322 research outputs found
On the Estimation of Confidence Intervals for Binomial Population Proportions in Astronomy: The Simplicity and Superiority of the Bayesian Approach
I present a critical review of techniques for estimating confidence intervals on binomial population proportions inferred from success counts in small to intermediate samples. Population proportions arise frequently as quantities of interest in astronomical research; for instance, in studies aiming to constrain the bar fraction, active galactic nucleus fraction, supermassive black hole fraction, merger fraction, or red sequence fraction from counts of galaxies exhibiting distinct morphological features or stellar populations. However, two of the most widely-used techniques for estimating binomial confidence intervals — the ‘normal approximation' and the Clopper & Pearson approach — are liable to misrepresent the degree of statistical uncertainty present under sampling conditions routinely encountered in astronomical surveys, leading to an ineffective use of the experimental data (and, worse, an inefficient use of the resources expended in obtaining that data). Hence, I provide here an overview of the fundamentals of binomial statistics with two principal aims: (I) to reveal the ease with which (Bayesian) binomial confidence intervals with more satisfactory behaviour may be estimated from the quantiles of the beta distribution using modern mathematical software packages (e.g. r, matlab, mathematica, idl, python); and (ii) to demonstrate convincingly the major flaws of both the ‘normal approximation' and the Clopper & Pearson approach for error estimatio
The star cluster mass--galactocentric radius relation: Implications for cluster formation
Whether or not the initial star cluster mass function is established through
a universal, galactocentric-distance-independent stochastic process, on the
scales of individual galaxies, remains an unsolved problem. This debate has
recently gained new impetus through the publication of a study that concluded
that the maximum cluster mass in a given population is not solely determined by
size-of-sample effects. Here, we revisit the evidence in favor and against
stochastic cluster formation by examining the young ( a few yr-old) star cluster mass--galactocentric radius relation in M33, M51,
M83, and the Large Magellanic Cloud. To eliminate size-of-sample effects, we
first adopt radial bin sizes containing constant numbers of clusters, which we
use to quantify the radial distribution of the first- to fifth-ranked most
massive clusters using ordinary least-squares fitting. We supplement this
analysis with an application of quantile regression, a binless approach to
rank-based regression taking an absolute-value-distance penalty. Both methods
yield, within the to uncertainties, near-zero slopes in the
diagnostic plane, largely irrespective of the maximum age or minimum mass
imposed on our sample selection, or of the radial bin size adopted. We conclude
that, at least in our four well-studied sample galaxies, star cluster formation
does not necessarily require an environment-dependent cluster formation
scenario, which thus supports the notion of stochastic star cluster formation
as the dominant star cluster-formation process within a given galaxy.Comment: ApJ, in press, 39 pages in AAS preprint format, 10 multi-panel
figures (some reduced in size to match arXiv compilation routines
- …