Peavoy, Daniel (2012) Methods of likelihood based inference for constructing stochastic climate models. PhD thesis, University of Warwick.

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Abstract

This thesis is about the construction of low dimensional diffusion models of climate
variables. It assesses the predictive skill of models derived from a principled averaging
procedure and a purely empirical approach. The averaging procedure starts from
the equations for the original system then approximates the \weather" variables by a
stochastic process. They are then averaged with respect to their invariant measure.
This assumes that they equilibriate much faster than the climate variables. The
empirical approach argues for a very general model form, then parameters are estimated
using likelihood based inference for Stochastic Differential Equations. This is
computationally demanding and relies upon Markov Chain Monte Carlo methods.
A large part of this thesis is focused upon techniques to improve the efficiency of
these algorithms.
The empirical approach works well on simple one dimensional models but
performs poorly on multivariate problems due to the rapid increase in unknown
parameters. The averaging procedure is skillful in multivariate problems but is
sensitive to lack of complete time scale separation in the system. In conclusion,
the averaging procedure is better and can be improved by estimating parameters in
a principled way based on the likelihood function and by including a latent noise
process in the model.

Item Type:	Thesis (PhD)
Subjects:	Q Science > QA Mathematics Q Science > QC Physics
Library of Congress Subject Headings (LCSH):	Climatology -- Mathematical models, Climatology -- Statistical methods, Stochastic processes, Meteorology -- Statistical methods, Meteorology -- Mathematical models
Official Date:	December 2012
Institution:	University of Warwick
Theses Department:	Centre for Complexity Science
Thesis Type:	PhD
Publication Status:	Unpublished
Supervisor(s)/Advisor:	Roberts, Gareth O.; Franzke, Christian
Sponsors:	Engineering and Physical Sciences Research Council (EPSRC); Natural Environment Research Council (Great Britain) (NERC)
Extent:	xx, 210 leaves : illustrations, charts.
Language:	eng

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