21,694 research outputs found
Bayesian mapping of brain regions using compound Markov random field priors
Human brain mapping, i.e. the detection of functional regions and their connections, has experienced enormous progress through the use of functional magnetic resonance imaging (fMRI). The massive spatio-temporal data sets generated by this imaging technique impose challenging problems for statistical analysis. Many approaches focus on adequate modeling of the temporal component. Spatial aspects are often considered only in a separate postprocessing step, if at all, or modeling is based on Gaussian random fields. A weakness of Gaussian spatial smoothing is possible underestimation of activation peaks or blurring of sharp transitions between activated and non-activated regions. In this paper we suggest Bayesian spatio-temporal models, where spatial adaptivity is improved through inhomogeneous or compound Markov random field priors. Inference is based on an approximate MCMC technique. Performance of our approach is investigated through a simulation study, including a comparison to models based on Gaussian as well as more robust spatial priors in terms of pixelwise and global MSEs. Finally we demonstrate its use by an application to fMRI data from a visual stimulation experiment for assessing activation in visual cortical areas
Hidden Gibbs random fields model selection using Block Likelihood Information Criterion
Performing model selection between Gibbs random fields is a very challenging
task. Indeed, due to the Markovian dependence structure, the normalizing
constant of the fields cannot be computed using standard analytical or
numerical methods. Furthermore, such unobserved fields cannot be integrated out
and the likelihood evaluztion is a doubly intractable problem. This forms a
central issue to pick the model that best fits an observed data. We introduce a
new approximate version of the Bayesian Information Criterion. We partition the
lattice into continuous rectangular blocks and we approximate the probability
measure of the hidden Gibbs field by the product of some Gibbs distributions
over the blocks. On that basis, we estimate the likelihood and derive the Block
Likelihood Information Criterion (BLIC) that answers model choice questions
such as the selection of the dependency structure or the number of latent
states. We study the performances of BLIC for those questions. In addition, we
present a comparison with ABC algorithms to point out that the novel criterion
offers a better trade-off between time efficiency and reliable results
Adaptive Gaussian Markov Random Fields with Applications in Human Brain Mapping
Functional magnetic resonance imaging (fMRI) has become the standard technology in human brain mapping. Analyses of the massive spatio-temporal fMRI data sets often focus on parametric or nonparametric modeling of the temporal component, while spatial smoothing is based on Gaussian kernels or random fields. A weakness of Gaussian spatial smoothing is underestimation of activation peaks or blurring of high-curvature transitions between activated and non-activated brain regions. In this paper, we introduce a class of inhomogeneous Markov random fields (MRF) with spatially adaptive interaction weights in a space-varying coefficient model for fMRI data. For given weights, the random field is conditionally Gaussian, but marginally it is non-Gaussian. Fully Bayesian inference, including estimation of weights and variance parameters, is carried out through efficient MCMC simulation. An application to fMRI data from a visual stimulation experiment demonstrates the performance of our approach in comparison to Gaussian and robustified non-Gaussian Markov random field models
Segmentation of skin lesions in 2D and 3D ultrasound images using a spatially coherent generalized Rayleigh mixture model
This paper addresses the problem of jointly estimating the statistical distribution and segmenting lesions in multiple-tissue high-frequency skin ultrasound images. The distribution of multiple-tissue images is modeled as a spatially coherent finite mixture of heavy-tailed Rayleigh distributions. Spatial coherence inherent to biological tissues is modeled by enforcing local dependence between the mixture components. An original Bayesian algorithm combined with a Markov chain Monte Carlo method is then proposed to jointly estimate the mixture parameters and a label-vector associating each voxel to a tissue. More precisely, a hybrid Metropolis-within-Gibbs sampler is used to draw samples that are asymptotically distributed according to the posterior distribution of the Bayesian model. The Bayesian estimators of the model parameters are then computed from the generated samples. Simulation results are conducted on synthetic data to illustrate the performance of the proposed estimation strategy. The method is then successfully applied to the segmentation of in vivo skin tumors in high-frequency 2-D and 3-D ultrasound images
Quantitative magnetic resonance image analysis via the EM algorithm with stochastic variation
Quantitative Magnetic Resonance Imaging (qMRI) provides researchers insight
into pathological and physiological alterations of living tissue, with the help
of which researchers hope to predict (local) therapeutic efficacy early and
determine optimal treatment schedule. However, the analysis of qMRI has been
limited to ad-hoc heuristic methods. Our research provides a powerful
statistical framework for image analysis and sheds light on future localized
adaptive treatment regimes tailored to the individual's response. We assume in
an imperfect world we only observe a blurred and noisy version of the
underlying pathological/physiological changes via qMRI, due to measurement
errors or unpredictable influences. We use a hidden Markov random field to
model the spatial dependence in the data and develop a maximum likelihood
approach via the Expectation--Maximization algorithm with stochastic variation.
An important improvement over previous work is the assessment of variability in
parameter estimation, which is the valid basis for statistical inference. More
importantly, we focus on the expected changes rather than image segmentation.
Our research has shown that the approach is powerful in both simulation studies
and on a real dataset, while quite robust in the presence of some model
assumption violations.Comment: Published in at http://dx.doi.org/10.1214/07-AOAS157 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
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