  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.
  Implementation difficulties are also addressed with a focus on dealing with
large data sets, where latent models are especially advantageous due the large
number of observations facilitating identification of hidden factors. Namely,
computational issues such as numerical underflow and high processing cost arise
in this context and in this paper, we produce procedures to overcome these
problems.
  This modelling framework is demonstrated using a large insurance data set to
illustrate theoretical, practical and computational contributions and an
empirical comparison to other count models highlight the advantages of the
proposed approach.
