Computational and inferential difficulties with mixture posterior distributions.
Computational and inferential difficulties with mixture posterior distributions.
复制标题
DOI：
10.2307/2669477
复制
发表时间：
2000-09-01
影响因子：
3.7
通讯作者：
Robert, CP
中科院分区：
文献类型：
--
作者：
Celeux, G;Hurn, M;Robert, CP
本文讨论混合模型后验分布的探索和解释问题。混合后验分布的规范意味着Ic！模式是立即知道的。标准的马尔可夫链蒙特卡罗（MCMC）技术通常有困难，以及分离的模式，如发生在这里; MCMC采样器停留在一个本地模式的邻域内，并未能访问其他同样重要的模式。我们发现，这些模式的探索可以施加使用回火过渡。然而，如果先验分布不能区分不同的成分，那么后验混合分布是对称的，不能使用标准估计量，如后验均值。我们提出了替代方案的贝叶斯推理置换不变后验，包括聚类设备和替代适当的损失函数。
This article dears with both exploration and interpretation problems related to posterior distributions for mixture models. The specification of mixture posterior distributions means that the presence of Ic! modes is known immediately. Standard Markov chain Monte Carlo (MCMC) techniques usually have difficulties with well-separated modes such as occur here; the MCMC sampler stays within a neighborhood of a local mode and fails to visit other equally important modes. We show that exploration of these modes can be imposed using tempered transitions. However, if the prior distribution does not distinguish between the different components, then the posterior mixture distribution is symmetric and standard estimators such as posterior means cannot be used. We propose alternatives for Bayesian inference for permutation invariant posteriors, including a clustering device and alternative appropriate loss functions.