167 research outputs found
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 -means-type algorithm for clustering datasets with incomplete records
The -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 -means algorithm that allows for clustering in the presence of
incomplete records. Our extension is called -means and reduces to the
-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 -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 -mixtures-model-based
clustering on all nine observed parameters (, , , ,
, , , , ) 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 ()) and spectrum (using
Hardness Ratio ) 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 , , and
) 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 -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
(, ), the peak flux () measured in 256-millisecond
bins, the total fluence () and the spectral hardness ratios ( and
) 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
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