Comparison of Bayesian Nonparametric Density Estimation Methods

TL;DR

This paper compares Bayesian nonparametric density estimation methods, including Lindsey, penalized Gaussian mixtures, and Dirichlet process models, highlighting their robustness and convergence properties through simulations and data analysis.

Contribution

It introduces a Bayesian nonparametric approach that is more robust to model misspecification and compares it with existing methods using MCMC techniques.

Findings

Posterior distribution of weights converges to a Normal distribution as sample size increases.

The proposed method demonstrates robustness in density estimation.

Simulation and data analysis validate the effectiveness of the approach.

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.