Dirichlet Processes in Nonlinear Mixed Effects Models

Abstract

In this article, we use two efficient approaches to deal with the difficulty in computing the intractable integrals when implementing Gibbs sampling in the nonlinear mixed effects model (NLMM) based on Dirichlet processes (DP). In the first approach, we compute the Laplace's approximation to the integral for its high accuracy, low cost, and ease of implementation. The second approach uses the no-gaps algorithm of MacEachern and Müller (1998) to perform Gibbs sampling without evaluating the difficult integral. We apply both approaches to real problems and simulations. Results show that both approaches perform well in density estimation and prediction and are superior to the parametric analysis in that they can detect important model features, such as skewness, long tails, and multimodality, whereas the parametric analysis cannot.

Keywords:

• Dirichlet processes
• Gibbs sampling
• Laplace's approximation
• Metropolis–Hastings algorithm
• No-gaps algorithm
• Nonlinear mixed effects model (NLMM)

Mathematics Subject Classification:

• 62G07
• 62G09
• 62-07

Acknowledgments

The author is grateful for the valuable suggestions provided by the reviewers and the Associate Editor which led to significant improvement of the earlier manuscript.