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Modelling and understanding count processes through a Markov-modulated non-homogeneous Poisson process framework

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  • Avanzi, Benjamin
  • Taylor, Greg
  • Wong, Bernard
  • Xian, Alan

Abstract

The Markov-modulated Poisson process is utilised for count modelling in a variety of areas such as queueing, reliability, network and insurance claims analysis. In this paper, we extend the Markov-modulated Poisson process framework through the introduction of a flexible frequency perturbation measure. This contribution enables known information of observed event arrivals to be naturally incorporated in a tractable manner, while the hidden Markov chain captures the effect of unobservable drivers of the data. In addition to increases in accuracy and interpretability, this method supplements analysis of the latent factors. Further, this procedure naturally incorporates data features such as over-dispersion and autocorrelation. Additional insights can be generated to assist analysis, including a procedure for iterative model improvement.

Suggested Citation

  • Avanzi, Benjamin & Taylor, Greg & Wong, Bernard & Xian, Alan, 2021. "Modelling and understanding count processes through a Markov-modulated non-homogeneous Poisson process framework," European Journal of Operational Research, Elsevier, vol. 290(1), pages 177-195.
    • Handle: RePEc:eee:ejores:v:290:y:2021:i:1:p:177-195
    DOI: 10.1016/j.ejor.2020.07.022
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