Stochastic realization theory for exact and approximate multiscale models

The thesis provides a detailed analysis of the independence structure possessed by multiscale models and demonstrates that such an analysis provides important insight into the multiscale stochastic realization problem. Multiscale models constitute a broad class of probabilistic models which includes the well--known subclass of multiscale autoregressive (MAR) models. MAR models have proven useful in a variety of different application areas, due to the fact that they provide a rich set of tools for various signal processing tasks. In order to use these tools, however, a MAR or multiscale model must first be constructed to provide an accurate probabilistic description of the particular application at hand. This thesis addresses this issue of multiscale model identification or realization. Previous work in the area of MAR model identification has focused on developing algorithms which decorrelate certain subsets of random vectors in an effort to design an accurate model. In this thesis, we develop a set-theoretic and graph-theoretic framework for better understanding these types of realization algorithms and for the purpose of designing new such algorithms.

Department dc:contributor.department

Massachusetts Institute of Technology. Dept. of Electrical Engineering and Computer Science.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2005

Author dc:creator

• Tucker, Dewey S. (Dewey Stanton)

Advisor dc:contributor.advisor

• Alan S. Willsky.

• Electrical Engineering and Computer Science.

Statement dc:rights

• M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/34468

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/34468