Gastric cancer is the third leading cause of cancer-related mortality and remains a major global health issue^([1]).Annually,approximately 479,000individuals in China are diagnosed with gastric cancer,accounting for a...Gastric cancer is the third leading cause of cancer-related mortality and remains a major global health issue^([1]).Annually,approximately 479,000individuals in China are diagnosed with gastric cancer,accounting for almost 45%of all new cases worldwide^([2]).展开更多
Piecewise linear regression models are very flexible models for modeling the data. If the piecewise linear regression models are matched against the data, then the parameters are generally not known. This paper studie...Piecewise linear regression models are very flexible models for modeling the data. If the piecewise linear regression models are matched against the data, then the parameters are generally not known. This paper studies the problem of parameter estimation ofpiecewise linear regression models. The method used to estimate the parameters ofpicewise linear regression models is Bayesian method. But the Bayes estimator can not be found analytically. To overcome these problems, the reversible jump MCMC （Marcov Chain Monte Carlo） algorithm is proposed. Reversible jump MCMC algorithm generates the Markov chain converges to the limit distribution of the posterior distribution of the parameters ofpicewise linear regression models. The resulting Markov chain is used to calculate the Bayes estimator for the parameters of picewise linear regression models.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
Caisson breakwaters are mainly constructed in deep waters to protect an area against waves.These breakwaters are con-ventionally designed based on the concept of the safety factor.However,the wave loads and resistance...Caisson breakwaters are mainly constructed in deep waters to protect an area against waves.These breakwaters are con-ventionally designed based on the concept of the safety factor.However,the wave loads and resistance of structures have epistemic or aleatory uncertainties.Furthermore,sliding failure is one of the most important failure modes of caisson breakwaters.In most previous studies,for assessment purposes,uncertainties,such as wave and wave period variation,were ignored.Therefore,in this study,Bayesian reliability analysis is implemented to assess the failure probability of the sliding of Tombak port breakwater in the Persian Gulf.The mean and standard deviations were taken as random variables to consider dismissed uncertainties.For this purpose,the frst-order reliability method(FORM)and the frst principal curvature cor-rection in FORM are used to calculate the reliability index.The performances of these methods are verifed by importance sampling through Monte Carlo simulation(MCS).In addition,the reliability index sensitivities of each random variable are calculated to evaluate the importance of diferent random variables while calculating the caisson sliding.The results show that the reliability index is most sensitive to the coefcients of friction,wave height,and caisson weight(or concrete density).The sensitivity of the failure probability of each of the random variables and their uncertainties are calculated by the derivative method.Finally,the Bayesian regression is implemented to predict the statistical properties of breakwater sliding with non-informative priors,which are compared to Goda’s formulation,used in breakwater design standards.The analysis shows that the model posterior for the sliding of a caisson breakwater has a mean and standard deviation of 0.039 and 0.022,respectively.A normal quantile analysis and residual analysis are also performed to evaluate the correctness of the model responses.展开更多
This study examines the relationship between macroeconomic variables and stock price indices of four prominent OPEC oil-exporting members.Bayesian model averaging(BMA)and regularized linear regression(RLR)are employed...This study examines the relationship between macroeconomic variables and stock price indices of four prominent OPEC oil-exporting members.Bayesian model averaging(BMA)and regularized linear regression(RLR)are employed to address uncertainties arising from different estimation models and variable selection.Jointness is utilized to determine the nature of relationships among variable pairs.The case study spans macroeconomic variables and stock prices from 1996 to 2018.BMA findings reveal a strong positive association between stock price indices and both consumer price index(CPI)and broad money growth in each analyzed OPEC country.Additionally,the study suggests a weak negative correlation between OPEC oil prices and the stock price index.RLR results align with BMA analysis,offering insights valuable for policymakers and international wealth managers.展开更多
[目的]探讨雌二醇(estradiol,E2)水平动态变化与乳腺癌患者生存预后的潜在关联,比较新辅助治疗与无新辅助治疗下乳腺癌患者生存率的差异性。[方法]基于2015—2019年新疆医科大学附属肿瘤医院随访的女性乳腺癌患者的临床数据,首先在不同...[目的]探讨雌二醇(estradiol,E2)水平动态变化与乳腺癌患者生存预后的潜在关联,比较新辅助治疗与无新辅助治疗下乳腺癌患者生存率的差异性。[方法]基于2015—2019年新疆医科大学附属肿瘤医院随访的女性乳腺癌患者的临床数据,首先在不同分位数下(=0.10,0.25,0.50,0.75)分别建立线性分位数混合模型拟合E2水平的动态变化,并通过赤池信息量准则(akaike information criterion,AIC)与贝叶斯信息准则(Bayesian information criteria,BIC)从中选择最优模型作为联合模型的纵向子模型。其次,基于扩展的Cox比例风险模型建立生存子模型;进一步通过共享随机效应建立纵向与生存数据的贝叶斯分位数联合模型,并通过马尔科夫链蒙特卡洛(Markov Chain Monte Carlo,MCMC)方法估计其关联系数()。[结果]最优子模型筛选结果显示,=0.50时,纵向子模型的AIC与BIC值最小。在=0.50下构建贝叶斯分位数联合模型。联合模型结果显示,E2水平的动态变化与乳腺癌患者的生存结局显著性相关(=0.59,HR=1.80,95%CI:1.47~2.24)。新辅助治疗是乳腺癌患者的保护因素(HR=0.155,95%CI:0.047~0.384),能够降低乳腺癌患者84.5%死亡风险。[结论]乳腺癌患者E2水平增加与不良生存预后相关,新辅助治疗可降低乳腺癌患者的死亡风险,并改善其生存预后。乳腺癌患者应采取积极治疗手段控制雌二醇水平升高、抑制肿瘤的生长和扩散,从而提高患者的生存率。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
基金supported by the Natural Science Foundation of Shanghai(23ZR1463600)Shanghai Pudong New Area Health Commission Research Project(PW2021A-69)Research Project of Clinical Research Center of Shanghai Health Medical University(22MC2022002)。
文摘Gastric cancer is the third leading cause of cancer-related mortality and remains a major global health issue^([1]).Annually,approximately 479,000individuals in China are diagnosed with gastric cancer,accounting for almost 45%of all new cases worldwide^([2]).
