9,424 research outputs found
Meta-analysis of functional neuroimaging data using Bayesian nonparametric binary regression
In this work we perform a meta-analysis of neuroimaging data, consisting of
locations of peak activations identified in 162 separate studies on emotion.
Neuroimaging meta-analyses are typically performed using kernel-based methods.
However, these methods require the width of the kernel to be set a priori and
to be constant across the brain. To address these issues, we propose a fully
Bayesian nonparametric binary regression method to perform neuroimaging
meta-analyses. In our method, each location (or voxel) has a probability of
being a peak activation, and the corresponding probability function is based on
a spatially adaptive Gaussian Markov random field (GMRF). We also include
parameters in the model to robustify the procedure against miscoding of the
voxel response. Posterior inference is implemented using efficient MCMC
algorithms extended from those introduced in Holmes and Held [Bayesian Anal. 1
(2006) 145--168]. Our method allows the probability function to be locally
adaptive with respect to the covariates, that is, to be smooth in one region of
the covariate space and wiggly or even discontinuous in another. Posterior
miscoding probabilities for each of the identified voxels can also be obtained,
identifying voxels that may have been falsely classified as being activated.
Simulation studies and application to the emotion neuroimaging data indicate
that our method is superior to standard kernel-based methods.Comment: Published in at http://dx.doi.org/10.1214/11-AOAS523 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Learning Sparse High Dimensional Filters: Image Filtering, Dense CRFs and Bilateral Neural Networks
Bilateral filters have wide spread use due to their edge-preserving
properties. The common use case is to manually choose a parametric filter type,
usually a Gaussian filter. In this paper, we will generalize the
parametrization and in particular derive a gradient descent algorithm so the
filter parameters can be learned from data. This derivation allows to learn
high dimensional linear filters that operate in sparsely populated feature
spaces. We build on the permutohedral lattice construction for efficient
filtering. The ability to learn more general forms of high-dimensional filters
can be used in several diverse applications. First, we demonstrate the use in
applications where single filter applications are desired for runtime reasons.
Further, we show how this algorithm can be used to learn the pairwise
potentials in densely connected conditional random fields and apply these to
different image segmentation tasks. Finally, we introduce layers of bilateral
filters in CNNs and propose bilateral neural networks for the use of
high-dimensional sparse data. This view provides new ways to encode model
structure into network architectures. A diverse set of experiments empirically
validates the usage of general forms of filters
Ray-tracing through the Millennium Simulation: Born corrections and lens-lens coupling in cosmic shear and galaxy-galaxy lensing
(abridged) We study the accuracy of various approximations to cosmic shear
and weak galaxy-galaxy lensing and investigate effects of Born corrections and
lens-lens coupling. We use ray-tracing through the Millennium Simulation to
calculate various cosmic-shear and galaxy-galaxy-lensing statistics. We compare
the results from ray-tracing to semi-analytic predictions. We find: (i) The
linear approximation provides an excellent fit to cosmic-shear power spectra as
long as the actual matter power spectrum is used as input. Common fitting
formulae, however, strongly underestimate the cosmic-shear power spectra. Halo
models provide a better fit to cosmic shear-power spectra, but there are still
noticeable deviations. (ii) Cosmic-shear B-modes induced by Born corrections
and lens-lens coupling are at least three orders of magnitude smaller than
cosmic-shear E-modes. Semi-analytic extensions to the linear approximation
predict the right order of magnitude for the B-mode. Compared to the
ray-tracing results, however, the semi-analytic predictions may differ by a
factor two on small scales and also show a different scale dependence. (iii)
The linear approximation may under- or overestimate the galaxy-galaxy-lensing
shear signal by several percent due to the neglect of magnification bias, which
may lead to a correlation between the shear and the observed number density of
lenses. We conclude: (i) Current semi-analytic models need to be improved in
order to match the degree of statistical accuracy expected for future
weak-lensing surveys. (ii) Shear B-modes induced by corrections to the linear
approximation are not important for future cosmic-shear surveys. (iii)
Magnification bias can be important for galaxy-galaxy-lensing surveys.Comment: version taking comments into accoun
MCMC with Strings and Branes: The Suburban Algorithm (Extended Version)
Motivated by the physics of strings and branes, we develop a class of Markov
chain Monte Carlo (MCMC) algorithms involving extended objects. Starting from a
collection of parallel Metropolis-Hastings (MH) samplers, we place them on an
auxiliary grid, and couple them together via nearest neighbor interactions.
