A nonstationary nonparametric Bayesian approach to dynamically modeling effective connectivity in functional magnetic resonance imaging experiments

Effective connectivity analysis provides an understanding of the functional organization of the brain by studying how activated regions influence one other. We propose a nonparametric Bayesian approach to model effective connectivity assuming a dynamic nonstationary neuronal system. Our approach uses the Dirichlet process to specify an appropriate (most plausible according to our prior beliefs) dynamic model as the "expectation" of a set of plausible models upon which we assign a probability distribution. This addresses model uncertainty associated with dynamic effective connectivity. We derive a Gibbs sampling approach to sample from the joint (and marginal) posterior distributions of the unknowns. Results on simulation experiments demonstrate our model to be flexible and a better candidate in many situations. We also used our approach to analyzing functional Magnetic Resonance Imaging (fMRI) data on a Stroop task: our analysis provided new insight into the mechanism by which an individual brain distinguishes and learns about shapes of objects.Comment: Published in at http://dx.doi.org/10.1214/11-AOAS470 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

An efficient kk-means-type algorithm for clustering datasets with incomplete records

The $k$-means algorithm is arguably the most popular nonparametric clustering method but cannot generally be applied to datasets with incomplete records. The usual practice then is to either impute missing values under an assumed missing-completely-at-random mechanism or to ignore the incomplete records, and apply the algorithm on the resulting dataset. We develop an efficient version of the $k$-means algorithm that allows for clustering in the presence of incomplete records. Our extension is called $k_m$-means and reduces to the $k$-means algorithm when all records are complete. We also provide initialization strategies for our algorithm and methods to estimate the number of groups in the dataset. Illustrations and simulations demonstrate the efficacy of our approach in a variety of settings and patterns of missing data. Our methods are also applied to the analysis of activation images obtained from a functional Magnetic Resonance Imaging experiment.Comment: 21 pages, 12 figures, 3 tables, in press, Statistical Analysis and Data Mining -- The ASA Data Science Journal, 201

Multivariate tt-Mixtures-Model-based Cluster Analysis of BATSE Catalog Establishes Importance of All Observed Parameters, Confirms Five Distinct Ellipsoidal Sub-populations of Gamma Ray Bursts

Determining the kinds of gamma-ray bursts (GRBs) has been of interest to astronomers for many years. We analyzed 1599 GRBs from the Burst and Transient Source Experiment (BATSE) 4Br catalogue using $t$-mixtures-model-based clustering on all nine observed parameters ($T_{50}$, $T_{90}$, $F_1$, $F_2$, $F_3$, $F_4$, $P_{64}$, $P_{256}$, $P_{1024}$) and found evidence of five types of GRBs. Our results further refine the findings of Chattopadhyay and Maitra (2017) by providing groups that are more distinct. Using the Mukherjee et al. (1998) classification scheme, also used by Chattopadhyay and Maitra (2017), of duration, total fluence ($F_t = F_1 + F_2 + F_3 + F_4$)) and spectrum (using Hardness Ratio $H_{321} = F_3/(F_1 + F_2)$) our five groups are classified as long-intermediate-intermediate, short-faint-intermediate, short-faint-soft, long-bright-hard, and long-intermediate-hard. We also classify 374 GRBs in the BATSE catalogue that have incomplete information in some of the observed variables (mainly the four time integrated fluences $F_1$, $F_2$, $F_3$ and $F_4$) to the five groups obtained, using the 1599 GRBs having complete information in all the observed variables. Our classification scheme puts 138 GRBs in the first group, 52 GRBs in the second group, 33 GRBs in the third group, 127 GRBs in the fourth group and 24 GRBs in the fifth group.Comment: 16 pages, 11 figures, 7 tables, in press, Monthly Notices of the Royal Astronomical Society, 201

Fast spatial inference in the homogeneous Ising model

The Ising model is important in statistical modeling and inference in many applications, however its normalizing constant, mean number of active vertices and mean spin interaction are intractable. We provide accurate approximations that make it possible to calculate these quantities numerically. Simulation studies indicate good performance when compared to Markov Chain Monte Carlo methods and at a tiny fraction of the time. The methodology is also used to perform Bayesian inference in a functional Magnetic Resonance Imaging activation detection experiment.Comment: 18 pages, 1 figure, 3 table

Gaussian-Mixture-Model-based Cluster Analysis Finds Five Kinds of Gamma Ray Bursts in the BATSE Catalog

