On the Estimation of Confidence Intervals for Binomial Population Proportions in Astronomy: The Simplicity and Superiority of the Bayesian Approach
TLDR
In this paper, a critical review of techniques for estimating confidence intervals on binomial population proportions inferred from success counts in small to intermediate samples is presented, revealing 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., matlab, mathematica, idl, python).Abstract:
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 estimation.read more
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References
More filters
Book
Bayesian Data Analysis
TL;DR: Detailed notes on Bayesian Computation Basics of Markov Chain Simulation, Regression Models, and Asymptotic Theorems are provided.
Journal ArticleDOI
The use of confidence or fiducial limits illustrated in the case of the binomial
C. J. Clopper,E. S. Pearson +1 more
Journal ArticleDOI
Approximate is Better than “Exact” for Interval Estimation of Binomial Proportions
Alan Agresti,Brent A. Coull +1 more
TL;DR: For example, this paper showed that using the adjusted Wald test with null rather than estimated standard error yields coverage probabilities close to nominal confidence levels, even for very small sample sizes, and that the 95% score interval has similar behavior as the adjusted-Wald interval obtained after adding two "successes" and two "failures" to the sample.
Journal ArticleDOI
Interval Estimation for a Binomial Proportion
TL;DR: In this paper, the problem of interval estimation of a binomial proportion is revisited, and a number of natural alternatives are presented, each with its motivation and con- text, each interval is examined for its coverage probability and its length.
Journal ArticleDOI
Confidence limits for small numbers of events in astrophysical data
TL;DR: The calculation of limits for small numbers of astronomical counts is based on standard equations derived from Poisson and binomial statistics; although the equations are straightforward, their direct use is cumbersome and involves both table-interpolations and several mathematical operations as discussed by the authors.
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