TY - JOUR
T1 - The multilevel hierarchical data EM-algorithm. Applications to discrete-time Markov chain epidemic models
AU - Wanduku, Divine
N1 - Publisher Copyright:
© 2022
PY - 2022/12
Y1 - 2022/12
N2 - 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.
AB - 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.
KW - Chain binomial models
KW - EM-algorithm
KW - Hierarchical data estimation
KW - Maximum likelihood estimator
KW - SEIR epidemic models
KW - Statistical inference
UR - http://www.scopus.com/inward/record.url?scp=85144988730&partnerID=8YFLogxK
U2 - 10.1016/j.heliyon.2022.e12622
DO - 10.1016/j.heliyon.2022.e12622
M3 - Article
AN - SCOPUS:85144988730
SN - 2405-8440
VL - 8
JO - Heliyon
JF - Heliyon
IS - 12
M1 - e12622
ER -