2019/10/26 by Belhal Karimi, Marc Lavielle, Karimi, Belhal +1
Computer Science · Mathematics · #Applications (stat.AP) #Bayesian Methods and Mixture Models #FOS: Computer and information sciences #Gaussian Processes and Bayesian Inference #Markov Chains and Monte Carlo Methods #Methodology (stat.ME)
paper · pdf · doi:10.48550/arxiv.1910.12090
openalex publication_date 2019/10/26 · 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 conduct such sampling, but such a method can\nconverge slowly for medium dimension problems, or when the joint structure of\nthe distributions to sample is complex. We propose a Metropolis Hastings (MH)\nalgorithm based on a multidimensional Gaussian proposal that takes into account\nthe joint conditional distribution of the random effects and does not require\nany tuning, in contrast with more sophisticated samplers such as the Metropolis\nAdjusted Langevin Algorithm or the No-U-Turn Sampler that involve costly tuning\nruns or intensive computation. Indeed, this distribution is automatically\nobtained thanks to a Laplace approximation of the original model. We show that\nsuch approximation is equivalent to linearizing the model in the case of\ncontinuous data. Numerical experiments based on real data highlight the very\ngood performances of the proposed method for continuous data model.\n