f-SAEM: A fast Stochastic Approximation of the EM algorithm for nonlinear mixed effects models

TL;DR

This paper introduces f-SAEM, a fast stochastic approximation EM algorithm that uses an independent Metropolis-Hastings sampler based on a Gaussian proposal derived from a Laplace approximation, improving sampling efficiency in nonlinear mixed effects models.

Contribution

It presents a novel MH algorithm that automatically adapts to the joint distribution of random effects without tuning, enhancing inference in nonlinear mixed effects models.

Findings

The proposed method outperforms traditional random walk Metropolis in medium-dimensional problems.

The Laplace approximation simplifies the joint distribution estimation, reducing computational complexity.

Numerical experiments demonstrate improved convergence and efficiency in real and simulated data.

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 perform such sampling, but this method is known to converge slowly for medium dimensional problems, or when the joint structure of the distributions to sample is spatially heterogeneous. The main contribution consists of an independent 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. Indeed, this distribution is automatically obtained thanks to a Laplace approximation of the incomplete data model. Such approximation is shown to be equivalent to linearizing the structural model in the case of continuous data. Numerical experiments based on simulated and real data illustrate the performance of the proposed methods. For fitting nonlinear mixed effects models, the suggested MH algorithm is efficiently combined with a stochastic approximation version of the EM algorithm for maximum likelihood estimation of the global parameters.