ORNSTEIN-UHLENBECK PROCESS AND OPTIMAL SAMPLING FOR ANALYSIS OF MICROBIOME DATA

Abstract

The Ornstein–Uhlenbeck (OU) process is a widely used model for stochastic processes, where the value drifts towards a fixed stable value. We examine how well the OU process fits the data by using likelihood ratio tests to compare models of temporal dynamics of OTUs. Then, we derive the Fisher information of the OU process and show how it can be used to maximize the temporal efficiency of sampling. We apply this to parameters estimated from real data to determine optimal sampling schemes for human microbiomes. We use simulations to show that the asymptotic theory applies to typical finite sample cases.