Efficient Metropolis-Hastings Sampling for Nonlinear Mixed Effects Models

TL;DR

This paper introduces a new Metropolis-Hastings sampling method for nonlinear mixed effects models that uses a Gaussian proposal based on Laplace approximation, offering efficient, tuning-free sampling especially for continuous data.

Contribution

The paper presents a novel MH algorithm leveraging Laplace approximation for joint conditional distribution sampling in mixed effects models, avoiding costly tuning.

Findings

Demonstrates superior performance on real continuous data

Achieves faster convergence without tuning

Effective for medium-dimensional problems

Abstract

The ability to generate samples of the random effects from their conditional distributions is fundamental for inference in mixed effects models. Random walk Metropolis is widely used to conduct such sampling, but such a method can converge slowly for medium dimension problems, or when the joint structure of the distributions to sample is complex. We propose a Metropolis Hastings (MH) algorithm based on a multidimensional Gaussian proposal that takes into account the joint conditional distribution of the random effects and does not require any tuning, in contrast with more sophisticated samplers such as the Metropolis Adjusted Langevin Algorithm or the No-U-Turn Sampler that involve costly tuning runs or intensive computation. Indeed, this distribution is automatically obtained thanks to a Laplace approximation of the original model. We show that such approximation is equivalent to linearizing the model in the case of continuous data. Numerical experiments based on real data highlight the very good performances of the proposed method for continuous data model.