arXiv subjects

I. Szapudi

Publications and source records attributed to I. Szapudi.

26 records · Page 2Linked to original sources

arXiv2003

Physical Evidence for Dark Energy

We present measurements of the angular cross-correlation between luminous red galaxies from the Sloan Digital Sky Survey and the cosmic microwave background temperature maps from the Wilkinson Microwave Anisotropy Probe. We find a statistically significant achromatic positive correlation between these two data sets, which is consistent with the expected signal from the late Integrated Sachs-Wolfe (ISW) effect. We do not detect any anti-correlation on small angular scales as would be produced from a large Sunyaev-Zel'dovich (SZ) effect, although we do see evidence for some SZ effect for our highest redshift samples. Assuming a flat universe, our preliminary detection of the ISW effect provides independent physical evidence for the existence of dark energy.

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arXiv2001

Computational AstroStatistics: Fast and Efficient Tools for Analysing Huge Astronomical Data Sources

I present here a review of past and present multi-disciplinary research of the Pittsburgh Computational AstroStatistics (PiCA) group. This group is dedicated to developing fast and efficient statistical algorithms for analysing huge astronomical data sources. I begin with a short review of multi-resolutional kd-trees which are the building blocks for many of our algorithms. For example, quick range queries and fast n-point correlation functions. I will present new results from the use of Mixture Models (Connolly et al. 2000) in density estimation of multi-color data from the Sloan Digital Sky Survey (SDSS). Specifically, the selection of quasars and the automated identification of X-ray sources. I will also present a brief overview of the False Discovery Rate (FDR) procedure (Miller et al. 2001a) and show how it has been used in the detection of ``Baryon Wiggles'' in the local galaxy power spectrum and source identification in radio data. Finally, I will look forward to new research on an automated Bayes Network anomaly detector and the possible use of the Locally Linear Embedding algorithm (LLE; Roweis & Saul 2000) for spectral classification of SDSS spectra.

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arXiv2001

Fast Clustering Analysis of Inhomogeneous Megapixel CMB maps

Szapudi et al (2001) introduced the method of estimating angular power spectrum of the CMB sky via heuristically weighted correlation functions. Part of the new technique is that all (co)variances are evaluated by massive Monte Carlo simulations, therefore a fast way to measure correlation functions in a high resolution map is essential. This letter presents a new algorithm to calculate pixel space correlation functions via fast spherical harmonics transforms. Our present implementation of the idea extracts correlations from a MAP-like CMB map (HEALPix resolution of 512, i.e. $ \simeq 3 \times 10^6$ pixels) in about 5 minutes on a 500MHz computer, including $C_\ell$ inversion; the analysis of one Planck-like map takes less then one hour. We use heuristic window and noise weighting in pixel space, and include the possibility of additional signal weighting as well, either in $\ell$ or pixel space. We apply the new code to an ensemble of MAP simulations, to test the response of our method to the inhomogenous sky coverage/noise of MAP. We show that the resulting $C_\ell$'s are very close to the theoretical expectations. The HEALPix based implementation of the method, SpICE (Spatially Inhomogenous Correlation Estimator) will be available to the public from the authors.

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arXiv2000

SDSS-RASS: Next Generation of Cluster-Finding Algorithms

We outline here the next generation of cluster-finding algorithms. We show how advances in Computer Science and Statistics have helped develop robust, fast algorithms for finding clusters of galaxies in large multi-dimensional astronomical databases like the Sloan Digital Sky Survey (SDSS). Specifically, this paper presents four new advances: (1) A new semi-parametric algorithm - nicknamed ``C4'' - for jointly finding clusters of galaxies in the SDSS and ROSAT All-Sky Survey databases; (2) The introduction of the False Discovery Rate into Astronomy; (3) The role of kernel shape in optimizing cluster detection; (4) A new determination of the X-ray Cluster Luminosity Function which has bearing on the existence of a ``deficit'' of high redshift, high luminosity clusters. This research is part of our ``Computational AstroStatistics'' collaboration (see Nichol et al. 2000) and the algorithms and techniques discussed herein will form part of the ``Virtual Observatory'' analysis toolkit.

