37,484 research outputs found
Nonparametric tests of structure for high angular resolution diffusion imaging in Q-space
High angular resolution diffusion imaging data is the observed characteristic
function for the local diffusion of water molecules in tissue. This data is
used to infer structural information in brain imaging. Nonparametric scalar
measures are proposed to summarize such data, and to locally characterize
spatial features of the diffusion probability density function (PDF), relying
on the geometry of the characteristic function. Summary statistics are defined
so that their distributions are, to first-order, both independent of nuisance
parameters and also analytically tractable. The dominant direction of the
diffusion at a spatial location (voxel) is determined, and a new set of axes
are introduced in Fourier space. Variation quantified in these axes determines
the local spatial properties of the diffusion density. Nonparametric hypothesis
tests for determining whether the diffusion is unimodal, isotropic or
multi-modal are proposed. More subtle characteristics of white-matter
microstructure, such as the degree of anisotropy of the PDF and symmetry
compared with a variety of asymmetric PDF alternatives, may be ascertained
directly in the Fourier domain without parametric assumptions on the form of
the diffusion PDF. We simulate a set of diffusion processes and characterize
their local properties using the newly introduced summaries. We show how
complex white-matter structures across multiple voxels exhibit clear
ellipsoidal and asymmetric structure in simulation, and assess the performance
of the statistics in clinically-acquired magnetic resonance imaging data.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS441 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Location Dependent Dirichlet Processes
Dirichlet processes (DP) are widely applied in Bayesian nonparametric
modeling. However, in their basic form they do not directly integrate
dependency information among data arising from space and time. In this paper,
we propose location dependent Dirichlet processes (LDDP) which incorporate
nonparametric Gaussian processes in the DP modeling framework to model such
dependencies. We develop the LDDP in the context of mixture modeling, and
develop a mean field variational inference algorithm for this mixture model.
The effectiveness of the proposed modeling framework is shown on an image
segmentation task
Bayesian nonparametric dependent model for partially replicated data: the influence of fuel spills on species diversity
We introduce a dependent Bayesian nonparametric model for the probabilistic
modeling of membership of subgroups in a community based on partially
replicated data. The focus here is on species-by-site data, i.e. community data
where observations at different sites are classified in distinct species. Our
aim is to study the impact of additional covariates, for instance environmental
variables, on the data structure, and in particular on the community diversity.
To that purpose, we introduce dependence a priori across the covariates, and
show that it improves posterior inference. We use a dependent version of the
Griffiths-Engen-McCloskey distribution defined via the stick-breaking
construction. This distribution is obtained by transforming a Gaussian process
whose covariance function controls the desired dependence. The resulting
posterior distribution is sampled by Markov chain Monte Carlo. We illustrate
the application of our model to a soil microbial dataset acquired across a
hydrocarbon contamination gradient at the site of a fuel spill in Antarctica.
This method allows for inference on a number of quantities of interest in
ecotoxicology, such as diversity or effective concentrations, and is broadly
applicable to the general problem of communities response to environmental
variables.Comment: Main Paper: 22 pages, 6 figures. Supplementary Material: 11 pages, 1
figur
A Tutorial on Bayesian Nonparametric Models
A key problem in statistical modeling is model selection, how to choose a
model at an appropriate level of complexity. This problem appears in many
settings, most prominently in choosing the number ofclusters in mixture models
or the number of factors in factor analysis. In this tutorial we describe
Bayesian nonparametric methods, a class of methods that side-steps this issue
by allowing the data to determine the complexity of the model. This tutorial is
a high-level introduction to Bayesian nonparametric methods and contains
several examples of their application.Comment: 28 pages, 8 figure
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