The Stochastic Quasi-chemical Model for Bacterial Growth: Variational Bayesian Parameter Update
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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.
KeywordsBayes rule Kullback–Leibler divergence Evidence lower bound Quasi-chemical model Gradient-based optimization
The authors gratefully acknowledge support from US Army Research Office Contract W911NF-14-C-0151.
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