Bayesian Nonlinear Models for Repeated Measurement Data: An Overview, Implementation, and Applications

TL;DR

This paper reviews Bayesian nonlinear mixed effects models, highlighting their advantages in uncertainty quantification, prior incorporation, and flexibility, along with implementation strategies and applications across various fields.

Contribution

It provides a comprehensive overview of Bayesian approaches for nonlinear mixed effects models, including modeling strategies, computational methods, and practical applications.

Findings

Bayesian methods improve uncertainty quantification.

Bayesian approaches incorporate prior knowledge effectively.

Applications span diverse scientific fields.

Abstract

Nonlinear mixed effects models have become a standard platform for analysis when data is in the form of continuous and repeated measurements of subjects from a population of interest, while temporal profiles of subjects commonly follow a nonlinear tendency. While frequentist analysis of nonlinear mixed effects models has a long history, Bayesian analysis of the models has received comparatively little attention until the late 1980s due primarily to the time-consuming nature of Bayesian computation. Since the early 1990s Bayesian approaches for the models began to emerge to leverage rapid developments in computing power, and recently, have received significant attention due to (1) superiority to quantify the uncertainty of parameter estimation; (2) utility to incorporate prior knowledge into the models; and (3) flexibility to match exactly the increasing complexity of scientific research arising from diverse industrial and academic fields. This review article presents an overview of modeling strategies to implement Bayesian approaches for the nonlinear mixed effects models, ranging from designing a scientific question out of real-life problems to practical computations.