A bivariate two-state Markov modulated Poisson process for failure modeling

The Markov Modulated Poisson Process and Markov Poisson Cascade with Applications to Web Traffic Modeling

A Markov modulated Poisson Process (MMPP) is a Poisson process whose rate varies according to a Markov process. The nonhomogeneous MMPP developed in this article is a natural model for point processes whose events combine irregular bursts of activity with predictable (e.g. daily and hourly) patterns. We show how the MMPP may be viewed as a superposition of unobserved Poisson processes that are ...

Estimating the parameters of a seasonal Markov-modulated Poisson process

Detecting Network Intrusion Using a Markov Modulated Nonhomogeneous Poisson Process

Network intrusion occurs when a criminal gains access to a customer's telephone, computer, bank, or other type of account. Detecting network intrusion is an important problem that has received little attention in the statistics literature. This article proposes a Markov modulated nonhomogeneous Poisson process (MMNHPP) to monitor transactions on a customer's account for deviations from the cust...

A Markov modulated Poisson model for software reliability

In this paper we consider a latent Markov process governing the intensity rate of software failures. The latent process represents the behavior of the debugging operations over time and enables us to deal with the imperfect debugging scenario. We develop the Bayesian inference for the model and also introduce a method to infer the unknown dimension of the Markov process. We illustrate the imple...

Double-observer line transect surveys with Markov-modulated Poisson process models for animal availability.

We develop maximum likelihood methods for line transect surveys in which animals go undetected at distance zero, either because they are stochastically unavailable while within view or because they are missed when they are available. These incorporate a Markov-modulated Poisson process model for animal availability, allowing more clustered availability events than is possible with Poisson avail...