Recursive estimation of parameters in Markovmodulated Poisson processes
(1995) In IEEE Transactions on Communications 43(11). p.28122820 Abstract
 A hidden Markov regime is a Markov process that governs the time or space dependent distributions of an observed stochastic process. Recursive algorithms can be used to estimate parameters in mixed distributions governed by a Markov regime. Here we derive a recursive algorithm for estimation of parameters in a Markovmodulated Poisson process also called a Cox point process. By this we mean a doubly stochastic Poisson process with a time dependent intensity that can take on a finite number of different values. The intensity switches randomly between the possible values according to a Markov process. We consider two different ways to observe the Markovmodulated Poisson process: in the first model the observations consist of the observed... (More)
 A hidden Markov regime is a Markov process that governs the time or space dependent distributions of an observed stochastic process. Recursive algorithms can be used to estimate parameters in mixed distributions governed by a Markov regime. Here we derive a recursive algorithm for estimation of parameters in a Markovmodulated Poisson process also called a Cox point process. By this we mean a doubly stochastic Poisson process with a time dependent intensity that can take on a finite number of different values. The intensity switches randomly between the possible values according to a Markov process. We consider two different ways to observe the Markovmodulated Poisson process: in the first model the observations consist of the observed time intervals between events, and in the second model we use the total number of events in successive intervals of fixed length. We derive an algorithm for recursive estimation of the Poisson intensities and the switch intensities between the two states and illustrate the algorithm in a simulation study. The estimates of the switch intensities are based on the observed conditional switch probabilities. (Less)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/record/1210431
 author
 Lindgren, Georg ^{LU} and Holst, Ulla ^{LU}
 organization
 publishing date
 1995
 type
 Contribution to journal
 publication status
 published
 subject
 keywords
 MODELS
 in
 IEEE Transactions on Communications
 volume
 43
 issue
 11
 pages
 2812  2820
 publisher
 IEEEInstitute of Electrical and Electronics Engineers Inc.
 external identifiers

 scopus:0029408477
 ISSN
 00906778
 language
 English
 LU publication?
 yes
 id
 76e6bb3c2b074671838f01a6f2fda89b (old id 1210431)
 alternative location
 http://ieeexplore.ieee.org/iel1/26/10304/00481232.pdf?tp=&arnumber=481232&isnumber=10304
 date added to LUP
 20080814 16:33:21
 date last changed
 20180529 09:41:36
@article{76e6bb3c2b074671838f01a6f2fda89b, abstract = {A hidden Markov regime is a Markov process that governs the time or space dependent distributions of an observed stochastic process. Recursive algorithms can be used to estimate parameters in mixed distributions governed by a Markov regime. Here we derive a recursive algorithm for estimation of parameters in a Markovmodulated Poisson process also called a Cox point process. By this we mean a doubly stochastic Poisson process with a time dependent intensity that can take on a finite number of different values. The intensity switches randomly between the possible values according to a Markov process. We consider two different ways to observe the Markovmodulated Poisson process: in the first model the observations consist of the observed time intervals between events, and in the second model we use the total number of events in successive intervals of fixed length. We derive an algorithm for recursive estimation of the Poisson intensities and the switch intensities between the two states and illustrate the algorithm in a simulation study. The estimates of the switch intensities are based on the observed conditional switch probabilities.}, author = {Lindgren, Georg and Holst, Ulla}, issn = {00906778}, keyword = {MODELS}, language = {eng}, number = {11}, pages = {28122820}, publisher = {IEEEInstitute of Electrical and Electronics Engineers Inc.}, series = {IEEE Transactions on Communications}, title = {Recursive estimation of parameters in Markovmodulated Poisson processes}, volume = {43}, year = {1995}, }