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The Markov Modulated Poisson Process and Markov Poisson Cascade with Applications to Web Traffic Modeling
| Content Provider | Semantic Scholar |
|---|---|
| Author | Bayarri, José Vicente Gómez Berger, J. O. Dawid, A. Philip Heckerman, David |
| Copyright Year | 2002 |
| Abstract | 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 activated and deactivated by an unobserved Markov process. The MMPP is a continuous time model which may also be viewed as a discretely indexed nonstationary hidden Markov model by viewing intervals between events as a sequence of dependent random variables. The HMM representation allows one to probabilistically reconstruct the latent Markov and Poisson processes using a set of forward-backward recursions. The recursions allow MMPP parameters to be estimated either by an EM algorithm or by a rapidly mixing Markov chain Monte Carlo algorithm which uses the recursions for data augmentation. The Markov-Poisson cascade (MPC) is an MMPP whose underlying Markov process obeys certain restrictions which uniquely order the event rates for the observed process. The ordering avoids a possible label switching issue without slowing down the rapidly mixing algorithms we use to implement the model. We apply the MPC to a data set containing click rate data for individual computer users browsing through the World Wide Web. Because the complete data posterior distribution for the MPC is a product of exponential family distributions we are able to incorporate data from multiple users into a hierarchical model using existing methods from hierarchical Poisson regression. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://www.datalab.uci.edu/papers/ScottSmythV7.pdf |
| Alternate Webpage(s) | http://www-rcf.usc.edu/~sls/ScottSmythV7.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
