Marginal likelihood from the Gibbs output
Marginal likelihood from the Gibbs output
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DOI：
10.2307/2291521
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发表时间：
1995-12-01
影响因子：
3.7
通讯作者：
Chib, S
中科院分区：
文献类型：
--
作者：
Chib, S
在贝叶斯估计的背景下，通过吉布斯抽样，有或没有数据增强，一个简单的方法来计算样本数据的边际密度（边际似然）给定的参数从后验分布。因此，用于模型比较的贝叶斯因子可以作为模拟的副产品进行常规计算。然而，事实证明，这种计算极具挑战性。我们的方法利用了这样一个事实，即边缘密度可以表示为先验时间的似然函数在后验密度。这个简单的恒等式适用于任何参数值。后验密度的估计示出是可用的，如果所有完整的条件密度中使用的吉布斯采样有封闭形式的表达式。为了提高精度，后验密度估计在一个高密度点，并得出了数字的标准误差估计结果。的想法被应用到概率单位回归和有限混合模型。
In the context of Bayes estimation via Gibbs sampling, with or without data augmentation, a simple approach is developed for computing the marginal density of the sample data (marginal likelihood) given parameter draws from the posterior distribution. Consequently, Bayes factors for model comparisons can be routinely computed as a by-product of the simulation. Hitherto, this calculation has proved extremely challenging. Our approach exploits the fact that the marginal density can be expressed as the prior times the likelihood function over the posterior density. This simple identity holds for any parameter value. An estimate of the posterior density is shown to be available if all complete conditional densities used in the Gibbs sampler have closed-form expressions. To improve accuracy, the posterior density is estimated at a high density point, and the numerical standard error of resulting estimate is derived. The ideas are applied to probit regression and finite mixture models.