Spatial Mixture Models with Applications in Medical Imaging and Spatial Point Processes
Licentiatavhandling, 2017

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.

Non-Gaussian

Bayesian level set inversion

Point processes

Spatial statistics

Substitute CT

Finite mixture models

Gaussian fields

Euler, Matematiska Vetenskaper, Chalmers Tvärgata 3, Göteborg
Opponent: Associate Professor Johan Lindström, Centre for Mathematical Sciences, Lund University, Sweden

Författare

Anders Hildeman

Chalmers, Matematiska vetenskaper, Tillämpad matematik och statistik

Hildeman, A., Bolin, S., Wallin, J,m Johansson, A., Nyholm, T., Asklund, T., Yu, J., Whole-brain substitute CT generation using Markov random field mixture models

Hildeman, A., Bolin, D., Wallin, J., Illian, J.B., Level set Cox processes

Ämneskategorier

Annan data- och informationsvetenskap

Sannolikhetsteori och statistik

Styrkeområden

Informations- och kommunikationsteknik

Livsvetenskaper och teknik

Infrastruktur

C3SE (Chalmers Centre for Computational Science and Engineering)

Utgivare

Chalmers tekniska högskola

Euler, Matematiska Vetenskaper, Chalmers Tvärgata 3, Göteborg

Opponent: Associate Professor Johan Lindström, Centre for Mathematical Sciences, Lund University, Sweden