Efficient Metropolis-Hastings Sampling for Nonlinear Mixed Effects Models

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.

Reduction of quantitative systems pharmacology models using artificial neural networks

“…La estimación de la integral se hace por un método de Monte Carlo, pero se distingue de otros métodos IS, por la utilización de un tercer nivel en la jerarquía correspondiente a la distribución de los efectos fijos y aleatorios a priori. En los métodos bayesianos se utilizan algoritmos como Metrópolis-Hastings que permiten el cálculo de la distribución marginal con el uso de cadenas de Markov, que generan muestras independientes [15].…”