Posterior Cumulant Relationships in Bayesian Inference Involving the Exponential Family
Posterior Cumulant Relationships in Bayesian Inference Involving the Exponential Family
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涉及指数族的贝叶斯推理中的后累积量关系
DOI：
10.1080/01621459.1993.10476427
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发表时间：
1993
影响因子：
3.7
通讯作者：
Adrian F. M. Smith
中科院分区：
文献类型：
--
作者：
L. Pericchi;B. Sansó;Adrian F. M. Smith
摘要 对于单参数上下文中的贝叶斯推理，其中似然性或先验具有指数族形式，推导了规范参数和期望参数（的函数）的后验矩和累积量的关系。所展示的恒等式概括了共轭分析案例中众所周知的简单关系。这些结果的应用表明在贝叶斯稳健性和近似领域。特别是，通过大规模观察的后验分布行为获得了结果，概括了 Meeden 和 Isaacson 的工作。
Abstract For Bayesian inference in one-parameter contexts where either the likelihood or the prior has an exponential family form, relationships are derived for posterior moments and cumulants of (functions of) both the canonical and the expectation parameters. The identities exhibited generalize the simple relationships well known in the conjugate analysis case. Applications of these results are indicated in the areas of Bayesian robustness and approximation. In particular, results are obtained on the behavior of the posterior distribution for a large observation, generalizing work of Meeden and Isaacson.