The Stochastic Quasi-chemical Model for Bacterial Growth: Variational Bayesian Parameter Update

• DOI: 10.1007/s00332-017-9411-4
• Publication Date: 2017-08-24T02:24:22Z
• Authors: Panagiotis Tsilifis; William J. Browning; Thomas E. Wood; Paul K. Newton; Roger G. Ghanem
• Keywords: Divergence (linguistics); Parametric model

We develop Bayesian methodologies for constructing and estimating a stochastic quasi-chemical model (QCM) for bacterial growth. The deterministic QCM, described as a nonlinear system of ODEs, is treated as a dynamical system with random parameters, and a variational approach is used to approximate their probability distributions and explore the propagation of uncertainty through the model. The approach consists of approximating the parameters’ posterior distribution by a probability measure chosen from a parametric family, through minimization of their Kullback–Leibler divergence.