Optimal Segmentation of Linear Regression Parameters
1990 (English)Licentiate thesis, monograph (Other academic)
The problem of detecting multiple changes in the dynamical properties of a measured signal, which we call segmentation, is studied. A Bayesian model-based approach is used. The signal is supposed to be described by a linear regression. The posterior distribution for the change instants is first derived for a quite general signal model. Three special choices of signal model are then proposed for segmentation. The maximum a posteriori (MAP) estimate is studied. It is shown that it contains the estimates from the maximum likelihood method and the generalized likelihood ratio test as special cases.
This posterior distribution contains a number of components which increases exponentially in the number of measurements, t. Nevertheless, it is shown that under certain assumptions on the parameter variation structure, the number of components that really ha veto be examined increases considerably less than t. This exact pruning possibility is shown to be asymptotically efficient in the ratio between the jump magnitude and the noise variance.
For the general signal model a recursive search scheme is proposed to approximate the MAP estimate. Segmentation examples and other possible applications of the search scheme are given.
Place, publisher, year, edition, pages
Linköping University , 1990. , 95 p.
Linköping Studies in Science and Technology. Thesis, ISSN 0280-7971 ; 246
IdentifiersURN: urn:nbn:se:liu:diva-98079Local ID: LIU-TEK-LIC-1990:46ISBN: 91-7870-712-9OAI: oai:DiVA.org:liu-98079DiVA: diva2:652084