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Pre-2010

Linear Regression for Astronomical Data with Measurement Errors and Intrinsic Scatter

Akritas, Michael G.; Bershady, Matthew A.

Two new methods are proposed for linear regression analysis for data with measurement errors. Both methods are designed to accommodate intrinsic scatter in addition to measurement errors. The first method is a direct extension of the ordinary least ...
A test for partial correlation with censored astronomical data

Akritas, M. G.; Siebert, J.

A new procedure is presented which allows, based on the Kendall tau-coefficient, one to test for partial correlation in the presence of censored data. Further, a significance level can be assigned to the partial correlation - an aspect which has not ...
Detecting non-sinusoidal periodicities in observational data using multiharmonic periodograms

Baluev, Roman V.

We address the problem of assessing the statistical significance of candidate periodicities found using the so-called `multiharmonic' periodogram, which is being used for detection of non-sinusoidal signals and is based on the least-squares fitting ...
Assessing the statistical significance of periodogram peaks

Baluev, R. V.

The least-squares (or Lomb-Scargle) periodogram is a powerful tool that is routinely used in many branches of astronomy to search for periodicities in observational data. The problem of assessing the statistical significance of candidate periodiciti ...
Data Mining and Machine Learning in Astronomy

Ball, Nicholas M.; Brunner, Robert J.

We review the current state of data mining and machine learning in astronomy. Data Mining can have a somewhat mixed connotation from the point of view of a researcher in this field. If used correctly, it can be a powerful approach, holding the poten ...
Random Forests: finding quasars

Breiman, Leo; Last, Michael; Rice, John

The automatic classification of objects from catalogues or other sources of data is a common statistical problem in many astronomical surveys. We describe an effective method, Random Forests, in which votes for class membership are polled from a lar ...
Frequency estimation and generalized Lomb-Scargle periodograms

Bretthorst, G. Larry

Using Bayesian probability theory we demonstrate that the Lomb-Scargle periodogram may be generalized in a straightforward manner to nonuniformly nonsimultaneously sampled quadrature data when the sinusoid has arbitrary amplitude modulation. This ge ...
Probabilistic Cross-Identification of Astronomical Sources

Budavári, Tamás; Szalay, Alexander S.

We present a general probabilistic formalism for cross-identifying astronomical point sources in multiple observations. Our Bayesian approach, symmetric in all observations, is the foundation of a unified framework for object matching, where not onl ...
A Unified Framework for Photometric Redshifts

Budavári, Tamás

We present a rigorous mathematical solution to photometric redshift estimation and the more general inversion problem. The challenge we address is to meaningfully constrain unknown properties of astronomical sources based on given observables, usual ...
Reliable eigenspectra for new generation surveys

Budavári, Tamás; Wild, Vivienne; Szalay, Alexander S.; Dobos, László; Yip, Ching-Wa

We present a novel technique to overcome the limitations of the applicability of principal component analysis to typical real-life data sets, especially astronomical spectra. Our new approach addresses the issues of outliers, missing information, la ...
Reliable eigenspectra for new generation surveys

Budavári, Tamás; Wild, Vivienne; Szalay, Alexander S.; Dobos, László; Yip, Ching-Wa

We present a novel technique to overcome the limitations of the applicability of principal component analysis to typical real-life data sets, especially astronomical spectra. Our new approach addresses the issues of outliers, missing information, la ...
Why isn't every physicist a Bayesian?

Cousins, Robert D.

Physicists embarking on seemingly routine error analyses are finding themselves grappling with major conceptual issues which have divided the statistics community for years. While the philosophical aspects of the debate may be endless, a practicing ...
Maximum-Likelihood Estimation of the Slope from Number-Flux Counts of Radio Sources

Crawford, David F.; Jauncey, David L.; Murdoch, Hugh S.

The application of the method of maximum likelihood (ML) to the determination of the slope of the number-flux-density distribution of radio sources is discussed. It is shown that the ML estimate of the slope, which uses the maximum available inform ...
A powerful test for weak periodic signals with unknown light curve shape in sparse data

de Jager, O. C.; Raubenheimer, B. C.; Swanepoel, J. W. H.

A problem with most tests for periodicity is that they are powerful enough to detect only certain kinds of periodic shapes (or 'light curves') in the case of weak signals. This causes a selection effect with the identification of weak periodic signa ...
Fourier Analysis with Unequally-Spaced Data

Deeming, T. J.

The general problems of Fourier and spectral analysis are discussed. A discrete Fourier transformF N (v) of a functionf(t) is presented which (i) is defined for arbitrary data spacing; (ii) is equal to the convolution of the true Fourier transform o ...
Fundamental properties of elliptical galaxies

Djorgovski, S.; Davis, Marc

The global properties of elliptical galaxies, such as luminosity, radius, projected velocity dispersion, projected luminosity, etc., form a two-dimensional family. This 'fundamental plane' of elliptical galaxies can be defined in observable terms by ...
A period-finding method for sparse randomly spaced observations of 'How long is a piece of string?'

Dworetsky, M. M.

A mathematical method for identifying the correct period of a variable star from a small number of unequally spaced observations is presented. Previous methods using Fourier-transform and least-squares techniques are reviewed. The true-string-length ...
Linear regression in astronomy. II

Feigelson, Eric D.; Babu, Gutti J.

A wide variety of least-squares linear regression procedures used in observational astronomy, particularly investigations of the cosmic distance scale, are presented and discussed. The classes of linear models considered are (1) unweighted regressio ...
Statistical methods for astronomical data with upper limits. I - Univariate distributions

Feigelson, E. D.; Nelson, P. I.

The authors discuss statistical techniques applicable when a portion of an object sample is not detected; i.e., when upper limits, or left-censored data, are present. An extensive field of statistics called "survival analysis" of "lifetime data" exi ...
Statistical methods for astronomical data with upper limits. II - Correlation and regression

Isobe, T.; Feigelson, E. D.; Nelson, P. I.

Statistical methods for calculating correlations and regressions in bivariate censored data where the dependent variable can have upper or lower limits are presented. Cox's regression and the generalization of Kendall's rank correlation coefficient ...