Stochastic parameterized grammars: Formalization, inference and modeling applications

The Stochastic Parameterized Grammar (SPG) forms a unifying framework for modeling systems of stochastic nature and dynamical structure. The modeling language is based on grammar-like collections of rewrite rules that define local interactions between objects or features and may involve creation or annihilation of objects. Local interactions may be either in the form of stochastic events or deterministic continuous dynamics. Such broad expressiveness makes the framework particularly suitable for applications in machine learning and multi-scale scientific modeling. This thesis introduces the SPG framework, its appropriate simulation methods and their computational cost. The problems of parameter learning and inference in SPG models are addressed by deriving exact and approximate sampling algorithms. As an application of SPG inference, the thesis includes an automated technique for inferring galaxy structure from images. The thesis concludes with two biological applications of the SPG framework: modeling root development and modeling the regeneration of neurons in the olfactory epithelium. The SPG model of the olfactory epithelium is a comprehensive spatial representation of the tissue that includes cellular level stochastic events and diffusion of signaling molecules. The model recapitulates the observed behavior of the tissue and provides interesting predictions about the dynamics of cell population.