The multilevel hierarchical data EM-algorithm. Applications to discrete-time Markov chain epidemic models.

Divine Wanduku
Author Information
  1. Divine Wanduku: Department 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 in the system is a stochastic incomplete data, and the missing data 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.

Keywords

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