Locally adaptive smoothing with Markov random fields and shrinkage priors

We present a locally adaptive nonparametric curve fitting method that operates within a fully Bayesian framework. This method uses shrinkage priors to induce sparsity in order-k differences in the latent trend function, providing a combination of local adaptation and global control. Using a scale mixture of normals representation of shrinkage priors, we make explicit connections between our method and kth order Gaussian Markov random field smoothing. We call the resulting processes shrinkage prior Markov random fields (SPMRFs). We use Hamiltonian Monte Carlo to approximate the posterior distribution of model parameters because this method provides superior performance in the presence of the high dimensionality and strong parameter correlations exhibited by our models. We compare the performance of three prior formulations using simulated data and find the horseshoe prior provides the best compromise between bias and precision. We apply SPMRF models to two benchmark data examples frequently used to test nonparametric methods. We find that this method is flexible enough to accommodate a variety of data generating models and offers the adaptive properties and computational tractability to make it a useful addition to the Bayesian nonparametric toolbox.Comment: 38 pages, to appear in Bayesian Analysi

GRAIN EXPORTS AS A SOURCE OF AGRICULTURAL INSTABILITY

International Relations/Trade,

Remote sensing and GIS analysis for demarcation of coastal hazard line along the highly eroding Krishna-Godavari delta front

Coastal regions, especially river deltas are highly resourceful and hence densely populated; but these extremely low-lying lands are vulnerable to rising sea levels due to global warming threatening the life and property in these regions. Recent IPCC (2013) predictions of 26-82cm global sea level rise are now considered conservative as subsequent investigations such as by Met Office, UK indicated a vertical rise of about 190cm, which would displace 10% of the world’s population living within 10 meters above the sea level. Therefore, predictive models showing the hazard line are necessary for efficient coastal zone management. Remote sensing and GIS technologies form the mainstay of such predictive models on coastal retreat and inundation to future sea-level rise. This study is an attempt to estimate the varying trends along the Krishna–Godavari (K–G) delta region. Detailed maps showing various coastal landforms in the K-G delta region were prepared using the IRS-P6 LISS 3 images. The rate of shoreline shift during a 31-year period along different sectors of the 330km long K-G delta coast was estimated using Landsat-2 and IRS-P6 LISS 3 images between 1977 and 2008. With reference to a selected baseline from along an inland position, End Point Rate (EPR), Shoreline Change Envelope (SCE) and Net Shoreline Movement (NSM) were calculated, using a GIS–based Digital Shoreline Analysis System (DSAS). The results showed that the shoreline migrated landward up to a maximum distance of 3.13km resulting in a net loss of about 42.10km2 area during this 31-year period. Further, considering the nature of landforms and EPR, the future hazard line is predicted for the area, which also indicated a net erosion of about 57.68km2 along the K-G delta coast by 2050 AD

Minimal Pati-Salam Model from String Theory Unification

We provide what we believe is the minimal three family ${\cal N} = 1$ SUSY and conformal Pati-Salam Model from type IIB superstring theory. This $Z_3$ orbifolded AdS$\otimes S^5$ model has long lived protons and has potential phenomenological consequences for LHC.Comment: 8 page

Environmental Impact on the Southeast Limb of the Cygnus Loop

We analyze observations from the Chandra X-ray Observatory of the southeast knot of the Cygnus Loop supernova remnant. In this region, the blast wave propagates through an inhomogeneous environment. Extrinsic differences and subsequent multiple projections along the line of sight rather than intrinsic shock variations, such as fluid instabilities, account for the apparent complexity of the images. Interactions between the supernova blast wave and density enhancements of a large interstellar cloud can produce the morphological and spectral characteristics. Most of the X-ray flux arises in such interactions, not in the diffuse interior of the supernova remnant. Additional observations at optical and radio wavelengths support this account of the existing interstellar medium and its role in shaping the Cygnus Loop, and they demonstrate that the southeast knot is not a small cloud that the blast wave has engulfed. These data are consistent with rapid equilibration of electron and ion temperatures behind the shock front, and the current blast wave velocity v_{bw} approx 330 km/s. Most of this area does not show strong evidence for non-equilibrium ionization conditions, which may be a consequence of the high densities of the bright emission regions.Comment: To appear in ApJ, April 1, 200

The Near Infrared and Multiwavelength Afterglow of GRB 000301c

We present near-infrared observations of the counterpart of GRB 000301c. The K' filter (2.1 micron) light curve shows a well-sampled break in the decay slope at t=3.5 days post-burst. The early time slope is very shallow (~ -0.1), while the late time slope is steep (-2.2). Comparison with the optical (R band) light curve shows marginally significant differences, especially in the early time decay slope (which is steeper in the optical) and the break time (which occurs later in the optical). This is contrary to the general expectation that light curve breaks should either be achromatic (e.g., for breaks due to collimation effects) or should occur later at longer wavelengths (for most other breaks). The observed color variations might be intrinsic to the afterglow, or might indicate systematic errors of > 0.08 magnitude in all fluxes. Even if the break is achromatic, we argue that its sharpness poses difficulties for explanations that depend on collimated ejecta. The R light curve shows further signs of fairly rapid variability (a bump, steep drop, and plateau) that are not apparent in the K' light curve. In addition, by combining the IR-optical-UV data with millimeter and radio fluxes, we are able to constrain the locations of the self-absorption break and cooling break and to infer the location of the spectral peak at t=3 days: f_nu = 3.4 mJy at nu=1e12 Hz. Using the multiwavelength spectral energy distribution, we are able to constrain the blast wave energy, which was E > 3e53 erg if the explosion was isotropic. This implies a maximum gamma ray production efficiency of ~ 0.15 for GRB 000301C.Comment: Accepted to The Astrophysical Journal. 24 pages, 4 figures, 3 tables; uses AASTeX 5 macros. This version includes a new figure (R-K' color vs. time), a better sampled R band light curve, and more extensive discussion of the optical data and error analysi