Bayesian Validation of Dynamic Systems for Biological Networks

Dynamic systems encompass a broad class of mathematical models used to describe the behavior of complex networks or systems over time. One of the most common approaches to modeling such dynamics is through a set of ordinary differential equations (ODEs), typically constructed based on hypotheses, known interactions, or observed trajectories. However, ODEs are deterministic and inflexible, while biological data are typically noisy. Thus, the model fit might not account for all possible data variations, and there might be a discrepancy between the actual biological process and the assumed model. This discrepancy could lead to inaccuracies in the prediction and interpretation of the biological networks. Therefore, it is required to validate ODE models in terms of observed data. Given that biological networks typically involve multiple sources of errors and uncertainties, the validation process should account for these factors. The Bayesian approaches offer a robust framework for quantifying errors and uncertainties. Thus, in this study, we propose a Bayesian validation method for ODE models that addresses model inadequacy, presented as bias. Since the proposed method estimates bias as a function of time, it can provide prediction bounds for the entire observed time interval. Consequently, it allows for a direct evaluation of the model's validity across the whole time interval, and it can lead to better prediction by correcting the bias.