The determination of the true source polarization given a set of measurements is complicated by the requirement that the polarization always be positive. This positive bias also hinders construction of upper limits, uncertainties, and confidence regions, especially at low signal-to-noise levels. We generate the likelihood function for linear polarization measurements and use it to create confid...

I discuss a number of issues which arise when computing confidence limits by frequentist or Bayesian methods. I begin with a reminder why P(hypothesis data) cannot be determined if the only input is the ‘objective’ data. I then discuss confidence intervals, with emphasis on the ‘unified approach’ based on likelihood-ratio ordering, and related methods. A number of issues arise, including condit...

A novel way of defining limits in classical statistics is proposed. This is a natural extension of the original Neyman’s method, and has the desirable property that only information relevant to the problem is used in making statistical inferences. The result is a strong restriction on the allowed confidence bands, excluding in full generality pathologies as empty confidence regions or unstable ...

Confidence intervals have a long history and have become an indispensable tool in statistical applications. The computation of confidence intervals for a mean based on normal (large sample) theory is straightforward and readily available in the SAS system through such procedures as PROC ANOV A and PROC GLM. For the case of small samples and non-normal distributions, however, normal theory based...

Context. Synthesis models predict the integrated properties of stellar populations. Several problems exist in this field, mostly related to the fact that integrated properties are distributed. To date, this aspect has been either ignored (as in standard synthesis models, which are inherently deterministic) or interpreted phenomenologically (as in Monte Carlo simulations, which describe distribu...