New Approaches To Photometric Redshift Prediction Via Gaussian Process Regression In The Sloan Digital Sky Survey

Expanding upon the work of Way and Srivastava 2006 we demonstrate how the use of training sets of comparable size continue to make Gaussian process regression (GPR) a competitive approach to that of neural networks and other least-squares fitting methods. This is possible via new large size matrix inversion techniques developed for Gaussian processes (GPs) that do not require that the kernel matrix be sparse. This development, combined with a neural-network kernel function appears to give superior results for this problem. Our best fit results for the Sloan Digital Sky Survey (SDSS) Main Galaxy Sample using u,g,r,i,z filters gives an rms error of 0.0201 while our results for the same filters in the luminous red galaxy sample yield 0.0220. We also demonstrate that there appears to be a minimum number of training-set galaxies needed to obtain the optimal fit when using our GPR rank-reduction methods. We find that morphological information included with many photometric surveys appears, for the most part, to make the photometric redshift evaluation slightly worse rather than better. This would indicate that most morphological information simply adds noise from the GP point of view in the data used herein. In addition, we show that cross-match catalog results involving combinations of the Two Micron All Sky Survey, SDSS, and Galaxy Evolution Explorer have to be evaluated in the context of the resulting cross-match magnitude and redshift distribution. Otherwise one may be misled into overly optimistic conclusions.Comment: 32 pages, ApJ in Press, 2 new figures, 1 new table of comparison methods, updated discussion, references and typos to reflect version in Pres

Structural Properties of Central Galaxies in Groups and Clusters

Using a representative sample of 911 central galaxies (CENs) from the SDSS DR4 group catalogue, we study how the structure of the most massive members in groups and clusters depend on (1) galaxy stellar mass (Mstar), (2) dark matter halo mass of the host group (Mhalo), and (3) their halo-centric position. We establish and thoroughly test a GALFIT-based pipeline to fit 2D Sersic models to SDSS data. We find that the fitting results are most sensitive to the background sky level determination and strongly recommend using the SDSS global value. We find that uncertainties in the background translate into a strong covariance between the total magnitude, half-light size (r50), and Sersic index (n), especially for bright/massive galaxies. We find that n depends strongly on Mstar for CENs, but only weakly or not at all on Mhalo. Less (more) massive CENs tend to be disk (spheroid)-like over the full Mhalo range. Likewise, there is a clear r50-Mstar relation for CENs, with separate slopes for disks and spheroids. When comparing CENs with satellite galaxies (SATs), we find that low mass (<10e10.75 Msun/h^2) SATs have larger median n than CENs of similar Mstar. Low mass, late-type SATs have moderately smaller r50 than late-type CENs of the same Mstar. However, we find no size differences between spheroid-like CENs and SATs, and no structural differences between CENs and SATs matched in both mass and colour. The similarity of massive SATs and CENs shows that this distinction has no significant impact on the structure of spheroids. We conclude that Mstar is the most fundamental property determining the basic structure of a galaxy. The lack of a clear n-Mhalo relation rules out a distinct group mass for producing spheroids, and the responsible morphological transformation processes must occur at the centres of groups spanning a wide range of masses. (abridged)Comment: 22 pages, 14 figures, submitted to MNRA

Moral Hazard and the Portfolio Management Problem.

This paper investigates the significance of nonlinear contracts on the incentive for portfolio managers to collect information. In addition, the manager must be motivated to disclose this information truthfully. The author analyzes three contracting regimes: (1) first-best where effort is observable, (2) linear with unobservable effort, and (3) the optimal contract within the Bhattacharya-Pfleiderer quadratic class. He finds that the linear contract leads to a serious lack of effort expenditure by the manager. This underinvestment problem can be successfully overcome through the use of quadratic contracts. These contracts are shown to be asymptotically optimal for very risk-tolerant principals. Copyright 1993 by American Finance Association.