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

Dynamic models in fMRI

Most statistical methods for assessing activated voxels in fMRI experiments are based on correlation or regression analysis. In this context the main assumptions are that the baseline can be described by a few known basis-functions or variables and that the effect of the stimulus, i.e. the activation, stays constant over time. As these assumptions are in many cases neither necessary nor correct, a new dynamic approach that does not depend on those suppositions will be presented. This allows for simultaneous nonparametric estimation of the baseline as well as the time-varying effect of stimulation. This method of estimating the stimulus related areas of the brain furthermore provides the possibility of an analysis of the temporal and spatial development of the activation within an fMRI-experiment

Bayesian analysis of logistic regression with an unknown change point

We discuss Bayesian estimation of a logistic regression model with an unknown threshold limiting value (TLV). In these models it is assumed that there is no effect of a covariate on the response under a certain unknown TLV. The estimation of these models with a focus on the TLV in a Bayesian context by Markov chain Monte Carlo (MCMC) methods is considered. We extend the model by accounting for measurement error in the covariate. The Bayesian solution is compared with the likelihood solution proposed by Kuechenhoff and Carroll (1997) using a data set concerning the relationship between dust concentration in the working place and the occurrence of chronic bronchitis

Bayesian Analysis of Logistic Regression With an Unknown Change Point

We discuss Bayesian estimation of a logistic regression model with an unknown threshold limiting value (TLV). In these models it is assumed that there is no effect of a covariate on the response under a certain unknown TLV. The estimation of these models with a focus on the TLV in a Bayesian context by Markov chain Monte Carlo (MCMC) methods is considered. We extend the model by accounting for measurement error in the covariate. The Bayesian solution is compared with the likelihood solution proposed by Kuchenhoff and Carroll (1997) using a data set concerning the relationship between dust concentration in the working place and the occurrence of chronic bronchitis. Keywords: threshold limiting value (TLV), segmented regression, measurement error, MCMC 1 Introduction In toxicology, environmental and occupational epidemiology the assessment of threshold limiting values (TLVs) is an important task. In a dose-response relationship the TLV is the dose of the toxin or a substance under whic..