This leads to a class of "suburban samplers" (i.e., spread out Metropolis).
Coupling the samplers in this way modifies the mixing rate and speed of
convergence for the Markov chain, and can in many cases allow a sampler to more
easily overcome free energy barriers in a target distribution. We test these
general theoretical considerations by performing several numerical experiments.
For suburban samplers with a fluctuating grid topology, performance is strongly
correlated with the average number of neighbors. Increasing the average number
of neighbors above zero initially leads to an increase in performance, though
there is a critical connectivity with effective dimension d_eff ~ 1, above
which "groupthink" takes over, and the performance of the sampler declines.Comment: v2: 55 pages, 13 figures, references and clarifications added.
Published version. This article is an extended version of "MCMC with Strings
and Branes: The Suburban Algorithm
Topological susceptibility and the sampling of field space in lattice QCD simulations
We present a measurement of the topological susceptibility in two flavor QCD.
In this observable, large autocorrelations are present and also sizable cutoff
effects have to be faced in the continuum extrapolation. Within the statistical
accuracy of the computation, the result agrees with the expectation from
leading order chiral perturbation theory.Comment: 22 pages, 7 figures; References added, minor clarifications in the
text, results unchange
Topological critical slowing down: variations on a toy model
Numerical simulations of lattice quantum field theories whose continuum
counterparts possess classical solutions with non-trivial topology face a
severe critical slowing down as the continuum limit is approached. Standard
Monte-Carlo algorithms develop a loss of ergodicity, with the system remaining
frozen in configurations with fixed topology. We analyze the problem in a
simple toy model, consisting of the path integral formulation of a quantum
mechanical particle constrained to move on a circumference. More specifically,
we implement for this toy model various techniques which have been proposed to
solve or alleviate the problem for more complex systems, like non-abelian gauge
theories, and compare them both in the regime of low temperature and in that of
very high temperature. Among the various techniques, we consider also a new
algorithm which completely solves the freezing problem, but unfortunately is
specifically tailored for this particular model and not easily exportable to
more complex systems.Comment: 18 pages, 14 eps figures. Some changes and references added. To be
published by Phys Rev
Adding Long Wavelength Modes to an -Body Simulation
We present a new method to add long wavelength power to an evolved -body
simulation, making use of the Zel'dovich (1970) approximation to change
positions and velocities of particles. We describe the theoretical framework of
our technique and apply it to a PM cosmological simulation performed on a
cube of Mpc on a side, obtaining a new ``simulation'' of Mpc on a
side. We study the effect of the power added by long waves by mean of several
statistics of the density and velocity field, and suggest possible applications
of our method to the study of the large-scale structure of the universe.Comment: Revised version, shortened. 15 pages without figures. Accepted for
publication in the Astrophysical Journal. Paper and 11 Figures available as
.ps.gz files by anonymous ftp at ftp://ftp.mpa-garching.mpg.de/pub/bepi/MA
Stationary Statistics of Turbulence as an Attractor
A calculational approach in fluid turbulence is presented. Use is made of the
attracting nature of the fluid-dynamic dynamical system. An approach is offered
that effectively propagates the statistics in time. Loss of sensitivity to an
initial probability density functional and generation of stationary statistical
effects is speculated.Comment: A correction to the integration measure on page 6 has been inserte
- …