Abstract

In this paper, we propose a nonparametric Bayesian approach for Lindsey and penalized Gaussian mixtures methods. We compare these methods with the Dirichlet process mixture model. Our approach is a Bayesian nonparametric method not based solely on a parametric family of probability distributions. Thus, the fitted models are more robust to model misspecification. Also, with the Bayesian approach, we have the entire posterior distribution of our parameter of interest; it can be summarized through credible intervals, mean, median, standard deviation, quantiles, etc. The Lindsey, penalized Gaussian mixtures, and Dirichlet process mixture methods are reviewed. The estimations are performed via Markov chain Monte Carlo (MCMC) methods. The penalized Gaussian mixtures method is implemented via Hamiltonian Monte Carlo (HMC). We show that under certain regularity conditions, and as n increases, the posterior distribution of the weights converges to a Normal distribution. Simulation results and data analysis are reported.

摘要

在本文中，我们提出了一种用于 Lindsey 和惩罚高斯混合方法的非参数贝叶斯方法。我们将这些方法与 Dirichlet 过程混合模型进行比较。我们的方法是一种贝叶斯非参数方法，它不仅仅基于概率分布的参数族。因此，拟合模型对模型错误指定更加稳健。此外，使用贝叶斯方法，我们得到了我们感兴趣的参数的整个后验分布；可以通过可信区间、均值、中位数、标准差、分位数等来概括。回顾了Lindsey、惩罚高斯混合和Dirichlet过程混合方法。估计是通过马尔可夫链蒙特卡罗 (MCMC) 方法进行的。惩罚高斯混合方法是通过哈密顿蒙特卡罗 (HMC) 实现的。我们表明，在某些规律性条件下，随着 n 的增加，权重的后验分布收敛到正态分布。报告模拟结果和数据分析。