Motivation: Multiple marker analysis of the genome-wide association study (GWAS) data has gained ample attention in recent years. However, because of the ultra high-dimensionality of GWAS data, such analysis is challenging. Frequently used penalized regression methods often lead to large number of false positives, whereas Bayesian methods are computationally very expensive. Motivated to ameliorate these issues simultaneously, we consider the novel approach of using non-local priors in an iterative variable selection framework. Results: We develop a variable selection method, named, iterative non-local prior based selection for GWAS, or GWASinlps, that combines, in an iterative variable selection framework, the computational efficiency of the screen-and-select approach based on some association learning and the parsimonious uncertainty quantification provided by the use of non-local priors. The hallmark of our method is the introduction of 'structured screen-and-select' strategy, that considers hierarchical screening, which is not only based on response-predictor associations, but also based on response-response associations and concatenates variable selection within that hierarchy. Extensive simulation studies with single nucleotide polymorphisms having realistic linkage disequilibrium structures demonstrate the advantages of our computationally efficient method compared to several frequentist and Bayesian variable selection methods, in terms of true positive rate, false discovery rate, mean squared error and effect size estimation error. Further, we provide empirical power analysis useful for study design. Finally, a real GWAS data application was considered with human height as phenotype. Availability and implementation: An R-package for implementing the GWASinlps method is available at https://cran.r-project.org/web/packages/GWASinlps/index.html. Supplementary information: Supplementary data are available at Bioinformatics online.

MOTIVATION: The advent of new genomic technologies has resulted in the production of massive data sets. Analyses of these data require new statistical and computational methods. In this article, we propose one such method that is useful in selecting explanatory variables for prediction of a binary response. Although this problem has recently been addressed using penalized likelihood methods, we adopt a Bayesian approach that utilizes a mixture of non-local prior densities and point masses on the binary regression coefficient vectors. RESULTS: The resulting method, which we call iMOMLogit, provides improved performance in identifying true models and reducing estimation and prediction error in a number of simulation studies. More importantly, its application to several genomic datasets produces predictions that have high accuracy using far fewer explanatory variables than competing methods. We also describe a novel approach for setting prior hyperparameters by examining the total variation distance between the prior distributions on the regression parameters and the distribution of the maximum likelihood estimator under the null distribution. Finally, we describe a computational algorithm that can be used to implement iMOMLogit in ultrahigh-dimensional settings ([Formula: see text]) and provide diagnostics to assess the probability that this algorithm has identified the highest posterior probability model. AVAILABILITY AND IMPLEMENTATION: Software to implement this method can be downloaded at: http://www.stat.tamu.edu/∼amir/code.html CONTACT: [email protected] or [email protected] SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

A model of object shape by nets of medial and boundary primitives is justified as richly capturing multiple aspects of shape and yet requiring representation space and image analysis work proportional to the number of primitives. Metrics are described that compute an object representation's prior probability of local geometry by reflecting variabilities in the net's node and link parameter values, and that compute a likelihood function measuring the degree of match of an image to that object representation. A paradigm for image analysis of deforming such a model to optimize a posteriori probability is described, and this paradigm is shown to be usable as a uniform approach for object definition, object-based registration between images of the same or different imaging modalities, and measurement of shape variation of an abnormal anatomical object, compared with a normal anatomical object. Examples of applications of these methods in radiotherapy, surgery, and psychiatry are given.

