In traditional Bayesian software reliability models, it was assume that all probabilities are precise. In practical applications the parameters of the probability distributions are often under uncertainty due to stron...In traditional Bayesian software reliability models, it was assume that all probabilities are precise. In practical applications the parameters of the probability distributions are often under uncertainty due to strong dependence on subjective information of experts＇ judgments on sparse statistical data. In this paper, a quasi-Bayesian software reliability model using interval-valued probabilities to clearly quantify experts＇ prior beliefs on possible intervals of the parameters of the probability distributions is presented. The model integrates experts＇ judgments with statistical data to obtain more convincible assessments of software reliability with small samples. For some actual data sets, the presented model yields better predictions than the Jelinski-Moranda （JM） model using maximum likelihood （ML）.展开更多
Propensity score (PS) adjustment can control confounding effects and reduce bias when estimating treatment effects in non-randomized trials or observational studies. PS methods are becoming increasingly used to estima...Propensity score (PS) adjustment can control confounding effects and reduce bias when estimating treatment effects in non-randomized trials or observational studies. PS methods are becoming increasingly used to estimate causal effects, including when the sample size is small compared to the number of confounders. With numerous confounders, quasi-complete separation can easily occur in logistic regression used for estimating the PS, but this has not been addressed. We focused on a Bayesian PS method to address the limitations of quasi-complete separation faced by small trials. Bayesian methods are useful because they estimate the PS and causal effects simultaneously while considering the uncertainty of the PS by modelling it as a latent variable. In this study, we conducted simulations to evaluate the performance of Bayesian simultaneous PS estimation by considering the specification of prior distributions for model comparison. We propose a method to improve predictive performance with discrete outcomes in small trials. We found that the specification of prior distributions assigned to logistic regression coefficients was more important in the second step than in the first step, even when there was a quasi-complete separation in the first step. Assigning Cauchy (0, 2.5) to coefficients improved the predictive performance for estimating causal effects and improving the balancing properties of the confounder.展开更多
基金supported by the National High-Technology Research and Development Program of China (Grant Nos.2006AA01Z187,2007AA040605)
文摘In traditional Bayesian software reliability models, it was assume that all probabilities are precise. In practical applications the parameters of the probability distributions are often under uncertainty due to strong dependence on subjective information of experts＇ judgments on sparse statistical data. In this paper, a quasi-Bayesian software reliability model using interval-valued probabilities to clearly quantify experts＇ prior beliefs on possible intervals of the parameters of the probability distributions is presented. The model integrates experts＇ judgments with statistical data to obtain more convincible assessments of software reliability with small samples. For some actual data sets, the presented model yields better predictions than the Jelinski-Moranda （JM） model using maximum likelihood （ML）.
文摘Propensity score (PS) adjustment can control confounding effects and reduce bias when estimating treatment effects in non-randomized trials or observational studies. PS methods are becoming increasingly used to estimate causal effects, including when the sample size is small compared to the number of confounders. With numerous confounders, quasi-complete separation can easily occur in logistic regression used for estimating the PS, but this has not been addressed. We focused on a Bayesian PS method to address the limitations of quasi-complete separation faced by small trials. Bayesian methods are useful because they estimate the PS and causal effects simultaneously while considering the uncertainty of the PS by modelling it as a latent variable. In this study, we conducted simulations to evaluate the performance of Bayesian simultaneous PS estimation by considering the specification of prior distributions for model comparison. We propose a method to improve predictive performance with discrete outcomes in small trials. We found that the specification of prior distributions assigned to logistic regression coefficients was more important in the second step than in the first step, even when there was a quasi-complete separation in the first step. Assigning Cauchy (0, 2.5) to coefficients improved the predictive performance for estimating causal effects and improving the balancing properties of the confounder.
