Confidence Intervals

PowerPoint slides for Confidence Intervals. Examples are taken from the Medical Literatur

The Power of Confidence Intervals

We consider the power to reject false values of the parameter in Frequentist methods for the calculation of confidence intervals. We connect the power with the physical significance (reliability) of confidence intervals for a parameter bounded to be non-negative. We show that the confidence intervals (upper limits) obtained with a (biased) method that near the boundary has large power in testing the parameter against larger alternatives and small power in testing the parameter against smaller alternatives are physically more significant. Considering the recently proposed methods with correct coverage, we show that the physical significance of upper limits is smallest in the Unified Approach and highest in the Maximum Likelihood Estimator method. We illustrate our arguments in the specific cases of a bounded Gaussian distribution and a Poisson distribution with known background.Comment: 13 pages, 5 figure

Frequentist confidence intervals for orbits

The problem of efficiently computing the orbital elements of a visual binary while still deriving confidence intervals with frequentist properties is treated. When formulated in terms of the Thiele-Innes elements, the known distribution of probability in Thiele-Innes space allows efficient grid-search plus Monte-Carlo-sampling schemes to be constructed for both the minimum-$\!\chi^{2}$ and Bayesian approaches to parameter estimation. Numerical experiments with $10^{4}$ independent realizations of an observed orbit confirm that the $1-$ and $2\sigma$ confidence and credibility intervals have coverage fractions close to their frequentist values. \keywords{binaries: visual - stars: fundamental parameters - methods:statistical}Comment: 7 pages, 2 figures. Minor changes. Accepted by Astronomy and Astrophysic

Confidence intervals for average success probabilities

We provide Buehler-optimal one-sided and some valid two-sided confidence intervals for the average success probability of a possibly inhomogeneous fixed length Bernoulli chain, based on the number of observed successes. Contrary to some claims in the literature, the one-sided Clopper-Pearson intervals for the homogeneous case are not completely robust here, not even if applied to hypergeometric estimation problems.Comment: Revised version for: Probability and Mathematical Statistics. Two remarks adde