Misspecification in infinite-dimensional Bayesian statistics
Misspecification in infinite-dimensional Bayesian statistics
复制标题
无限维贝叶斯统计中的错误指定
DOI：
10.1214/009053606000000029
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发表时间：
2006
影响因子：
4.5
通讯作者：
Van der Vaart
中科院分区：
文献类型：
--
作者：
B. Kleijn;W. A.;Van der Vaart
我们考虑了模型错误指定时后验分布的渐近行为。给定一个先验分布和一个随机样本的分布P 0，这可能不是在支持的前，我们表明，后集中其质量附近的点在支持的前，最大限度地减少Kullback-Leibler分歧相对于P 0。熵条件和先验质量条件决定收敛速度。该方法适用于几个例子，特别感兴趣的无穷维模型。这些包括高斯混合，非参数回归和参数模型。
We consider the asymptotic behavior of posterior distributions if the model is misspecified. Given a prior distribution and a random sample from a distribution P 0 , which may not be in the support of the prior, we show that the posterior concentrates its mass near the points in the support of the prior that minimize the Kullback-Leibler divergence with respect to P 0 . An entropy condition and a prior-mass condition determine the rate of convergence. The method is applied to several examples, with special interest for infinite-dimensional models. These include Gaussian mixtures, nonparametric regression and parametric models.