Asymptotic behaviour of the posterior distribution in overfitted mixture models
Asymptotic behaviour of the posterior distribution in overfitted mixture models
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DOI：
10.1111/j.1467-9868.2011.00781.x
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发表时间：
2011-01-01
影响因子：
5.8
通讯作者：
Mengersen, Kerrie
中科院分区：
文献类型：
--
作者：
Rousseau, Judith;Mengersen, Kerrie
我们研究了当混合模型中成分数大于真实成分数时后验分布的渐近行为：这种情况通常被称为过拟合混合。我们特别证明了后验分布通常具有稳定和有趣的行为，因为它倾向于清空额外的分量。这种稳定性是在对先验的一定限制下实现的，这可以作为选择先验的指导方针。给出了一些模拟来说明这种行为。
We study the asymptotic behaviour of the posterior distribution in a mixture model when the number of components in the mixture is larger than the true number of components: a situation which is commonly referred to as an overfitted mixture. We prove in particular that quite generally the posterior distribution has a stable and interesting behaviour, since it tends to empty the extra components. This stability is achieved under some restriction on the prior, which can be used as a guideline for choosing the prior. Some simulations are presented to illustrate this behaviour.