Colloque / Séminaire

The Markov-modulated Poisson process is comprised of a latent Markov process which controls the intensity of a Poisson process. This model is utilised in count models in a large variety of areas including the natural sciences, economics, finance and operational research. Inferences obtained about the latent process can be useful, particularly as the underlying causes of this process may be unobservable or extremely difficult to model. However, it is often the case that additional information on observed event arrivals is available and incorporation of these features may enhance accuracy, realism and interpretability.

In this paper, an extension is provided through a Markov-modulated non-homogeneous Poisson process, which is comprised of a frequency perturbation component in addition to the Markov latent process. The introduced frequency perturbation is highly flexible, allowing various known periodic and non-periodic drivers of event observations to be taken into account. An intuitive interpretation of the model is provided through an operational time transform. Procedures are developed to produce inferential insights that may assist analysis. Further, practical considerations are taken into account such as calibration efficiency and numerical underflow in large data sets. Procedures are developed to produce inferential insights that may assist analysis. Finally, implementation is demonstrated on a large set of real insurance claims data and additional insights extracted through the proposed model are discussed.

This is joint work with Greg Taylor, Bernard Wong, and Alan Xian.