Autocorrelated measurement processes and inference for ordinary differential equation models of biological systems

TL;DR

This paper investigates the limitations of assuming independent Gaussian noise in ODE models of biological systems, demonstrating the presence of persistent measurement errors and proposing methods to diagnose and incorporate correlated noise for improved inference.

Contribution

It introduces a workflow to detect persistent measurement errors and provides a modeling approach that accounts for correlated noise in biological ODE models.

Findings

Persistent measurement errors can significantly bias parameter estimates.

Assuming independent noise underestimates uncertainty in parameter inference.

A diagnostic workflow helps identify when correlated noise modeling is necessary.

Abstract

Ordinary differential equation models are used to describe dynamic processes across biology. To perform likelihood-based parameter inference on these models, it is necessary to specify a statistical process representing the contribution of factors not explicitly included in the mathematical model. For this, independent Gaussian noise is commonly chosen, with its use so widespread that researchers typically provide no explicit justification for this choice. This noise model assumes `random' latent factors affect the system in ephemeral fashion resulting in unsystematic deviation of observables from their modelled counterparts. However, like the deterministically modelled parts of a system, these latent factors can have persistent effects on observables. Here, we use experimental data from dynamical systems drawn from cardiac physiology and electrochemistry to demonstrate that highly persistent differences between observations and modelled quantities can occur. Considering the case when persistent noise arises due only to measurement imperfections, we use the Fisher information matrix to quantify how uncertainty in parameter estimates is artificially reduced when erroneously assuming independent noise. We present a workflow to diagnose persistent noise from model fits and describe how to remodel accounting for correlated errors.