Bayesian model selection in finite mixtures by marginal density decompositions
Bayesian model selection in finite mixtures by marginal density decompositions
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DOI：
10.1198/016214501753382255
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发表时间：
2001-12-01
影响因子：
3.7
通讯作者：
Sun, JY
中科院分区：
文献类型：
--
作者：
Ishwaran, H;James, LF;Sun, JY
我们考虑在有限混合模型中估计分量 d 的数量和未知混合分布的问题，其中 d 由某个固定的有限数 N 界定。我们的方法依赖于在最多具有 N 个分量的混合分布空间上使用先验。通过分解在此先验条件下得到的边际密度，我们发现了一种用于一致估计 d 的加权贝叶斯因子方法，该方法可以通过独立同分布广义加权中餐馆 (GWCR) 蒙特卡罗算法来实现。我们还讨论了用于估计 d 和混合分布的吉布斯采样方法（阻塞吉布斯采样器）。我们表明，我们得到的后验是一致的，并且达到了频率论最优 O-p(n(-1/4)) 估计率。我们将新的 GWCR 模型选择过程的性能与通过 EM 算法实现的 Akaike 信息准则和 Bayes 信息准则的性能进行了比较。考虑将我们的方法应用于五个真实数据集和模拟。
We consider the problem of estimating the number of components d and the unknown mixing distribution in a finite mixture model, in which d is bounded by some fixed finite number N. Our approach relies on the use of a prior over the space of mixing distributions with at most N components. By decomposing the resulting marginal density under this prior, we discover a weighted Bayes factor method for consistently estimating d that can be implemented by an iid generalized weighted Chinese restaurant (GWCR) Monte Carlo algorithm. We also discuss a Gibbs sampling method (the blocked Gibbs sampler) for estimating d and also the mixing distribution. We show that our resulting posterior is consistent and achieves the frequentist optimal O-p(n(-1/4)) rate of estimation. We compare the performance of the new GWCR model selection procedure with that of the Akaike information criterion and the Bayes information criterion implemented through an EM algorithm. Applications of our methods to five real datasets and simulations are considered.