文摘Piecewise linear regression models are very flexible models for modeling the data. If the piecewise linear regression models are matched against the data, then the parameters are generally not known. This paper studies the problem of parameter estimation ofpiecewise linear regression models. The method used to estimate the parameters ofpicewise linear regression models is Bayesian method. But the Bayes estimator can not be found analytically. To overcome these problems, the reversible jump MCMC （Marcov Chain Monte Carlo） algorithm is proposed. Reversible jump MCMC algorithm generates the Markov chain converges to the limit distribution of the posterior distribution of the parameters ofpicewise linear regression models. The resulting Markov chain is used to calculate the Bayes estimator for the parameters of picewise linear regression models.
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Caisson breakwaters are mainly constructed in deep waters to protect an area against waves.These breakwaters are con-ventionally designed based on the concept of the safety factor.However,the wave loads and resistance of structures have epistemic or aleatory uncertainties.Furthermore,sliding failure is one of the most important failure modes of caisson breakwaters.In most previous studies,for assessment purposes,uncertainties,such as wave and wave period variation,were ignored.Therefore,in this study,Bayesian reliability analysis is implemented to assess the failure probability of the sliding of Tombak port breakwater in the Persian Gulf.The mean and standard deviations were taken as random variables to consider dismissed uncertainties.For this purpose,the frst-order reliability method(FORM)and the frst principal curvature cor-rection in FORM are used to calculate the reliability index.The performances of these methods are verifed by importance sampling through Monte Carlo simulation(MCS).In addition,the reliability index sensitivities of each random variable are calculated to evaluate the importance of diferent random variables while calculating the caisson sliding.The results show that the reliability index is most sensitive to the coefcients of friction,wave height,and caisson weight(or concrete density).The sensitivity of the failure probability of each of the random variables and their uncertainties are calculated by the derivative method.Finally,the Bayesian regression is implemented to predict the statistical properties of breakwater sliding with non-informative priors,which are compared to Goda’s formulation,used in breakwater design standards.The analysis shows that the model posterior for the sliding of a caisson breakwater has a mean and standard deviation of 0.039 and 0.022,respectively.A normal quantile analysis and residual analysis are also performed to evaluate the correctness of the model responses.
文摘This study examines the relationship between macroeconomic variables and stock price indices of four prominent OPEC oil-exporting members.Bayesian model averaging(BMA)and regularized linear regression(RLR)are employed to address uncertainties arising from different estimation models and variable selection.Jointness is utilized to determine the nature of relationships among variable pairs.The case study spans macroeconomic variables and stock prices from 1996 to 2018.BMA findings reveal a strong positive association between stock price indices and both consumer price index(CPI)and broad money growth in each analyzed OPEC country.Additionally,the study suggests a weak negative correlation between OPEC oil prices and the stock price index.RLR results align with BMA analysis,offering insights valuable for policymakers and international wealth managers.
文摘[目的]探讨雌二醇(estradiol,E2)水平动态变化与乳腺癌患者生存预后的潜在关联,比较新辅助治疗与无新辅助治疗下乳腺癌患者生存率的差异性。[方法]基于2015—2019年新疆医科大学附属肿瘤医院随访的女性乳腺癌患者的临床数据,首先在不同分位数下(=0.10,0.25,0.50,0.75)分别建立线性分位数混合模型拟合E2水平的动态变化,并通过赤池信息量准则(akaike information criterion,AIC)与贝叶斯信息准则(Bayesian information criteria,BIC)从中选择最优模型作为联合模型的纵向子模型。其次,基于扩展的Cox比例风险模型建立生存子模型;进一步通过共享随机效应建立纵向与生存数据的贝叶斯分位数联合模型,并通过马尔科夫链蒙特卡洛(Markov Chain Monte Carlo,MCMC)方法估计其关联系数()。[结果]最优子模型筛选结果显示,=0.50时,纵向子模型的AIC与BIC值最小。在=0.50下构建贝叶斯分位数联合模型。联合模型结果显示,E2水平的动态变化与乳腺癌患者的生存结局显著性相关(=0.59,HR=1.80,95%CI:1.47~2.24)。新辅助治疗是乳腺癌患者的保护因素(HR=0.155,95%CI:0.047~0.384),能够降低乳腺癌患者84.5%死亡风险。[结论]乳腺癌患者E2水平增加与不良生存预后相关,新辅助治疗可降低乳腺癌患者的死亡风险,并改善其生存预后。乳腺癌患者应采取积极治疗手段控制雌二醇水平升高、抑制肿瘤的生长和扩散,从而提高患者的生存率。
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.
