Applications of MCMC methods on function spaces
Cotter, Simon L. (2010) Applications of MCMC methods on function spaces. PhD thesis, University of Warwick.
WRAP_THESIS_Cotter_2010.pdf - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader
Official URL: http://webcat.warwick.ac.uk/record=b2341075~S15
In the course of this thesis, several different applications of data assimilation will
be looked at. In each case, a rigorous mathematical framework will be constructed,
in a Bayesian context, to enable the use of various types of data to infer on various
infinite dimensional parameters of the system that has been observed. After careful
consideration of the forward problem, well-defined posterior distributions on function
space are constructed. Using MCMC methods which are defined on these function
spaces themselves, we can construct Markov chains whose invariant measures are the
posterior of interest. From this point, we can implement these methods on a computer,
having finally discretised the problem.
The philosophy that we adhere to throughout, is the idea that numerical methods
formulated on function space are robust under discretisation, and do not suffer from
the curse of dimensionality typically suffered by sampling methods formulated after
The first few chapters (after the introductory chapter) will focus on various
aspects of data assimilation of observations of Stokes
ow dynamics. Chapter 2 will
focus on Eulerian data where direct observations of the velocity of the
fluid at various
points in time and space will be made. Chapter 3 will concentrate on data assimilation
of indirect observations of the field, in the form of the positions of passive tracers in the flow. In these two chapters we will assume that the forcing of the system is known and
that we are merely trying to recover the initial condition of the flow field.
In chapter 4 we will consider both Eulerian and Lagrangian data assimilation,
with the added complexity of trying to use the data to not only infer on the initial
condition but also on the space-time dependant forcing of the system.
In chapter 5 we will try to show how these smoothing methods could be adapted
into a filtering algorithm, and a simple example will be presented.
In the final chapter, 6, this Bayesian framework on function space will be applied
to a shape matching problem with applications in the biomedical sciences.
|Item Type:||Thesis or Dissertation (PhD)|
|Subjects:||Q Science > QA Mathematics|
|Library of Congress Subject Headings (LCSH):||Monte Carlo method, Markov processes, Function spaces, Bayesian statistical decision theory, Stokes flow|
|Official Date:||April 2010|
|Institution:||University of Warwick|
|Theses Department:||Mathematics Institute|
|Supervisor(s)/Advisor:||Stuart, A. M.|
|Sponsors:||Engineering and Physical Sciences Research Council (EPSRC)|
|Extent:||xix, 238 leaves : charts|
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