Bayesian analysis of elapsed times in continuous-time Markov chains
Bayesian analysis of elapsed times in continuous-time Markov chains
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DOI：
10.1002/cjs.5550360302
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发表时间：
2008-09-01
影响因子：
0.6
通讯作者：
Suchard, Marc A.
中科院分区：
文献类型：
--
作者：
Ferreira, Marco A. R.;Suchard, Marc A.
作者考虑了基于条件参考先验的连续时间马尔可夫链模型的贝叶斯分析。对于此类模型，链观测之间经过时间的推断在很大程度上取决于随着经过时间的增加先验的衰减率。此外，对经过时间的不正确的先验可能会导致不正确的后验分布。此外，无穷小速率矩阵也是此类模型的特征。专家通常对该矩阵的参数有很好的先验知识。作者表明，使用速率矩阵参数的适当先验以及经过时间的条件参考先验可以产生适当的后验分布。作者还证明，与文献中先前提出的基于先验的分析相比，基于条件参考先验的对经过时间的贝叶斯分析具有更好的频率特性。因此，先验类型代表了估计软件更好的默认先验选择。
The authors consider Bayesian analysis for continuous-time Markov chain models based on a conditional reference prior. For such models, inference of the elapsed time between chain observations depends heavily on the rate of decay of the prior as the elapsed time increases. Moreover, improper priors on the elapsed time may lead to improper posterior distributions. In addition, an infinitesimal rate matrix also characterizes this class of models. Experts often have good prior knowledge about the parameters of this matrix. The authors show that the use of a proper prior for the rate matrix parameters together with the conditional reference prior for the elapsed time yields a proper posterior distribution. The authors also demonstrate that, when compared to analyses based on priors previously proposed in the literature, a Bayesian analysis on the elapsed time based on the conditional reference prior possesses better frequentist properties. The type of prior thus represents a better default prior choice for estimation software.