Uncertainty in counts and operating time in estimating Poisson occurrence rates

When quantifying a plant-specific Poisson event occurrence rate λ in PRA studies, it is sometimes the case that either the reported plant-specific number of events x or the operating time t (or both) are uncertain. We present a Bayesian Markov chain Monte Carlo method that can be used to obtain the required average posterior distribution of λ which reflects the corresponding uncertainty in x and/or t. The method improves upon existing methods and is also easy to implement using hierarchical Bayesian software that is freely available from the Web.     

A fully Bayesian approach for combining multi-level information in multi-state fault tree quantification

This paper presents a fully Bayesian approach that simultaneously combines non-overlapping (in time) basic event and higher-level event failure data in fault tree quantification with multi-state events. Such higher-level data often correspond to train, subsystem or system failure events. The fully Bayesian approach also automatically propagates the highest-level data to lower levels in the fault tree. A simple example illustrates our approach.     

Bayesian inference in probabilistic risk assessment—The current state of the art

Markov chain Monte Carlo (MCMC) approaches to sampling directly from the joint posterior distribution of aleatory model parameters have led to tremendous advances in Bayesian inference capability in a wide variety of fields, including probabilistic risk analysis. The advent of freely available software coupled with inexpensive computing power has catalyzed this advance. This paper examines where the risk assessment community is with respect to implementing modern computational-based Bayesian approaches to inference. Through a series of examples in different topical areas, it introduces salient concepts and illustrates the practical application of Bayesian inference via MCMC sampling to a variety of important problems.     

利用贝叶斯推理估计二维含源对流扩散方程参数

为了克服观测数据的不确定性给参数反演带来的困难,利用贝叶斯推理建立了二维含源对流扩散方程参数估计的数学模型。通过贝叶斯定理,获得了模型参数的后验分布,从而获得反问题的解。对于多参数反演问题,基于数值解计算得到的参数后验分布很难直观地表现出来,采用马尔科夫链蒙特卡罗方法对参数的后验分布进行采样,获得了扩散系数和降解系数的估计值。研究了观测点位置对计算结果的影响;同时研究了似然函数的形式对估计结果的影响,结果表明在异常值可能出现时采用Laplace分布型的似然函数可以获得稳健估计。对不同观测点数目下的估计值进行了对比,认为对于二维稳态对流扩散方程的双参数估计问题,至少需要两个观测点才有可能得到合理的解。     

A fully Bayesian approach for combining multilevel failure information in fault tree quantification and optimal follow-on resource allocation

This paper presents a fully Bayesian approach that simultaneously combines non-overlapping (in time) basic event and higher-level event failure data in fault tree quantification. Such higher-level data often correspond to train, subsystem or system failure events. The fully Bayesian approach also automatically propagates the highest-level data to lower levels in the fault tree. A simple example illustrates our approach. The optimal allocation of resources for collecting additional data from a choice of different level events is also presented. The optimization is achieved using a genetic algorithm.