Conditionally reducible natural exponential families and enriched conjugate priors
Conditionally reducible natural exponential families and enriched conjugate priors
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DOI：
10.1111/1467-9469.00243
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发表时间：
2001-06-01
影响因子：
1
通讯作者：
Veronese, P
中科院分区：
文献类型：
--
作者：
Consonni, G;Veronese, P
考虑一个指数族的向量参数的先验分布的标准共轭族。两个不同的模型参数化可能会导致标准的共轭家庭是不一致的，即一个家庭不能从另一个通过通常的变量变化技术。这就提出了一个问题，找到合适的参数化，可能会导致丰富的共轭家庭比传统的更灵活。在此基础上定义了指数族的一个新性质--条件可约性，并对条件可约自然指数族的性质进行了深入的研究。特别是，我们与这个新的属性的概念，削减，并表明条件可约家庭承认一个reparameterization在一个向量具有似然独立的组件。详细描述了一种获得条件可约族的丰富共轭分布的一般方法，推广了以前的工作和该领域的最新贡献，并以具有简单二次方差函数的自然指数族为例说明了该理论。
Consider a standard conjugate family of prior distributions for a vector-parameter indexing an exponential family. Two distinct model parameterizations may well lead to standard conjugate families which are not consistent, i.e. one family cannot be derived from the other by the usual change-of-variable technique. This raises the problem of finding suitable parameterizations that may lead to enriched conjugate families which are more flexible than the traditional ones. The previous remark motivates the definition of a new property for an exponential family, named conditional reducibility, Features of conditionally-reducible natural exponential families are investigated thoroughly. In particular, we relate this new property to the notion of cut, and show that conditionally-reducible families admit a reparameterization in terms of a vector having Likelihood-independent components. A general methodology to obtain enriched conjugate distributions for conditionally-reducible families is described in detail, generalizing previous works and more recent contributions in the area, The theory is illustrated with reference to natural exponential families having simple quadratic variance function.