Posterior contraction rates in a sparse nonlinear mixedeffects model
Abstract
Recent works have shown an interest in investigating the frequentist asymptotic properties of Bayesian procedures for highdimensional linear models under sparsity constraints. However, there exists a gap in the literature regarding analogous theoretical findings for nonlinear models within the highdimensional setting. The current study provides a novel contribution, focusing specifically on a nonlinear mixedeffects model. In this model, the residual variance is assumed to be known, while the covariance matrix of the random effects and the regression vector are unknown and must be estimated. The prior distribution for the sparse regression coefficients consists of a mixture of a point mass at zero and a Laplace distribution, while an InverseWishart prior is employed for the covariance parameter of the random effects. First, the effective dimension of this model is bounded with high posterior probabilities. Subsequently, we derive posterior contraction rates for both the covariance parameter and the prediction term of the response vector. Finally, under additional assumptions, the posterior distribution is shown to contract for recovery of the unknown sparse regression vector at the same rate as observed in the linear case.
 Publication:

arXiv eprints
 Pub Date:
 May 2024
 DOI:
 10.48550/arXiv.2405.01206
 arXiv:
 arXiv:2405.01206
 Bibcode:
 2024arXiv240501206N
 Keywords:

 Mathematics  Statistics Theory