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 $\sim 0.01$ days and ending at $\sim 0.03$ 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 $\gamma_0>120$, the magnetic energy fraction $\epsilon_B>4\times10^{-6}$, and the medium density $n<2 {\rm cm^{-3}}$. 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 $e^\pm$ pairs. The resulting $e^\pm$ 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 $10^{-18}{\rm G}$ 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 ($z=0.129$), 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 $w_{DE}=w_0+w_a(1-a)$ with $a$ 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 $w_a$, which delineates the evolution of dark energy.Comment: 7 pages and 3 figures. Replaced with version accepted for publication in Phys. Lett.