5,970 research outputs found
Estimating Time-Varying Effective Connectivity in High-Dimensional fMRI Data Using Regime-Switching Factor Models
Recent studies on analyzing dynamic brain connectivity rely on sliding-window
analysis or time-varying coefficient models which are unable to capture both
smooth and abrupt changes simultaneously. Emerging evidence suggests
state-related changes in brain connectivity where dependence structure
alternates between a finite number of latent states or regimes. Another
challenge is inference of full-brain networks with large number of nodes. We
employ a Markov-switching dynamic factor model in which the state-driven
time-varying connectivity regimes of high-dimensional fMRI data are
characterized by lower-dimensional common latent factors, following a
regime-switching process. It enables a reliable, data-adaptive estimation of
change-points of connectivity regimes and the massive dependencies associated
with each regime. We consider the switching VAR to quantity the dynamic
effective connectivity. We propose a three-step estimation procedure: (1)
extracting the factors using principal component analysis (PCA) and (2)
identifying dynamic connectivity states using the factor-based switching vector
autoregressive (VAR) models in a state-space formulation using Kalman filter
and expectation-maximization (EM) algorithm, and (3) constructing the
high-dimensional connectivity metrics for each state based on subspace
estimates. Simulation results show that our proposed estimator outperforms the
K-means clustering of time-windowed coefficients, providing more accurate
estimation of regime dynamics and connectivity metrics in high-dimensional
settings. Applications to analyzing resting-state fMRI data identify dynamic
changes in brain states during rest, and reveal distinct directed connectivity
patterns and modular organization in resting-state networks across different
states.Comment: 21 page
A fast Bayesian approach to discrete object detection in astronomical datasets - PowellSnakes I
A new fast Bayesian approach is introduced for the detection of discrete
objects immersed in a diffuse background. This new method, called PowellSnakes,
speeds up traditional Bayesian techniques by: i) replacing the standard form of
the likelihood for the parameters characterizing the discrete objects by an
alternative exact form that is much quicker to evaluate; ii) using a
simultaneous multiple minimization code based on Powell's direction set
algorithm to locate rapidly the local maxima in the posterior; and iii)
deciding whether each located posterior peak corresponds to a real object by
performing a Bayesian model selection using an approximate evidence value based
on a local Gaussian approximation to the peak. The construction of this
Gaussian approximation also provides the covariance matrix of the uncertainties
in the derived parameter values for the object in question. This new approach
provides a speed up in performance by a factor of `hundreds' as compared to
existing Bayesian source extraction methods that use MCMC to explore the
parameter space, such as that presented by Hobson & McLachlan. We illustrate
the capabilities of the method by applying to some simplified toy models.
Furthermore PowellSnakes has the advantage of consistently defining the
threshold for acceptance/rejection based on priors which cannot be said of the
frequentist methods. We present here the first implementation of this technique
(Version-I). Further improvements to this implementation are currently under
investigation and will be published shortly. The application of the method to
realistic simulated Planck observations will be presented in a forthcoming
publication.Comment: 30 pages, 15 figures, revised version with minor changes, accepted
for publication in MNRA
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