针刺阳明经穴可以稳定调节缺血性卒中后运动障碍患者优势侧运动-感觉系统功能活动。
文摘针对传统高斯正态似然函数(Gaussian likelihood function,GLF)在观测数据存在测量误差和模型算法结构复杂时无法描述模型残差异方差特点,造成马尔科夫链蒙特卡洛(Markov chain Monte Carlo,MCMC)算法进行模型参数校正时结果存在偏差的问题,通过引入变异系数(coefficient of variation,CV)变换的高斯似然函数(GLF with CV transformation,GLF-CV)和BC(Box-Cox)变换的高斯似然函数(GLF with BC transformation,GLF-BC)对观测数据和模型结构造成的异方差进行特征描述,并比较了参数校正效果及模型不确定度(uncertainty ratio,UR)。以2004—2009年高要雪花粘(早熟)、2001—2004年兴化武育粳3号(中熟)、1991—2004年六安汕优63号(晚熟)3个生态点的田间栽培试验数据为基础,RiceGrow和Oryza2000物候期模型为对象,利用仿射不变马尔科夫链蒙特卡洛集成采样(ensemble sampling for affine-invariant MCMC,EMCEE)算法实现模型参数校正,并比较了GLF-CV、GLF-BC、GLF对校正结果的影响。研究表明:1)3种似然函数下,RiceGrow和Oryza2000物候期模型预测均方根误差(root mean square error,RMSE)范围分别2.66~4.54d、2.30~4.41 d,表明3种似然函数用于参数校正均有效果。2)在RiceGrow物候期模型中,3个水稻品种参数相对均方根偏差(relative root mean square deviation,RRMSD)和模型预测RMSE均是GLF-BC最小,在GLF-BC下模型预测RMSE比GLF-CV小0.09、0.07、0.80 d,比GLF小1.21、0.20、0.07 d,表明GLF-BC对RiceGrow物候期模型具有良好的适应性。3)在Oryza2000物候期模型中,雪花粘、武育粳3号、汕优63号3个水稻品种的模型预测RMSE最小的是GLF、GLF-BC和GLF-CV,分别为2.30、4.17、3.50 d。可以看出LF的选择与模型残差异方差的主要来源有关,当主要来源为观测数据时,GLF-CV好于其他;当主要来源为模型结构本身时,GLF-BC好于其他;当模型残差的异方差性较小时,可使用GLF。
文摘In this article, we propose a generalized empirical likelihood inference for the parametric component in semiparametric generalized partially linear models with longitudinal data. Based on the extended score vector, a generalized empirical likelihood ratios function is defined, which integrates the within-cluster?correlation meanwhile avoids direct estimating the nuisance parameters in the correlation matrix. We show that the proposed statistics are asymptotically?Chi-squared under some suitable conditions, and hence it can be used to construct the confidence region of parameters. In addition, the maximum empirical likelihood estimates of parameters and the corresponding asymptotic normality are obtained. Simulation studies demonstrate the performance of the proposed method.
