An Inverse Problem Formulation Methodology for Stochastic Models
NORTH CAROLINA STATE UNIV AT RALEIGH CENTER FOR RESEARCH IN SCIENTIFIC COMPUTATION
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A method for estimating parameters in dynamic stochastic Markov Chain models based on Kurtzs limit theory coupled with inverse problem methods developed for deterministic dynamical systems is proposed and illustrated in the context of disease dynamics. This methodology relies on finding an approximate large-population behavior of an appropriate scaled stochastic system. This approach leads to a deterministic approximation obtained as solutions of rate equations ordinary differential equations in terms of the large sample size average over sample paths or trajectories limits of pure jump Markov processes. Using the resulting deterministic model we select parameter subset combinations that can be estimated using an ordinary-least- squares OLS or generalized-least-squares GLS inverse problem formulation with a given data set. The selection is based on two criteria of the sensitivity matrix the degree of sensitivity measure in the form of its condition number and the degree of uncertainty measured in the form of its parameter selection score. We illustrate the ideas with a stochastic model for the transmission of vancomycin-resistant enterococcus VRE in hospitals and VRE surveillance data from an oncology unit.
- Theoretical Mathematics