An importance sampling approach for reliable and efficient inference in Bayesian ordinary differential equation models

Abstract

Statistical models can involve implicitly defined quantities, such as solutions to nonlinear ordinary differential equations (ODEs), that unavoidably need to be numerically approximated in order to evaluate the model. The approximation error inherently biases statistical inference results, but the amount of this bias is generally unknown and often ignored in Bayesian parameter inference. We propose a computationally efficient method for verifying the reliability of posterior inference for such models, when the inference is performed using Markov chain Monte Carlo methods. We validate the efficiency and reliability of our workflow in experiments using simulated and real data, and different ODE solvers. We highlight problems that arise with commonly used adaptive ODE solvers, and propose robust and effective alternatives which, accompanied by our workflow, can now be taken into use without losing reliability of the inferences.

Bayesian Regression Facilitates Quantitative Modeling of Cell Metabolism

“…The speed at which this problem can be solved is tightly coupled with the size and complexity of metabolic network that can practically be modeled. See Timonen et al 42 for more about considerations involved in this kind of modeling.…”