论文标题
贝叶斯非参数密度估计方法的比较
Comparison of Bayesian Nonparametric Density Estimation Methods
论文作者
论文摘要
在本文中，我们提出了一种非参数贝叶斯方法，用于林赛和惩罚高斯混合物方法。我们将这些方法与Dirichlet工艺混合模型进行了比较。我们的方法是一种贝叶斯非参数方法，不仅基于概率分布的参数家族。因此，拟合的模型更适合模型错误指定。同样，通过贝叶斯方法，我们具有关注参数的全部后验分布。可以通过可靠的间隔，平均值，中位数，标准偏差，分位数等进行总结。审查了Lindsey，受惩罚的高斯混合物和Dirichlet过程混合方法。估计是通过马尔可夫链蒙特卡洛（MCMC）方法进行的。受到惩罚的高斯混合方法是通过汉密尔顿蒙特卡洛（HMC）实施的。我们表明，在某些规律性条件下，随着n的增加，权重的后验分布会收敛到正态分布。报告了仿真结果和数据分析。
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.
