Published

2020-01-01

Generalized Poisson Hidden Markov Model for Overdispersed or Underdispersed Count Data

Modelo oculto de Markov de Poisson generalizado para datos de recuento sobredispersados o subdispersos

DOI:

https://doi.org/10.15446/rce.v43n1.77542

Keywords:

EM algorithm, Generalized Poisson distribution, Hidden Markov Model, Overdispersion (en)
Algoritmo EM, Distribución generalizada de Poisson, Modelo oculto de Markov, Sobredispersión (es)

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Authors

  • Sebastian George St. Thomas College, Palai
  • Ambily Jose St.Thomas College, Palai
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.
El método estadístico más adecuado para explicar la dependencia serial en los datos de recuento de series de tiempo se basan en los modelos ocultos de Markov (HMM). Estos modelos suponen que las observaciones se generan a partir de un finito mezcla de distribuciones regidas por el principio de la cadena de Markov (MC). El modelo de Markov oculto de Poisson (P-HMM) puede ser el método más utilizado  para modelar las situaciones mencionadas anteriormente. Sin embargo, en el escenario de la vida real, este modelo no puede considerarse como la mejor opción. Teniendo en cuenta este hecho, nosotros, en este artículo, apostamos por la distribución generalizada de Poisson (GPD) para modelar datos de conteo. Este método puede rectificar la sobredispersión y subdispersión en el modelo de Poisson. Aquí desarrollamos Poisson generalizado Modelo de Markov oculto (GP-HMM) combinando GPD con HMM para modelando tales datos. Los resultados del estudio sobre datos simulados y una aplicación  de datos reales, casos mensuales de leptospirosis en el estado de Kerala en South India, muestra buenas propiedades de convergencia, lo que demuestra que el GP-HMM Es un método mejor en comparación con P-HMM.

References

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How to Cite

APA

George, S. and Jose, A. (2020). Generalized Poisson Hidden Markov Model for Overdispersed or Underdispersed Count Data. Revista Colombiana de Estadística, 43(1), 71–82. https://doi.org/10.15446/rce.v43n1.77542

ACM

[1]
George, S. and Jose, A. 2020. Generalized Poisson Hidden Markov Model for Overdispersed or Underdispersed Count Data. Revista Colombiana de Estadística. 43, 1 (Jan. 2020), 71–82. DOI:https://doi.org/10.15446/rce.v43n1.77542.

ACS

(1)
George, S.; Jose, A. Generalized Poisson Hidden Markov Model for Overdispersed or Underdispersed Count Data. Rev. colomb. estad. 2020, 43, 71-82.

ABNT

GEORGE, S.; JOSE, A. Generalized Poisson Hidden Markov Model for Overdispersed or Underdispersed Count Data. Revista Colombiana de Estadística, [S. l.], v. 43, n. 1, p. 71–82, 2020. DOI: 10.15446/rce.v43n1.77542. Disponível em: https://revistas.unal.edu.co/index.php/estad/article/view/77542. Acesso em: 28 mar. 2025.

Chicago

George, Sebastian, and Ambily Jose. 2020. “Generalized Poisson Hidden Markov Model for Overdispersed or Underdispersed Count Data”. Revista Colombiana De Estadística 43 (1):71-82. https://doi.org/10.15446/rce.v43n1.77542.

Harvard

George, S. and Jose, A. (2020) “Generalized Poisson Hidden Markov Model for Overdispersed or Underdispersed Count Data”, Revista Colombiana de Estadística, 43(1), pp. 71–82. doi: 10.15446/rce.v43n1.77542.

IEEE

[1]
S. George and A. Jose, “Generalized Poisson Hidden Markov Model for Overdispersed or Underdispersed Count Data”, Rev. colomb. estad., vol. 43, no. 1, pp. 71–82, Jan. 2020.

MLA

George, S., and A. Jose. “Generalized Poisson Hidden Markov Model for Overdispersed or Underdispersed Count Data”. Revista Colombiana de Estadística, vol. 43, no. 1, Jan. 2020, pp. 71-82, doi:10.15446/rce.v43n1.77542.

Turabian

George, Sebastian, and Ambily Jose. “Generalized Poisson Hidden Markov Model for Overdispersed or Underdispersed Count Data”. Revista Colombiana de Estadística 43, no. 1 (January 1, 2020): 71–82. Accessed March 28, 2025. https://revistas.unal.edu.co/index.php/estad/article/view/77542.

Vancouver

1.
George S, Jose A. Generalized Poisson Hidden Markov Model for Overdispersed or Underdispersed Count Data. Rev. colomb. estad. [Internet]. 2020 Jan. 1 [cited 2025 Mar. 28];43(1):71-82. Available from: https://revistas.unal.edu.co/index.php/estad/article/view/77542

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