In Bayesian inference for mixture models with an unknown number of components, a finite mixture model is usually employed that assumes prior distributions for mixing weights and the number of components. This model is called a mixture of finite mixtures (MFM). As a prior distribution for the weights, a (symmetric) Dirichlet distribution is widely used for conjugacy and computational simplicity, while the selection of the concentration parameter influences the estimate of the number of components. In this paper, we focus on estimating the number of components. As a robust alternative Dirichlet weights, we present a method based on a mixture of finite mixtures with normalized inverse Gaussian weights. The motivation is similar to the use of normalized inverse Gaussian processes instead of Dirichlet processes for infinite mixture modeling. Introducing latent variables, the posterior computation is carried out using block Gibbs sampling without using the reversible jump algorithm. The performance of the proposed method is illustrated through some numerical experiments and real data examples, including clustering, density estimation, and community detection.

翻译：在具有未知分量数的混合模型的贝叶斯推断中，通常采用有限混合模型，该模型为混合权重和分量数设定先验分布。此模型称为有限混合模型之混合。作为权重的先验分布，（对称）狄利克雷分布因其共轭性和计算简便性而被广泛使用，然而浓度参数的选择会影响分量数的估计。本文聚焦于分量数的估计。作为狄利克雷权重的一种稳健替代方案，我们提出了一种基于具有归一化逆高斯权重的有限混合模型之混合的方法。其动机类似于在无限混合建模中使用归一化逆高斯过程替代狄利克雷过程。通过引入潜变量，后验计算采用分块吉布斯采样进行，无需使用可逆跳转算法。通过若干数值实验和真实数据示例（包括聚类、密度估计和社区检测）展示了所提方法的性能。