In recent years, many investigators have proposed Gibbs prior models to regularize images reconstructed from emission computed tomography data. Unfortunately, hyperparameters used to specify Gibbs priors can greatly influence the degree of regularity imposed by such priors and, as a result, numerous procedures have been proposed to estimate hyperparameter values from observed image data. Many of these procedures attempt to maximize the joint posterior distribution on the image scene. To implement these methods, approximations to the joint posterior densities are required, because the dependence of the Gibbs partition function on the hyperparameter values is unknown. In this paper, we use recent results in Markov chain Monte Carlo (MCMC) sampling to estimate the relative values of Gibbs partition functions and using these values, sample from joint posterior distributions on image scenes. This allows for a fully Bayesian procedure which does not fix the hyperparameters at some estimated or specified value, but enables uncertainty about these values to be propagated through to the estimated intensities. We utilize realizations from the posterior distribution for determining credible regions for the intensity of the emission source. We consider two different Markov random field (MRF) models-the power model and a line-site model. As applications we estimate the posterior distribution of source intensities from computer simulated data as well as data collected from a physical single photon emission computed tomography (SPECT) phantom.

A Bayesian method is presented for simultaneously segmenting and reconstructing emission computed tomography (ECT) images and for incorporating high-resolution, anatomical information into those reconstructions. The anatomical information is often available from other imaging modalities such as computed tomography (CT) or magnetic resonance imaging (MRI). The Bayesian procedure models the ECT radiopharmaceutical distribution as consisting of regions, such that radiopharmaceutical activity is similar throughout each region. It estimates the number of regions, the mean activity of each region, and the region classification and mean activity of each voxel. Anatomical information is incorporated by assigning higher prior probabilities to ECT segmentations in which each ECT region stays within a single anatomical region. This approach is effective because anatomical tissue type often strongly influences radiopharmaceutical uptake. The Bayesian procedure is evaluated using physically acquired single-photon emission computed tomography (SPECT) projection data and MRI for the three-dimensional (3-D) Hoffman brain phantom. A clinically realistic count level is used. A cold lesion within the brain phantom is created during the SPECT scan but not during the MRI to demonstrate that the estimation procedure can detect ECT structure that is not present anatomically.

The use of the expectation-maximization algorithm to obtain pseudo-maximum likelihood estimates (i.e. the EM-ML algorithm) of radiopharmaceutical distributions based on data collected from emission computed tomography (ECT) systems is now a well developed area, as witnessed by a number of recent articles on that topic, including the detailed study of the relative performance of EM-ML and FBP reconstructions provided in J. Llacer et al. (ibid., vol. 12, p. 215-31, 1993). However, there remains considerable confusion in the field regarding appropriate stopping rules for EM-ML algorithms, and in this correspondence the author attempts to detail a shortcoming of one of the more recent and innovative stopping rule criteria. In particular, the author discusses the effect of total photon counts on stopping criteria based on cross-validation.

Reports on a new method in which spatially correlated magnetic resonance (MR) or X-ray computed tomography (CT) images are employed as a source of prior information in the Bayesian reconstruction of positron emission tomography (PET) images. This new method incorporates the correlated structural images as anatomic templates which can be used for extracting information about boundaries that separate regions exhibiting different tissue characteristics. In order to avoid the possible introduction of artifacts caused by discrepancies between functional and anatomic boundaries, the authors propose a new method called the "weighted line site" method, in which a prior structural image is employed in a modified updating scheme for the boundary variable used in the iterative Bayesian reconstruction. This modified scheme is based on the joint probability of structural and functional boundaries. As to the structural information provided by CT or MR images, only those which have high joint probability with the corresponding PET data are used; whereas other boundary information that is not supported by the PET image is suppressed. The new method has been validated by computer simulation and phantom studies. The results of these validation studies indicate that this new method offers significant improvements in image quality when compared to other reconstruction algorithms, including the filtered backprojection method and the maximum likelihood approach, as well as the Bayesian method without the use of the prior boundary information.

The authors propose a Bayesian model for the restoration of images based on counts of emitted photons. The model treats blurring within the context of an incomplete data problem and utilizes a Gibbs prior to model the spatial correlation of neighboring regions. The Gibbs prior includes line sites to account for boundaries between regions, and the line sites are assigned continuous values to permit efficient estimation using a method called iterative conditional averages. In addition, the effect of blurring in masking differences between images and the effects of misspecifying the amount of blurring are discussed.>