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

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 the 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 owing 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.

Automated summary

Ordinary differential equation models are commonly used in biology to describe dynamic processes. However, when performing likelihood-based parameter inference on these models, the contribution of factors not explicitly included in the mathematical model needs to be represented. Independent Gaussian noise is often chosen as a statistical process, assuming random latent factors. This study demonstrates that highly persistent differences between observations and model quantities can occur, and using the wrong noise assumption can lead to artificial reduction of uncertainty in parameter estimation. They propose a workflow to diagnose and remodel for correlated errors.