Do higher-order moments improve inference of population dynamics?

Abstract

Fitting mathematical models of population dynamics to microbial time-series data allows us to estimate the ecological processes and interactions taking place in the microbiome. Repeated experiments of microbial systems yield replicates which slightly differ from each other. Some of this variability arises due to the fact that births and deaths occur at random. Most prior work focuses on fitting a deterministic mathematical model to the average across replicates. We use a stochastic model to fit the variability to the observed variability across replicates. Using a simulation-driven approach, we study the conditions under which our approach allows us to infer a larger fraction of ecological parameters correctly. We observe a substantial improvement in parameter inference. Lastly, our Bayesian approach not only allows us to incorporate prior information about the system, but also provides a distribution of parameters which conveys some idea of the uncertainty of the estimates.