Bayesian adaptive estimation of arbitrary points on a psychometric function

Bayesian adaptive methods have been extensively used in psychophysics to estimate the point at which performance on a task attains arbitrary percentage levels, although the statistical properties of these estimators have never been assessed. We used simulation techniques to determine the small-sample properties of Bayesian estimators of arbitrary performance points, specifically addressing the issues of bias and precision as a function of the target percentage level. The study covered three major types of psychophysical task (yes-no detection, 2AFC discrimination and 2AFC detection) and explored the entire range of target performance levels allowed for by each task. Other factors included in the study were the form and parameters of the actual psychometric function Psi, the form and parameters of the model function M assumed in the Bayesian method, and the location of Psi within the parameter space. Our results indicate that Bayesian adaptive methods render unbiased estimators of any arbitrary point on psi only when M=Psi, and otherwise they yield bias whose magnitude can be considerable as the target level moves away from the midpoint of the range of Psi. The standard error of the estimator also increases as the target level approaches extreme values whether or not M=Psi. Contrary to widespread belief, neither the performance level at which bias is null nor that at which standard error is minimal can be predicted by the sweat factor. A closed-form expression nevertheless gives a reasonable fit to data describing the dependence of standard error on number of trials and target level, which allows determination of the number of trials that must be administered to obtain estimates with prescribed precision.

The impact of the air-fluorescence yield on the reconstructed shower parameters of ultra-high energy cosmic rays.

An accurate knowledge of the fluorescence yield and its dependence on atmospheric properties such as pressure, temperature or humidity is essential to obtain a reliable measurement of the primary energy of cosmic rays in experiments using the fluorescence technique. In this work, several sets of fluorescence yield data (i.e. absolute value and quenching parameters) are described and compared. A simple procedure to study the effect of the assumed fluorescence yield on the reconstructed shower parameters (energy and shower maximum depth) as a function of the primary features has been developed. As an application, the effect of water vapor and temperature dependence of the collisional cross section on the fluorescence yield and its impact on the reconstruction of primary energy and shower maximum depth has been studied. Published by Elsevier B.V.