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Abstract:
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In this poster we would like to present an integrated scheme of statistical inference on dynamical system models, with emphasis on a set of nonlinear ordinary differential equations with possibly no analytic solutions and multiple observation units. We combined the differential equation model with mixed effect model to characterize the typical parameter values in the population and the extent of their variation. The estimation methodology includes implementation of Stochastic Approximation Expectation Maximization (SAEM) algorithm with numerical ODE solvers, derivative-free optimization algorithms, such as differential evolution, and parallel Markov chain Monte Carlo (MCMC) algorithms. Both maximum likelihood and restricted maximum likelihood estimation are derived. The validity of the inference is based on detailed analysis of simulation and case studies.
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