Smith, J. Q. (1977) Problems in Bayesian statistics relating to discontinuous phenomena, catastrophe theory and forecasting. PhD thesis, University of Warwick.

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Abstract

The aim of this thesis is to generalise Bayesian Forecasting
processes to models where normality assumptions are, not appropriate.
In particular I develop models that can change their minds and I
utilise Catastrophe Theory in their description.
Under squared-error loss types of criteria the estimates
will be smoothed out, so for model description and prediction I need
to use bounded loss functions. Unfortunately the induced types of
estimators have not been investigated very fully and so two chapters
of the thesis represent an attempt to develop theory up to a necessary
level to be used on Times Series models of the above kind.
An introduction to Catastrophe Theory is then given.
Catastrophe Theory is basically a classification of C∞-potential
functions and since the expected loss function is in fact itself
a potential function, I can use the classification on them. Chapters
6 and 7 relate the topologies of the posterior distribution and loss
function to the topologies of the posterior expected loss hence a
Bayes classification of posterior distributions is possible.
In Chapter 8, I relate these results to the forecasting of
non-stationary time series obtaining models which are very much
akin to the simple weighted moving average processes under which
lies this firm mathematical foundation. From this I can generate
pleasing models which adjust in a "Catastrophic" way to changes
in the underlying process generating the data.

Item Type:	Thesis (PhD)
Subjects:	Q Science > QA Mathematics
Library of Congress Subject Headings (LCSH):	Bayesian statistical decision theory, Catastrophes (Mathematics), Time-series analysis
Official Date:	November 1977
Dates:	Date Event November 1977 Submitted
Institution:	University of Warwick
Theses Department:	Department of Statistics
Thesis Type:	PhD
Publication Status:	Unpublished
Supervisor(s)/Advisor:	Harrison, Jeff
Extent:	[11], 218 p.
Language:	eng

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