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The Markov-modulated Poisson process is utilised for count modelling in avariety of areas such as queueing, reliability, network and insurance claimsanalysis. In this paper, we extend the Markov-modulated Poisson processframework through the introduction of a flexible frequency perturbationmeasure. This contribution enables known information of observed event arrivalsto be naturally incorporated in a tractable manner, while the hidden Markovchain captures the effect of unobservable drivers of the data. In addition toincreases in accuracy and interpretability, this method supplements analysis ofthe latent factors. Further, this procedure naturally incorporates datafeatures such as over-dispersion and autocorrelation. Additional insights canbe generated to assist analysis, including a procedure for iterative modelimprovement.  Implementation difficulties are also addressed with a focus on dealing withlarge data sets, where latent models are especially advantageous due the largenumber of observations facilitating identification of hidden factors. Namely,computational issues such as numerical underflow and high processing cost arisein this context and in this paper, we produce procedures to overcome theseproblems.  This modelling framework is demonstrated using a large insurance data set toillustrate theoretical, practical and computational contributions and anempirical comparison to other count models highlight the advantages of theproposed approach.

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