Bayesian Nonlinear Models

The review article Bayesian Nonlinear Models for Repeated Measurement Data gives a valuation of the use for the Bayesian Model to solve complex problems.

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, primarily due 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 have recently 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.

The Bayesian research cycle. A research cycle using Bayesian nonlinear mixed effects model comprises two steps:
(a) standard research cycle and
(b) Bayesian-specific workflow.
Standard research cycle involves literature review, defining a problem and specifying the research question and hypothesis.
Bayesian-specific workflow comprises three sub-steps:
(b)–(i) formalizing prior distributions based on background knowledge and prior elicitation;
(b)–(ii) determining the likelihood function based on a nonlinear function f; and
(b)–(iii) making a posterior inference. The resulting posterior inference can be used to start a new research cycle.

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