Abstract

GEORGE, Sebastian  and  JOSE, Ambily. Generalized Poisson Hidden Markov Model for Overdispersed or Underdispersed Count Data. Rev.Colomb.Estad. [online]. 2020, vol.43, n.1, pp.71-82.  Epub June 05, 2020. ISSN 0120-1751.  https://doi.org/10.15446/rce.v43n1.77542.

The most suitable statistical method for explaining serial dependency in time series count data is that based on Hidden Markov Models (HMMs). These models assume that the observations are generated from a finite mixture of distributions governed by the principle of Markov chain (MC). Poisson-Hidden Markov Model (P-HMM) may be the most widely used method for modelling the above said situations. However, in real life scenario, this model cannot be considered as the best choice. Taking this fact into account, we, in this paper, go for Generalised Poisson Distribution (GPD) for modelling count data. This method can rectify the overdispersion and underdispersion in the Poisson model. Here, we develop Generalised Poisson Hidden Markov model (GP-HMM) by combining GPD with HMM for modelling such data. The results of the study on simulated data and an application of real data, monthly cases of Leptospirosis in the state of Kerala in South India, show good convergence properties, proving that the GP-HMM is a better method compared to P-HMM.

Keywords : EM algorithm; Generalized Poisson distribution; Hidden Markov Model; Overdispersion.

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