🤖 AI Summary
This study addresses the structural identifiability of model parameters in partially observed stochastic processes, focusing on parameter uniqueness from two data modalities: single-particle trajectories and population density measurements. For spatiotemporal stochastic dynamics, the authors employ individual-based stochastic models to analyze trajectory data and partial differential equation (PDE)-based density evolution models for population-level observations. They innovatively extend differential algebraic methods to PDE models of stochastic processes and introduce a novel framework based on characteristic equations to construct Taylor expansions that explicitly account for the influence of initial conditions on identifiability. Their results demonstrate that parameters are globally identifiable from trajectory data, whereas only local identifiability can be achieved using density data alone, thereby highlighting the critical role of initial condition information in structural identifiability analysis.
📝 Abstract
The increasing availability of experimental data has intensified interest in calibrating stochastic models, raising fundamental questions about parameter identifiability. Structural identifiability determines whether parameters can be uniquely recovered from idealised, noise-free data, a prerequisite to allow for parameter estimation. However, existing methods to assess structural identifiability are not generally applicable to stochastic processes. We develop a methodology to analyse structural identifiability for a class of spatio-temporal stochastic processes. We investigate how identifiability depends on the type of available data, distinguishing between single-particle trajectories and total particle density measurements. For trajectory data, we use the individual-based model description that explicitly represents single-particle dynamics. For population-level data, we derive a partial differential equation model representation, that describes the evolution of total particle density, and apply a differential algebra approach, common to ordinary differential equations analysis. We further introduce a novel method to study the initial condition, based on characteristic equations to construct a Taylor expansion of the density evolution, enabling identification of additional identifiable parameter combinations. We apply our methodology to a model, and show it is identifiable with trajectory data but only locally identifiable with density data, and demonstrate the critical role of initial conditions in the identifiability analysis.