GRS 1915+105 the first stellar-scale, highly relativistic jet source identified is a key system for our understanding of the disc-jet coupling in accreting black hole systems. Comprehending the coupling between inflow and outflow in this source not …

A method was developed for the detection and measurement of a periodic signal with unknown characteristics in a data set where the existence of such signal was not known. The method detects a signal by using Bayesian probability theory to compare a …

Five methods for obtaining linear regression fits to bivariate data with unknown or insignificant measurement errors are discussed: ordinary least-squares (OLS) regression of Y on X, OLS regression of X on Y, the bisector of the two OLS lines, ortho …

This paper discusses the theory and assumptions involved in the use of periodograms for seeking periodicities in astronomical time series. It is shown that previously derived formula for ‘false alarm’ probabilities severely underestimates the potent …

I describe a Bayesian method to account for measurement errors in linear regression of astronomical data. The method allows for heteroscedastic and possibly correlated measurement errors and intrinsic scatter in the regression relationship. The meth …

The application of autoregressive moving-average (ARMA) modelling to discrete time or indexed data is discussed. An essential tool is the autocorrelation function, and its utility is demonstrated with some examples. Extensions of the ARMA models to …

If X, which follows a power-law distribution, is observed subject to Gaussian measurement error e, then X + e is distributed as the convolution of the power-law and Gaussian distributions. Maximum-likelihood estimation of the parameters of the two d …

We study the statistical characteristics of a box-fitting algorithm to analyze stellar photometric time series in the search for periodic transits by extrasolar planets. The algorithm searches for signals characterized by a periodic alternation betw …

The Rayleigh test has been recently invoked as a method of searching a time series for periodic pulsations. In this paper, this technique is discussed and compared to epoch folding, a technique which has had widespread use in X-ray astronomy. It is …

Multiplicative random processes in (not necessarily equilibrium or steady state) stochastic systems with many degrees of freedom lead to Boltzmann distributions when the dynamics is expressed in terms of the logarithm of the elementary variables. In …

The statistical properties of least-squares frequency analysis of unequally spaced data are examined. It is shown that, in the least-squares spectrum of gaussian noise, the reduction in the sum of squares at a particular frequency is a chi2-squared …

An iterative technique is described for generating estimates to the solutions of rectification and deconvolution in statistical astronomy. The technique, which derives from Bayes’ Theorem on conditional probabilities, conserves the constraints on f …

We present a comprehensive statistical analysis of the properties of Type Ia supernova (SN Ia) light curves in the near-infrared using recent data from Peters Automated InfraRed Imaging TELescope and the literature. We construct a hierarchical Bayes …

Many objects studied in astronomy follow a power-law distribution function (DF), for example the masses of stars or star clusters. A still used method by which such data is analysed is to generate a histogram and fit a straight line to it. The param …

A multivariate analysis of gamma-ray burst (GRB) bulk properties is presented to discriminate between distinct classes of GRBs. Several variables representing burst duration, fluence, and spectral hardness are considered. Two multivariate clustering …

We use high-resolution N-body simulations to study the equilibrium density profiles of dark matter halos in hierarchically clustering universes. We find that all such profiles have the same shape, independent of the halo mass, the initial density fl …

When the probability of measuring a particular value of some quantity varies inversely as a power of that value, the quantity is said to follow a power law, also known variously as Zipf’s law or the Pareto distribution. Power laws appear widely in p …

A new, computationally and statistically efficient algorithm, the Fast χ2 algorithm (Fχ2), can find a periodic signal with harmonic content in irregularly sampled data with nonuniform errors. The algorithm calculates the minimized χ2 as a functio …

A commonly used measure to summarize the nature of a photon spectrum is the so-called hardness ratio, which compares the numbers of counts observed in different passbands. The hardness ratio is especially useful to distinguish between and categorize …

The Lomb-Scargle method performs spectral analysis on unevenly sampled data and is known to be a powerful way to find, and test the significance of, weak periodic signals. The method has previously been thought to be ‘slow’, requiring of order 10(2) …