2019/10/27 by Belhal Karimi, Marc Lavielle, Karimi, Belhal +3
Computer Science · Mathematics · #Applications (stat.AP) #FOS: Computer and information sciences #Gaussian Processes and Bayesian Inference #Markov Chains and Monte Carlo Methods #Methodology (stat.ME) #Statistical Methods and Bayesian Inference #Statistical Methods and Inference
paper · pdf · doi:10.48550/arxiv.1910.12222
openalex publication_date 2019/10/27 · openalex created_date 2022/07/19 · openalex updated_date 2026/07/28
The ability to generate samples of the random effects from their conditional\ndistributions is fundamental for inference in mixed effects models. Random walk\nMetropolis is widely used to perform such sampling, but this method is known to\nconverge slowly for medium dimensional problems, or when the joint structure of\nthe distributions to sample is spatially heterogeneous. The main contribution\nconsists of an independent Metropolis-Hastings (MH) algorithm based on a\nmultidimensional Gaussian proposal that takes into account the joint\nconditional distribution of the random effects and does not require any tuning.\nIndeed, this distribution is automatically obtained thanks to a Laplace\napproximation of the incomplete data model. Such approximation is shown to be\nequivalent to linearizing the structural model in the case of continuous data.\nNumerical experiments based on simulated and real data illustrate the\nperformance of the proposed methods. For fitting nonlinear mixed effects\nmodels, the suggested MH algorithm is efficiently combined with a stochastic\napproximation version of the EM algorithm for maximum likelihood estimation of\nthe global parameters.\n