Kolossiatis, Michalis (2009) Modelling via normalisation for parametric and nonparametric inference. PhD thesis, University of Warwick.

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Abstract

Bayesian nonparametric modelling has recently attracted a lot of attention, mainly due to the advancement
of various simulation techniques, and especially Monte Carlo Markov Chain (MCMC)
methods. In this thesis I propose some Bayesian nonparametric models for grouped data, which
make use of dependent random probability measures. These probability measures are constructed
by normalising infinitely divisible probability measures and exhibit nice theoretical properties. Implementation
of these models is also easy, using mainly MCMC methods. An additional step in
these algorithms is also proposed, in order to improve mixing. The proposed models are applied
on both simulated and real-life data and the posterior inference for the parameters of interest are
investigated, as well as the effect of the corresponding simulation algorithms. A new, n-dimensional
distribution on the unit simplex, that contains many known distributions as special cases, is also
proposed. The univariate version of this distribution is used as the underlying distribution for modelling
binomial probabilities. Using simulated and real data, it is shown that this proposed model is
particularly successful in modelling overdispersed count data.

Item Type:	Thesis or Dissertation (PhD)
Subjects:	H Social Sciences > HG Finance H Social Sciences > HA Statistics
Library of Congress Subject Headings (LCSH):	Mathematical statistics -- Research, Bayesian statistical decision theory, Mathematical models -- Research, Monte Carlo method, Markov processes
Official Date:	September 2009
Dates:	Date Event September 2009 Submitted
Institution:	University of Warwick
Theses Department:	Department of Statistics
Thesis Type:	PhD
Publication Status:	Unpublished
Supervisor(s)/Advisor:	Steel, Mark F. J. ; Griffin, Jim E.
Sponsors:	Engineering and Physical Sciences Research Council (Great Britain) (EPSRC) ; University of Warwick. Centre for Research in Statistical Methodology (CRiSM) ; Cyprus. Hypourgeio Oikonomikōn [Cyprus. Ministry of Finance] (C.MoF)
Format of File:	pdf
Extent:	206 leaves : charts
Language:	eng

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