Changing Parameters by Partial Mappings
Changing Parameters by Partial Mappings
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DOI：
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发表时间：
2010
影响因子：
1.4
通讯作者：
M. Wiedenbeck;N. Wermuth
中科院分区：
文献类型：
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作者：
M. Wiedenbeck;N. Wermuth
在穆尔统计建模中经常需要不同参数集之间的变化，例如线性回归或指数模型中的转换。例如，可能存在基于主题解释的特定推理问题，替代拟合良好的约束模型，看似不同的约束模型的兼容性判断，或替代参数化下的不同参考先验。我们介绍并讨论了部分映射，称为部分复制，并将其与更复杂的映射，称为部分反转。这两种操作都用于分解矩阵运算，解释线性参数集之间的递归关系，在不同类型的线性模型之间切换，在独立约束下近似指数族模型中的最大似然估计，以及在指数族分布中的正则和矩参数集之间或相应的最大似然估计集之间部分切换。
Changes between different sets of parameters are often needed in mul- tivariate statistical modeling, such as transformations within linear regression or in exponential models. There may, for instance, be specific inference questions based on subject matter interpretations, alternative well-fitting constrained mod- els, compatibility judgements of seemingly distinct constrained models, or different reference priors under alternative parameterizations. We introduce and discuss a partial mapping, called partial replication, and re- late it to a more complex mapping, called partial inversion. Both operations are used to decompose matrix operations, to explain recursion relations among sets of linear parameters, to change between different types of linear models, to approxi- mate maximum-likelihood estimates in exponential family models under indepen- dence constraints, and to switch partially between sets of canonical and moment parameters in exponential family distributions or between sets of corresponding maximum-likelihood estimates.