Recursions for the MMPP Score Vector and Observed Information Matrix

Abstract

Exact forward recursions for the score vector and observed information matrix of the Markov-modulated Poisson process (MMPP) are developed. The recursions are motivated by similar recursions developed for hidden Markov models by Lystig and Hughes who extended earlier work by LeGland and Mèvel. Explicit expressions for the first derivative and Hessian of the MMPP transition density matrix are developed and coupled with the recursions. The recursions are implemented and applied to confidence interval estimation in a simulation study.

Keywords:

• Hidden Markov model
• MMPP
• Observed information
• Score

Mathematics Subject Classification:

• Primary 60J22
• Secondary 60J27