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Spatial Mixture Models with Applications in Medical Imaging and Spatial Point Processes

Anders Hildeman (Institutionen för matematiska vetenskaper, Tillämpad matematik och statistik)
Gothenburg : Chalmers University of Technology, 2017.
[Licentiatavhandling]

Finite mixture models have proven to be a great tool for both modeling non-standard probability distributions and for classification problems (using the latent variable interpretation). In this thesis we are building spatial models by incorporating spatially dependent categorical latent random fields in a hierarchical manner similar to that of finite mixture models. This allows for non-linear prediction, better interpretation of estimated model parameters, and the added possibility of addressing questions related to classification.

This thesis consists of two papers.
The first paper concerns a problem in medical imaging where substitutes of computed tomography (CT) images are demanded due to the risks associated with X-radiation. This problem is addressed by modeling the dependency between CT images and magnetic resonance (MR) images.
The model proposed incorporates multidimensional normal inverse Gaussian distributions and a spatially dependent Potts model for the latent classification. Parameter estimation is suggested using a maximum pseudo-likelihood approach implemented using the EM gradient method. The model is evaluated using cross-validation on three dimensional data of human brains.

The second paper concerns modeling of spatial point patterns. A novel hierarchical Bayesian model is constructed by using Gaussian random fields and level sets in a Cox process. The model is an extension to the popular log-Gaussian Cox process and incorporates a latent classification field in order to handle sudden jumps in the intensity surface and to address classification problems.
For inference, a Markov chain Monte Carlo method based on the preconditioned Crank-Nicholson MALA method is suggested. Finally, the model is applied to a popular data set of tree locations in a rainforest and the results show the advantage of the proposed model compared to the log-Gaussian Cox process that has been applied to the very same data set in several earlier publications.

Nyckelord: Non-Gaussian,Bayesian level set inversion,Point processes,Substitute CT,Finite mixture models,Spatial statistics,Gaussian fields



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Denna post skapades 2017-09-01. Senast ändrad 2017-09-12.
CPL Pubid: 251569

 

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Institutioner (Chalmers)

Institutionen för matematiska vetenskaper, Tillämpad matematik och statistikInstitutionen för matematiska vetenskaper, Tillämpad matematik och statistik (GU)

Ämnesområden

Informations- och kommunikationsteknik
Livsvetenskaper
Sannolikhetsteori och statistik
Annan data- och informationsvetenskap

Chalmers infrastruktur

C3SE/SNIC (Chalmers Centre for Computational Science and Engineering)

Examination

Datum: 2017-09-28
Tid: 10:15
Lokal: Euler, Matematiska Vetenskaper, Chalmers Tvärgata 3, Göteborg
Opponent: Associate Professor Johan Lindström, Centre for Mathematical Sciences, Lund University, Sweden