组合概率分布：扩展对数池方法
Combining probability distributions: Extending the logarithmic pooling approach
摘要：
组合分布是决策理论和贝叶斯推断中的一个重要问题。对数池是一种通过使用一组反映每个信息源可靠性的权重来聚合专家意见的流行方法。然而，由此产生的汇总分布在很大程度上取决于给每个意见/先验的权重集，因此必须仔细考虑权重的选择。在本文中，我们回顾和扩展的对数池的统计理论，侧重于使用分层先验分布的权重分配。我们探讨了几个统计应用，如生存概率的估计，荟萃分析和贝叶斯融合的人口增长和流行病的确定性模型。我们表明，它是可以学习的权重数据，虽然可识别性问题可能会出现一些配置的先验知识和数据。此外，我们展示了如何分层的方法导致后验分布，能够适应复杂模型中的先验数据冲突。
英文摘要：
Combining distributions is an important issue in decision theory and Bayesian inference. Logarithmic pooling is a popular method to aggregate expert opinions by using a set of weights that reflect the reliability of each information source. However, the resulting pooled distribution depends heavily on set of weights given to each opinion/prior and thus careful consideration must be given to the choice of weights. In this paper we review and extend the statistical theory of logarithmic pooling, focusing on the assignment of the weights using a hierarchical prior distribution. We explore several statistical applications, such as the estimation of survival probabilities, meta-analysis and Bayesian melding of deterministic models of population growth and epidemics. We show that it is possible learn the weights from data, although identifiability issues may arise for some configurations of priors and data. Furthermore, we show how the hierarchical approach leads to posterior distributions that are able to accommodate prior-data conflict in complex models.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
