Wanduku D. The multilevel hierarchical data EM-algorithm. Applications to discrete-time Markov chain epidemic models.
Heliyon 2022;
8:e12622. [PMID:
36643325 PMCID:
PMC9834773 DOI:
10.1016/j.heliyon.2022.e12622]
[Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/19/2021] [Revised: 06/21/2022] [Accepted: 12/16/2022] [Indexed: 12/24/2022] Open
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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