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On observational variance learning for multivariate Bayesian time series and related models
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Triantafyllopoulos, K. (2002) On observational variance learning for multivariate Bayesian time series and related models. PhD thesis, University of Warwick.
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WRAP_THESIS_Triantafyllopoulos_2002.pdf - Submitted Version Download (10Mb) | Preview |
Official URL: http://webcat.warwick.ac.uk/record=b1378015~S1
Abstract
This thesis is concerned with variance learning in multivariate dynamic linear
models (DLMs).
Three new models are developed in this thesis. The first one is a dynamic
regression model with no distributional assumption of the unknown
variance matrix. The second is an extension of a known model that enables
comprehensive treatment of any missing observations. For this purpose new
distributions that replace the inverse Wishart and matrix T and that allow
conjugacy are introduced. The third model is the general multivariate DLM
without any precise assumptions of the error sequences and of the unknown
variance matrix. We find analytic updatings of the first two moments based
on weak assumptions that are satisfied for the usual models.
Missing observations and time varying variances are considered in detail
for every model. For the first time, deterministic and stochastic variance laws
for the general multivariate DLM are presented. Also, by introducing a new distribution that replaces the matrix-beta of a previous work, we prove results
on stochastic changes in variance that are in line with missing observation
analysis and variance intervention.
Item Type: | Thesis (PhD) | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Library of Congress Subject Headings (LCSH): | Multivariate analysis | ||||
Official Date: | February 2002 | ||||
Dates: |
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Institution: | University of Warwick | ||||
Theses Department: | Department of Statistics | ||||
Thesis Type: | PhD | ||||
Publication Status: | Unpublished | ||||
Supervisor(s)/Advisor: | Harrison, Jeff ; Smith, J. Q., 1953- | ||||
Sponsors: | University of Warwick. Dept. of Statistics | ||||
Extent: | xx, 279 p. | ||||
Language: | eng |
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