The likelihood ratio test (LRT) and the related F-test, popularized in astrophysics by Eadie and coworkers in 1971, Bevington in 1969, Lampton, Margon, & Bowyer, in 1976, Cash in 1979, and Avni in 1978, do not (even asymptotically) adhere to their n …

Context: Identifying frequencies with low signal-to-noise ratios in time series of stellar photometry and spectroscopy, and measuring their amplitude ratios and peak widths accurately, are critical goals for asteroseismology. These are also challeng …

Detection of a periodic signal hidden in noise is frequently a goal in astronomical data analysis. This paper does not introduce a new detection technique, but instead studies the reliability and efficiency of detection with the most commonly used t …

We present evidence that the quasi-periodic oscillations (QPO) and very low frequency noise (VLFN) characteristic of many accretion sources are different aspects of the same physical process. We analyzed a long, high time resolution EXOSAT observati …

I describe a new time-domain algorithm for detecting localized structures (bursts), revealing pulse shapes, and generally characterizing intensity variations. The input is raw counting data, in any of three forms: time-tagged photon events (TTE), bi …

Statistical techniques suitable for the analysis of censored data, i.e., data containing both flux measurements and upper limits, are adapted to astronomical usage from the field of survival analysis, and are used in a statistical analysis of X-ray …

One-way analysis of variance (AoV) is recommended as a method for detection of sharp periodic signals. Application of the method requires folding and binning data with a trial period. Among several methods of this type employed in astronomy, AoV has …

Flicker of extragalactic sources was investigated by observing 14 flat and 20 steep spectrum sources at 1410 and 2380 MHz from the Arecibo Observatory on 20 successive days. The rms intensity variation of flat spectrum sources is, on average, higher …

We derive a period determination technique that is well suited to the case of nonsinusoidal time variation covered by only a few irregularly spaced observations. A detailed statistical analysis allows comparison with other techniques and indicates t …

Over the past 10 years Bayesian methods have rapidly grown more popular in many scientific disciplines as several computationally intensive statistical algorithms have become feasible with increased computer power. In this paper we begin with a gene …

Thanks to instrumental advances, new, very large kinematic data sets for nearby dwarf spheroidal (dSph) galaxies are on the horizon. A key aim of these data sets is to help determine the distribution of dark matter in these galaxies. Past analyses h …

A large number of observational parameters for the Rubin et al. sample of 60 spiral galaxies, ranging from Sa to Sc, have been compiled. A principal component analysis carried out on this sample shows that about 85 percent of the observational varia …

The Lomb-Scargle periodogram is a common tool in the frequency analysis of unequally spaced data equivalent to least-squares fitting of sine waves. We give an analytic solution for the generalisation to a full sine wave fit, including an offset and …