Criteria for Bayesian model choice with application to variable selection

In objective Bayesian model selection, no single criterion has emerged as dominant in defining objective prior distributions. Indeed, many criteria have been separately proposed and utilized to propose differing prior choices. We first formalize the most general and compelling of the various criteria that have been suggested, together with a new criterion. We then illustrate the potential of these criteria in determining objective model selection priors by considering their application to the problem of variable selection in normal linear models. This results in a new model selection objective prior with a number of compelling properties.Comment: Published in at http://dx.doi.org/10.1214/12-AOS1013 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

About the linearity of the color-magnitude relation of early-type galaxies in the Virgo cluster

We revisit the color-magnitude relation (CMR) of the Virgo cluster early-type galaxies in order to explore its alleged non-linearity. To this aim, we reanalyze the relation already published from data obtained within the ACS Virgo Cluster Survey of the Hubble Space Telescope, and perform our own photometry and analysis of the images of the 100 early-type galaxies observed as part of this survey. In addition, we compare our results with those reported in the literature from data of the Sloan Digital Sky Survey. We have found that when the brightest galaxies and untypical systems are excluded from the sample, a linear relation arises in agreement with what is observed in other groups and clusters. The central regions of the brightest galaxies also follow this relation. In addition, we notice that Virgo contains at least four compact elliptical galaxies besides the well known object VCC 1297 (NGC 4486B). Their locations in the -luminosity diagram define a different trend to that followed by normal early-type dwarf galaxies, setting an upper limit in effective surface brightness and a lower limit in effective radius for their luminosities. Based on the distribution of different galaxy sub-samples in the color-magnitude and -luminosity diagrams we draw some conclusions on their formation and the history of their evolution.Comment: 21 pages, 4 figures, 2 tables. Accepted for publication in Ap

Small Angle Polarization in High Energy P--P Scattering Through Nonperturbative Chiral Symmetry Breaking

We show that a large anomalous contribution due to nonperturbative instanton-like gluonic field configurations to the axial charge of the proton implies high-energy spin effects in $p-p$ elastic scattering. This is the same mechanism which is responsible for anomalous baryon number violation at high energy in the standard model. We compute the proton polarization due to these effects and we show that it is proportional to the center-of-mass scattering angle with a universal (energy-independent) slope of order unity.Comment: (13 pages, 2 figures

Topological Phases emerging from Spin-Orbital Physics

We study the evolution of spin-orbital correlations in an inhomogeneous quantum system with an impurity replacing a doublon by a holon orbital degree of freedom. Spin-orbital entanglement is large when spin correlations are antiferromagnetic, while for a ferromagnetic host we obtain a pure orbital description. In this regime the orbital model can be mapped on spinless fermions and we uncover topological phases with zero energy modes at the edge or at the domain between magnetically inequivalent regions.Comment: 6 pages, 5 figures, submitte

A reappraisal of postglacial decay times from Richmond Gulf and James Bay, Canada

Decay times inferred from relative sea-level (RSL) histories of previously glaciated regions provide a potentially important constraint on mantle rheology. We present a new compilation of RSL data from Richmond Gulf and James Bay, Canada. This recompilation reveals errors in previous compilations that led to inaccurate estimates for the Richmond Gulf decay time in a series of recently published articles. We derive updated estimates for the decay time at Richmond Gulf and James Bay using a methodology that incorporates errors in both the age and the height of the sea-level markers. This exercise is guided by a series of synthetic RSL calculations that show that decay time estimates in the region can be significantly biased if the RSL time-series are not corrected for global eustatic sea-level trends, or if the estimates are based on composite RSL histories derived by combining data from both the Richmond Gulf and the James Bay regions. Our decay time analysis for Richmond Gulf applies the pioneering approach of Walcott (1980) to a large database and we derive a value of 4.0-6.6 kyr, where the range is defined by a misfit tolerance 10 per cent higher than the minimum. Our analysis for James Bay is based on the uplift curve derived by Hardy (1976), and we estimate a decay time of about 2.0-2.8 kyr. The difference between our estimates for Richmond Gulf and James Bay may be due to errors in the observational record from these regions, but could also be influenced by lateral variations in lithospheric structure associated with the assembly of Laurentia