We study Bayesian estimation of mixture models and argue in favor of fitting the marginal posterior distribution over component assignments directly, rather than Gibbs sampling from the joint posterior on components and parameters as is commonly done. Some previous authors have found the former approach to have slow mixing, but we show that, implemented correctly, it can achieve excellent performance. In particular, we describe a new Monte Carlo algorithm for sampling from the marginal posterior of a general integrable mixture that makes use of rejection-free sampling from the prior over component assignments to achieve excellent mixing times in typical applications, outperforming standard Gibbs sampling, in some cases by a wide margin. We demonstrate the approach with a selection of applications to Gaussian, Poisson, and categorical models.

翻译：本文研究混合模型的贝叶斯估计，主张直接拟合分量分配上的边缘后验分布，而非如常规做法般对分量与参数的联合后验进行吉布斯采样。先前有研究者认为前一种方法混合速度较慢，但我们证明若正确实施，该方法可获得优异性能。具体而言，我们提出一种新的蒙特卡洛算法，用于对一般可积混合模型的边缘后验进行采样。该算法利用分量分配先验的无拒绝采样特性，在典型应用中实现了优异的混合时间，其性能超越标准吉布斯采样，在某些案例中优势显著。我们通过高斯模型、泊松模型及分类模型的一系列应用案例验证了该方法的有效性。