Penalized loss functions for Bayesian model comparison
Penalized loss functions for Bayesian model comparison
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DOI：
10.1093/biostatistics/kxm049
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发表时间：
2008-07-01
期刊：
影响因子：
2.1
通讯作者：
Plummer, Martyn
中科院分区：
文献类型：
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作者：
Plummer, Martyn
偏差信息准则（DIC）被广泛用于贝叶斯模型的比较，但缺乏明确的理论基础。DIC被证明是基于偏差的惩罚损失函数的近似值，惩罚来自交叉验证参数。只有当模型中参数的有效数目远远小于独立观测的数目时，这种近似才有效。在疾病制图（DIC的典型应用）中，这一假设不成立，DIC对更复杂的模型惩罚不足。另一种基于偏差的损失函数，来源于相同的决策理论框架，被应用于混合模型，这在以前被认为是不适合DIC的应用。
The deviance information criterion (DIC) is widely used for Bayesian model comparison, despite the lack of a clear theoretical foundation. DIC is shown to be an approximation to a penalized loss function based on the deviance, with a penalty derived from a cross-validation argument. This approximation is valid only when the effective number of parameters in the model is much smaller than the number of independent observations. In disease mapping, a typical application of DIC, this assumption does not hold and DIC under-penalizes more complex models. Another deviance-based loss function, derived from the same decision-theoretic framework, is applied to mixture models, which have previously been considered an unsuitable application for DIC.