Poisson hidden Markov model
Encyclopedia
In statistics
, Poisson hidden Markov models (PHMM) are a special case of hidden Markov model
s where a Poisson process
has a rate which varies in association with changes between the different states of a Markov model. PHMMs are not necessarily Markovian processes themselves because the underlying Markov chain
or Markov process
cannot be observed and only the Poisson signal is observed.
Statistics
Statistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....
, Poisson hidden Markov models (PHMM) are a special case of hidden Markov model
Hidden Markov model
A hidden Markov model is a statistical Markov model in which the system being modeled is assumed to be a Markov process with unobserved states. An HMM can be considered as the simplest dynamic Bayesian network. The mathematics behind the HMM was developed by L. E...
s where a Poisson process
Poisson process
A Poisson process, named after the French mathematician Siméon-Denis Poisson , is a stochastic process in which events occur continuously and independently of one another...
has a rate which varies in association with changes between the different states of a Markov model. PHMMs are not necessarily Markovian processes themselves because the underlying Markov chain
Markov chain
A Markov chain, named after Andrey Markov, is a mathematical system that undergoes transitions from one state to another, between a finite or countable number of possible states. It is a random process characterized as memoryless: the next state depends only on the current state and not on the...
or Markov process
Markov process
In probability theory and statistics, a Markov process, named after the Russian mathematician Andrey Markov, is a time-varying random phenomenon for which a specific property holds...
cannot be observed and only the Poisson signal is observed.