13,707 research outputs found
Nonparametric Independence Screening in Sparse Ultra-High Dimensional Varying Coefficient Models
The varying-coefficient model is an important nonparametric statistical model
that allows us to examine how the effects of covariates vary with exposure
variables. When the number of covariates is big, the issue of variable
selection arrives. In this paper, we propose and investigate marginal
nonparametric screening methods to screen variables in ultra-high dimensional
sparse varying-coefficient models. The proposed nonparametric independence
screening (NIS) selects variables by ranking a measure of the nonparametric
marginal contributions of each covariate given the exposure variable. The sure
independent screening property is established under some mild technical
conditions when the dimensionality is of nonpolynomial order, and the
dimensionality reduction of NIS is quantified. To enhance practical utility and
the finite sample performance, two data-driven iterative NIS methods are
proposed for selecting thresholding parameters and variables: conditional
permutation and greedy methods, resulting in Conditional-INIS and Greedy-INIS.
The effectiveness and flexibility of the proposed methods are further
illustrated by simulation studies and real data applications
Three-dimensional Radial Visualization of High-dimensional Datasets with Mixed Features
We develop methodology for 3D radial visualization (RadViz) of
high-dimensional datasets. Our display engine is called RadViz3D and extends
the classical 2D RadViz that visualizes multivariate data in the 2D plane by
mapping every record to a point inside the unit circle. We show that
distributing anchor points at least approximately uniformly on the 3D unit
sphere provides a better visualization with minimal artificial visual
correlation for data with uncorrelated variables. Our RadViz3D methodology
therefore places equi-spaced anchor points, one for every feature, exactly for
the five Platonic solids, and approximately via a Fibonacci grid for the other
cases. Our Max-Ratio Projection (MRP) method then utilizes the group
information in high dimensions to provide distinctive lower-dimensional
projections that are then displayed using Radviz3D. Our methodology is extended
to datasets with discrete and continuous features where a Gaussianized
distributional transform is used in conjunction with copula models before
applying MRP and visualizing the result using RadViz3D. A R package radviz3d
implementing our complete methodology is available.Comment: 12 pages, 10 figures, 1 tabl
A Reverse-Shock Model for the Early Afterglow of GRB 050525A
The prompt localization of gamma-ray burst (GRB) 050525A by {\em Swift}
allowed the rapid follow-up of the afterglow. The observations revealed that
the optical afterglow had a major rebrightening starting at days
and ending at days, which was followed by an initial power-law
decay. Here we show that this early emission feature can be interpreted as the
reverse shock emission superposed by the forward shock emission in an
interstellar medium environment. By fitting the observed data, we further
constrain some parameters of the standard fireball-shock model: the initial
Lorentz factor of the ejecta , the magnetic energy fraction
, and the medium density . These
limits are consistent with those from the other very-early optical afterglows
observed so far. In principle, a wind environment for GRB 050525A is
disfavored.Comment: 11 pages, 1 figure, accepted for publication in Ap
Strong GeV Emission Accompanying TeV Blazar H1426+428
For High frequency BL Lac objects (HBLs) like H1426+428, a significant
fraction of their TeV gamma-rays emitted are likely to be absorbed in
interactions with the diffuse IR background, yielding pairs. The
resulting pairs generate one hitherto undiscovered GeV emission by
inverse Compton scattering with the cosmic microwave background photons
(CMBPs). We study such emission by taking the 1998-2000 CAT data, the
reanalyzed 1999 & 2000 HEGRA data and the corresponding intrinsic spectra
proposed by Aharonian et al. (2003a). We numerically calculate the scattered
photon spectra for different intergalactic magnetic field (IGMF) strengths. If
the IGMF is about or weaker, there comes very strong GeV
emission, whose flux is far above the detection sensitivity of the upcoming
satellite GLAST! Considered its relatively high redshift (), the
detected GeV emission in turn provides us a valuable chance to calibrate the
poor known spectral energy distribution of the intergalactic infrared
background, or provides us some reliable constraints on the poorly known IGMF
strength.Comment: 5 pages, 1 figure. A&A in Pres
Behavior of X-Ray Dust Scattering and Implications for X-Ray Afterglows of Gamma-Ray Bursts
The afterglows of gamma-ray bursts (GRBs) have commonly been assumed to be
due to shocks sweeping up the circum-stellar medium. However, most GRBs have
been found in dense star-forming regions where a significant fraction of the
prompt X-ray emission can be scattered by dust grains. Here we revisit the
behavior of dust scattering of X-rays in GRBs. We find that the features of
some X-ray afterglows from minutes to days after the gamma-ray triggers are
consistent with the scattering of prompt X-ray emission from GRBs off host dust
grains. This implies that some of the observed X-ray afterglows (especially
those without sharp rising and decaying flares) could be understood with a
dust-scattering--driven emission model.Comment: ApJ, in pres
Constraints on Dark Energy Models Including Gamma Ray Bursts
In this paper we analyze the constraints on the property of dark energy from
cosmological observations. Together with SNe Ia Gold sample, WMAP, SDSS and
2dFGRS data, we include 69 long Gamma-Ray Bursts (GRBs) data in our study and
perform global fitting using Markov Chain Monte Carlo (MCMC) technique. Dark
energy perturbations are explicitly considered. We pay particular attention to
the time evolution of the equation of state of dark energy parameterized as
with the scale factor of the universe, emphasizing
the complementarity of high redshift GRBs to other cosmological probes. It is
found that the constraints on dark energy become stringent by taking into
account high redshift GRBs, especially for , which delineates the
evolution of dark energy.Comment: 7 pages and 3 figures. Replaced with version accepted for publication
in Phys. Lett.
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