Clustering methods are an important tool to enumerate and describe the different coherent kinds of Gamma Ray Bursts (GRBs). But their performance can be affected by a number of factors such as the choice of clustering algorithm and inherent associated assumptions, the inclusion of variables in clustering, nature of initialization methods used or the iterative algorithm or the criterion used to judge the optimal number of groups supported by the data. We analyzed GRBs from the BATSE 4Br catalog using $k$-means and Gaussian Mixture Models-based clustering methods and found that after accounting for all the above factors, all six variables -- different subsets of which have been used in the literature -- and that are, namely, the flux duration variables ($T_{50}$, $T_{90}$), the peak flux ($P_{256}$) measured in 256-millisecond bins, the total fluence ($F_t$) and the spectral hardness ratios ($H_{32}$ and $H_{321}$) contain information on clustering. Further, our analysis found evidence of five different kinds of GRBs and that these groups have different kinds of dispersions in terms of shape, size and orientation. In terms of duration, fluence and spectrum, the five types of GRBs were characterized as intermediate/faint/intermediate, long/intermediate/soft, intermediate/intermediate/intermediate, short/faint/hard and long/bright/intermediate.Comment: 17 pages, 12 figures, 6 table

On the Expectation-Maximization Algorithm for Rice-Rayleigh Mixtures With Application to Noise Parameter Estimation in Magnitude MR Datasets

Magnitude magnetic resonance (MR) images are noise-contaminated measurements of the true signal, and it is important to assess the noise in many applications. A recently introduced approach models the magnitude MR datum at each voxel in terms of a mixture of upto one Rayleigh and an a priori unspecified number of Rice components, all with a common noise parameter. The Expectation-Maximization (EM) algorithm was developed for parameter estimation, with the mixing component membership of each voxel as the missing observation. This paper revisits the EM algorithm by introducing more missing observations into the estimation problem such that the complete (observed and missing parts) dataset can be modeled in terms of a regular exponential family. Both the EM algorithm and variance estimation are then fairly straightforward without any need for potentially unstable numerical optimization methods. Compared to local neighborhood- and wavelet-based noise-parameter estimation methods, the new EMbased approach is seen to perform well not only on simulation datasets but also on physical phantom and clinical imaging data

Efficient Bandwidth Estimation in 2D Filtered Backprojection Reconstruction

A generalized cross-validation approach to estimate the reconstruction filter bandwidth in 2D filtered backprojection is presented. The method writes the reconstruction equation in equivalent backprojected filtering form, derives results on eigendecomposition of symmetric 2D circulant matrices, and applies them to make bandwidth estimation a computationally efficient operation within the context of standard backprojected filtering reconstruction. Performance evaluations on a range of simulated emission tomography experiments give promising results. The superior performance holds at both low and high total expected counts, pointing to the method\u27s applicability even in weak signal-to-noise-ratio situations. The approach also applies to the more general class of elliptically symmetric filters, with the reconstructed estimate\u27s performance often better than even that obtained with the true optimal radially symmetric filter

Assessing certainty of activation or inactivation in test–retest fMRI studies

Functional Magnetic Resonance Imaging (fMRI) is widely used to study activation in the human brain. In most cases, data are commonly used to construct activation maps corresponding to a given paradigm. Results can be very variable, hence quantifying certainty of identified activation and inactivation over studies is important. This paper provides a model-based approach to certainty estimation from data acquired over several replicates of the same experimental paradigm. Specifically, the p-values derived from the statistical analysis of the data are explicitly modeled as a mixture of their underlying distributions; thus, unlike the methodology currently in use, there is no subjective thresholding required in the estimation process. The parameters governing the mixture model are easily obtained by the principle of maximum likelihood. Further, the estimates can also be used to optimally identify voxel-specific activation regions along with their corresponding certainty measures. The methodology is applied to a study involving a motor paradigm performed on a single subject several times over a period of two months. Simulation experiments used to calibrate performance of the method are promising. The methodology is also seen to be robust in determining areas of activation and their corresponding certainties

A re-defined and generalized percent-overlap-of-activation measure for studies of fMRI reproducibility and its use in identifying outlier activation maps

Functional Magnetic Resonance Imaging (fMRI) is a popular noninvasive modality to investigate activation in the human brain. The end result of most fMRI experiments is an activation map corresponding to the given paradigm. These maps can vary greatly from one study to the next, so quantifying the reliability of identified activation over several fMRI studies is important. The percent overlap of activation (Rombouts et al., 1998 and Machielsen et al., 2000) is a global reliability measure between activation maps drawn from any two fMRI studies. A slightly modified but more intuitive measure is provided by the Jaccard (1901) coefficient of similarity, whose use we study in this paper. A generalization of these measures is also proposed to comprehensively summarize the reliability of multiple fMRI studies. Finally, a testing mechanism to flag potentially anomalous studies is developed. The methodology is illustrated on studies involving left- and right-hand motor task paradigms performed by a right-hand dominant male subject several times over a period of two months, with excellent results