633 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
Structure Learning in Coupled Dynamical Systems and Dynamic Causal Modelling
Identifying a coupled dynamical system out of many plausible candidates, each
of which could serve as the underlying generator of some observed measurements,
is a profoundly ill posed problem that commonly arises when modelling real
world phenomena. In this review, we detail a set of statistical procedures for
inferring the structure of nonlinear coupled dynamical systems (structure
learning), which has proved useful in neuroscience research. A key focus here
is the comparison of competing models of (ie, hypotheses about) network
architectures and implicit coupling functions in terms of their Bayesian model
evidence. These methods are collectively referred to as dynamical casual
modelling (DCM). We focus on a relatively new approach that is proving
remarkably useful; namely, Bayesian model reduction (BMR), which enables rapid
evaluation and comparison of models that differ in their network architecture.
We illustrate the usefulness of these techniques through modelling
neurovascular coupling (cellular pathways linking neuronal and vascular
systems), whose function is an active focus of research in neurobiology and the
imaging of coupled neuronal systems
Time-varying parametric modelling and time-dependent spectral characterisation with applications to EEG signals using multi-wavelets
A new time-varying autoregressive (TVAR) modelling approach is proposed for nonstationary signal processing and analysis, with application to EEG data modelling and power spectral estimation. In the new parametric modelling framework, the time-dependent coefficients of the TVAR model are represented using a novel multi-wavelet decomposition scheme. The time-varying modelling problem is then reduced to regression selection and parameter estimation, which can be effectively resolved by using a forward orthogonal regression algorithm. Two examples, one for an artificial signal and another for an EEG signal, are given to show the effectiveness and applicability of the new TVAR modelling method
A Power Variance Test for Nonstationarity in Complex-Valued Signals
We propose a novel algorithm for testing the hypothesis of nonstationarity in
complex-valued signals. The implementation uses both the bootstrap and the Fast
Fourier Transform such that the algorithm can be efficiently implemented in
O(NlogN) time, where N is the length of the observed signal. The test procedure
examines the second-order structure and contrasts the observed power variance -
i.e. the variability of the instantaneous variance over time - with the
expected characteristics of stationary signals generated via the bootstrap
method. Our algorithmic procedure is capable of learning different types of
nonstationarity, such as jumps or strong sinusoidal components. We illustrate
the utility of our test and algorithm through application to turbulent flow
data from fluid dynamics
Automated analysis of quantitative image data using isomorphic functional mixed models, with application to proteomics data
Image data are increasingly encountered and are of growing importance in many
areas of science. Much of these data are quantitative image data, which are
characterized by intensities that represent some measurement of interest in the
scanned images. The data typically consist of multiple images on the same
domain and the goal of the research is to combine the quantitative information
across images to make inference about populations or interventions. In this
paper we present a unified analysis framework for the analysis of quantitative
image data using a Bayesian functional mixed model approach. This framework is
flexible enough to handle complex, irregular images with many local features,
and can model the simultaneous effects of multiple factors on the image
intensities and account for the correlation between images induced by the
design. We introduce a general isomorphic modeling approach to fitting the
functional mixed model, of which the wavelet-based functional mixed model is
one special case. With suitable modeling choices, this approach leads to
efficient calculations and can result in flexible modeling and adaptive
smoothing of the salient features in the data. The proposed method has the
following advantages: it can be run automatically, it produces inferential
plots indicating which regions of the image are associated with each factor, it
simultaneously considers the practical and statistical significance of
findings, and it controls the false discovery rate.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS407 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
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