Inference and prediction for stochastic models of biological populations undergoing migration and proliferation.

Abstract

Parameter inference is a critical step in the process of interpreting biological data using mathematical models. Inference provides a means of deriving quantitative, mechanistic insights from sparse, noisy data. While methods for parameter inference, parameter identifiability and model prediction are well developed for deterministic continuum models, working with biological applications often requires stochastic modelling approaches to capture inherent variability and randomness that can be prominent in biological measurements and data. Random walk models are especially useful for capturing spatio-temporal processes, such as ecological population dynamics, molecular transport phenomena and collective behaviour associated with multicellular phenomena. This review focuses on parameter inference, identifiability analysis and model prediction for a suite of biologically inspired, stochastic agent-based models relevent to animal dispersal and populations of biological cells. With a particular emphasis on model prediction, we highlight roles for numerical optimization and automatic differentiation. Open-source Julia code is provided to support scientific reproducibility. We encourage readers to use this code directly or adapt it to suit their interests and applications.