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arXiv2000

Cosmic Statistics of Statistics: N-point Correlations

The fully general calculation of the cosmic error on N-point correlation functions and related quantities is presented. More precisely, the variance caused by the finite volume, discreteness, and edge effects is determined for {\em any} estimator which is based on a general function of N-tuples, such as multi-point correlation functions and multi-spectra. The results are printed explicitly for the two-point correlation function (or power-spectrum), and for the three-point correlation (or bispectrum). These are the most popular statistics in the study of large scale structure, yet, the a general calculation of their variance has not been performed until now.

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arXiv1999

Cosmic Statistics of Statistics

The errors on statistics measured in finite galaxy catalogs are exhaustively investigated. The theory of errors on factorial moments by Szapudi & Colombi (1996) is applied to cumulants via a series expansion method. All results are subsequently extended to the weakly non-linear regime. Together with previous investigations this yields an analytic theory of the errors for moments and connected moments of counts in cells from highly nonlinear to weakly nonlinear scales. The final analytic formulae representing the full theory are explicit but somewhat complicated. Therefore as a companion to this paper we supply a FORTRAN program capable of calculating the described quantities numerically (abridged).

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arXiv1998

The Cosmic Distribution of Clustering

For a given statistic, A, the cosmic distribution function, Upsilon(VA), is the probability of measuring a value VA in a finite galaxy catalog. For statistics related to count-in-cells, such as factorial moments, F_k, the average correlation function, xiav, and cumulants, S_N, the functions Upsilon(VF_k), Upsilon(Vxiav), and Upsilon(VS_N) were measured in a large tauCDM simulation. This N-body experiment simulates almost the full ``Hubble Volume'' of the universe, thus, for the first time, it allowed for an accurate analysis of the cosmic distribution function, and, in particular, of its variance (Delta A)^2, the cosmic error. The resulting detailed knowledge about the shape of Upsilon is crucial for likelihood analyses. The measured cosmic error agrees remarkably well with the theoretical predictions of Szapudi & Colombi (1996) and Szapudi, Bernardeau & Colombi (1998) in the weakly non-linear regime, while the predictions are slightly above the measurements in the highly nonlinear regime. When the relative cosmic error is small, (Delta A/A)^2, function Upsilon is nearly Gaussian. When (Delta A/A)^2 approaches unity or is larger, function Upsilon(VA) is increasingly skewed and well approximated by a lognormal distribution for A=F_k, or A=xiav. The measured cumulants follow accurately the perturbation theory predictions in the weakly nonlinear regime. Extended perturbation theory is an excellent approximation for all the available dynamic range.

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arXiv1997

Effects of Sampling on Statistics of Large Scale Structure

The effects of sampling are investigated on measurements of counts-in-cells in three-dimensional magnitude limited galaxy surveys, with emphasis on moments of the underlying smooth galaxy density field convolved with a spherical window. A new estimator is proposed for measuring the k-th order moment < rho^k >: the weighted factorial moment F_k[w], corrected for the effects of the varying selection function. The cosmic error on the measurement of F_k[w] is computed via the the formalism of Szapudi & Colombi (1996), which is generalized to include selection effects. The integral equation for finding the minimum variance weight is solved numerically, and an intuitive analytical approximation is derived. The resulting estimator is more accurate than the traditional method of counts-in-cells in volume limited samples, which discards useful information. As a practical example we consider the case of the future Sloan Digital Sky Survey. Optimal (sparse) sampling strategies for designing magnitude limited redshift surveys are investigated as well. It is found that the optimal strategy depends greatly on the statistics and scales considered. Finally we consider the issue of designing the geometry of a catalog, when it covers only a small fraction of the sky.

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