### CAS Seminar

# Melanie Terörde

### (Jacobs University)

## "Introduction to observable operator models"

** Date: ** |
Thu, April 19, 2012 |

** Time: ** |
9:45 |

** Place: ** |
Research I Seminar Room |

**Abstract:** Observable operator models (OOMs) are mathematical models for stochastic processes and
are usually treated as a generalization of hidden Markov models (HMMs). Every stochastic
process that can be described by a finite-dimensional HMM can also be modeled by a finite-
dimensional OOM, but the other direction is not always possible.
Both OOMs and HMMs can be expressed in structurally identical matrix formalisms. In
contrast with HMMs where vectors and matrices contain only non-negative probabilities the
corresponding entries in OOMs may contain negative components leading to algebraic
properties that differ from HMMs.
A hidden observable operator model is a new model similar to an HMM but with the
crucial difference that the underlying process is modeled by an operator model instead of a
Markov chain. The main idea behind H-OOMs is to unify the advantages of both OOMs and
HMMs.