Multiple regression of GRB luminosity on light-curve properties

Statistical relations between the luminosity L of gamma-ray burster (GRBs) and several of their other observable properties have been discovered. Four of these properties are considered here: the spectral lag; a measure of the light-curve variability; peak energy and the minimum light-curve rise time. Data are taken from a tabulation by Schaefer. Log–log regression of L on various combinations of the four light-curve properties, as well as redshift, is considered, using conventional multiple linear regression, and multiple errors-in-variables regression. Several cases are found in which the regression coefficients of more than one luminosity indicators are significant. In particular, the simultaneous regression of luminosity on peak energy, spectral lag, minimum rise time and redshift is meaningful.     

Recovering the real-space correlation function from photometric redshift surveys

Measurements of clustering in large-scale imaging surveys that make use of photometric redshifts depend on the uncertainties in the redshift determination. We have used light-cone simulations to show how the deprojection method successfully recovers the real-space correlation function when applied to mock photometric redshift surveys. We study how the errors in the redshift determination affect the quality of the recovered two-point correlation function. Considering the expected errors associated with the planned photometric redshift surveys, we conclude that this method provides information on the clustering of matter useful for the estimation of cosmological parameters that depend on the large-scale distribution of galaxies.     

Non-Gaussian distribution and clustering of hot and cold pixels in the five-year WMAP sky

We present measurements of the clustering of hot and cold patches in the microwave background sky as measured from the Wilkinson Microwave Anisotropy Probe 5-year data. These measurements are compared with theoretical predictions which assume that the cosmological signal obeys Gaussian statistics. We find significant differences from the simplest Gaussian-based prediction. However, the measurements are sensitive to the fact that the noise is spatially inhomogeneous (e.g. because different parts of the sky were observed for different lengths of time). We show how to account for this spatial inhomogeneity when making predictions. Differences from the Gaussian-based expectation remain even after this more careful accounting of the noise. In particular, we note that hot and cold pixels cluster differently within the same temperature thresholds at few-degree scales. While these findings may indicate primordial non-Gaussianity, we discuss other plausible explanations for these discrepancies. In addition, we find some deviations from Gaussianity at sub-degree scales, especially in the W band, whose origin may be associated with extragalactic dust emission.     

Fisher matrix decomposition for dark energy prediction

Within the context of constraining an expansion of the dark energy equation of state   w ( z ),  we show that the eigendecomposition of Fisher matrices is sensitive to both the maximum order of the expansion and the basis set choice. We investigate the Fisher matrix formalism in the case that a particular function is expanded in some basis set. As an example we show results for an all-sky weak lensing tomographic experiment. We show that the set of eigenfunctions is not unique and that the best constrained functions are only reproduced accurately at very higher order   N ≳ 100  , a top-hat basis set requires an even higher order. We show that the common approach used for finding the marginalized eigenfunction errors is sensitive to the choice of  non- w ( z )  parameters and priors. The eigendecomposition of Fisher matrices is a potentially useful tool that can be used to determine the predicted accuracy with which an experiment could constrain   w ( z )  . It also allows for the reconstruction of the redshift sensitivity of the experiment to changes in   w ( z )  . However, the technique is sensitive to both the order and the basis set choice. Publicly available code is available as part of icosmo at http://www.icosmo.org .     

Cosmological systematics beyond nuisance parameters: form-filling functions

In the absence of any compelling physical model, cosmological systematics are often misrepresented as statistical effects and the approach of marginalizing over extra nuisance systematic parameters is used to gauge the effect of the systematic. In this article, we argue that such an approach is risky at best since the key choice of function can have a large effect on the resultant cosmological errors.
As an alternative we present a functional form-filling technique in which an unknown, residual, systematic is treated as such. Since the underlying function is unknown, we evaluate the effect of every functional form allowed by the information available (either a hard boundary or some data). Using a simple toy model, we introduce the formalism of functional form filling. We show that parameter errors can be dramatically affected by the choice of function in the case of marginalizing over a systematic, but that in contrast the functional form-filling approach is independent of the choice of basis set.
We then apply the technique to cosmic shear shape measurement systematics and show that a shear calibration bias of  | m ( z )| ≲ 10⁻³ (1 + z )^0.7  is required for a future all-sky photometric survey to yield unbiased cosmological parameter constraints to per cent accuracy.
A module associated with the work in this paper is available through the open source icosmo code available at http://www.icosmo.org .