Mider, Marcin (2019) Simulation of conditioned diffusions. PhD thesis, University of Warwick.

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Abstract

Diffusion processes are important tools for modelling time-evolution of natural, as well as man-made phenomena. Unfortunately, due to intractability of the likelihood functions performing many standard, statistical analyses for such processes is challenging. For a number of modern, Bayesian techniques the difficulty of dealing with those objects can be reduced to the problem of simulating diffusions conditioned on suitable random variables or events—solving the latter problem is precisely the topic of this thesis. The aim of this thesis is to propose novel extensions to the existing methodologies for simulating diffusions conditioned on an end-point, on partial and noisy observation of the process and on first passage times. I give a comprehensive introduction to this topic in the first part of this document. In the second part I first show how to reduce the computational cost of the so-called exact samplers (whose distinguishing feature is lack of any discretisation errors) in the setting of distant bridges and I provide a quantitative asymptotic analysis of this cost reduction. Then, I re-formulate the main computational routines of the algorithm termed guided proposals, which results in the reduced computational cost of the procedure as well as simplification of its implementation. Finally, I show how to extend a number of algorithms discussed in this thesis to conditioning on first passage times to a threshold. I apply those results to problems encountered in neuroscience: inference from first passage times for leaky integrate-and-fire models as well as for the FitzHugh-Nagumo model.

Item Type:	Thesis or Dissertation (PhD)
Subjects:	Q Science > QA Mathematics
Library of Congress Subject Headings (LCSH):	Diffusion processes -- Computer simulation, Bayesian statistical decision theory
Official Date:	September 2019
Dates:	Date Event September 2019 UNSPECIFIED
Institution:	University of Warwick
Theses Department:	Department of Statistics
Thesis Type:	PhD
Publication Status:	Unpublished
Supervisor(s)/Advisor:	Jenkins, Paul A. ; Pollock, Murray ; Roberts, Gareth O.
Sponsors:	Engineering and Physical Sciences Research Council
Format of File:	pdf
Extent:	231 leaves : colour illustrations
Language:	eng

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