Quantitative assessment of biological dynamics with aggregate data

We develop and apply a learning framework for parameter estimation in initial value problems that are assessed only indirectly via aggregate data such as sample means and/or standard deviations. Our comprehensive framework follows Bayesian principles and consists of specialized Markov chain Monte Carlo computational schemes that rely on modified Hamiltonian Monte Carlo to align with constraints induced by summary statistics and a novel elliptical slice sampler adapted to the parameters of biological models. We benchmark our methods with synthetic data on microbial growth in batch culture and test them with real growth curve data from laboratory replication experiments on $\textit{Prochlorococcus}$ microbes. The results indicate that our learning framework can utilize experimental or historical data and lead to robust parameter estimation and data assimilation in ODE models that outperform least-squares fitting.