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The multilevel hierarchical data EM-algorithm. Applications to discrete-time Markov chain epidemic models
1Department of Mathematical Sciences, Georgia Southern University, 65 Georgia Ave, Room 3309, Statesboro, GA, 30460, USA.
Abstract:
The theory of multilevel hierarchical data Expectation Maximization (EM)-algorithm is introduced via discrete time Markov chain (DTMC) epidemic models. A general model for a multilevel hierarchical discrete data is derived. The observed sample Y in the system is a stochastic incomplete data, and the missing data Z exhibits a multilevel hierarchical data structure. The EM-algorithm to find ML-estimates for parameters in the stochastic system is derived. Applications of the EM-algorithm are exhibited in the two DTMC models, to find ML-estimates of the system parameters. Numerical results are given for influenza epidemics in the state of Georgia (GA), USA.
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