Estimating Markov Switching Model Using Differential Evolution Algorithm in Prospective Infectious Disease Outbreak Detection

Abstract

Prospective infectious disease outbreak detection has long been a major concern in public health. Using time series analysis method for the outbreak detection, a nonlinear Markov switching model is better than linear models in modelling time series, due to its ability to describe the switching process of time series variables in different states. However the estimation difficulty of Markov switching model hinders the model's extensive application in practice. The paper proposes using Differential Evolution (termed DE) algorithm to obtain maximum likelihood estimator of Markov switching model in consideration of DE's good global optimization ability. In addition, to effectively reduce negative impact of label switching problem on disease outbreak detection validity of the estimated model by maximum likelihood estimation (termed MLE) method, the paper introduces identifiability constraint on estimation parameters constructed with the heuristic information about difference between durations of different states into MLE using DE. Encouraging experimental study has demonstrated the effectiveness and efficiency of DE in maximizing likelihood function of the studied Markov switching model as well as the effectiveness of the proposed identifiability constraint on improving disease outbreak detection validity of the estimated Markov switching model by MLE.