Techniques for Model Comparison for Stochastic Models: CTMC,SDE, RDE
Wednesday, June 6, 2018 - 9:00am - 9:50am
We report on a major effort on model comparison for stochastic model comparison. In a series of efforts, we considered model comparison techniques for three different classes of stochastic models: continuous time Markov chains (CTMC), stochastic differential equations (SDE), and random differential equations (RDE). For nested models, we extended the statistically-based ideas and techniques developed earlier by Banks and Fitzpatrick for deterministic differential equation models to these three types of stochastic systems. For non-nested models, we formulated the use of the Akiake Information Criterion and its related model comparison indices (usually derived for maximum likelihood estimator inverse problem formulations) in the context of least squares (ordinary, weighted, iterative weighted or “generalized”, etc.) based inverse problem formulations. We illustrate use of the developed methods on longitudinal data collected from algae growth. In an effort in our lab [Applied Sciences, 6 (2016), 155–173], longitudinal data was collected from four replicate population experiments with green algae, formally known as Raphidocelis subcapitata. This is a major food source for our experiments with daphne (toxicologists modern day versions of the ‘’canary in the mine shaft’’) which we discuss in our presentations.