A practical introduction to ODE modelling in Stan for biological systems

TL;DR

This paper provides a practical, step-by-step guide to using Stan for parameter estimation and model evaluation of ODE models in biological systems, combining theory and real data applications.

Contribution

It offers the first comprehensive tutorial on applying Stan's ODE capabilities specifically for biological systems, including both pedagogical examples and real data analysis.

Findings

Effective parameter estimation for biological ODE models using Stan

Demonstrated Stan's utility with real biological data

Clarified statistical methods underpinning Bayesian inference in this context

Abstract

Integrating dynamical systems models with time series data is a central part of contemporary mathematical biology. With the rich variety of available models and data, numerous methods and computational tools have been developed for these purposes. One such tool is Stan, a freely available and open-source probabilistic programming framework that provides efficient methods for estimating model parameters from data using computational Bayesian inference algorithms. Stan includes built-in mechanisms for working with ordinary differential equation (ODE) models, which are widely used in mathematical biology and related fields to study simulated, experimental, and real-world systems that change over time. Through step-by-step worked examples, including both pedagogical toy models and applications with real data, this article provides a practical, self-contained introduction to performing parameter estimation and model evaluation for first-order linear and nonlinear ODE models in Stan. The article also explains key statistical methods that underpin Stan and discusses computational Bayesian modelling in the context of biological applications.