Application of the Iterated Weighted Least-Squares Fit to counting experiments

Least-squares fits are an important tool in many data analysis applications. In this paper, we review theoretical results, which are relevant for their application to data from counting experiments. Using a simple example, we illustrate the well known fact that commonly used variants of the least-squares fit applied to Poisson-distributed data produce biased estimates. The bias can be overcome with an iterated weighted least-squares method, which produces results identical to the maximum-likelihood method. For linear models, the iterated weighted least-squares method converges faster than the equivalent maximum-likelihood method, and does not require problem-specific starting values, which may be a practical advantage. The equivalence of both methods also holds for binomially distributed data. We further show that the unbinned maximum-likelihood method can be derived as a limiting case of the iterated least-squares fit when the bin width goes to zero, which demonstrates a deep connection between the two methods.Comment: Accepted by NIM

The Incompleteness of the Economy and Business: A Forceful Reminder

Many different but related arguments developed in the Caritas in Veritate converge on one central, yet not clearly stated, conclusion or thesis: economic and business activities are ‘incomplete'. This article will explore the above-mentioned ‘incompleteness' thesis or argument from three different perspectives: the role, the practice and the purpose of economic and business activities in contemporary societies. In doing so, the paper will heavily draw on questions and, still not fully learned, lessons derived from the present financial and economic crisis. Caritas in Veritate provides an appealing moral framework in which many of these lessons take a deeper sense and a more comprehensive meaning. The notion of ‘incompleteness' is applied here to economic and business theory and practice in the sense derived from Gödel's theorems. They state in terms of logical and mathematical demonstrations that no system of axiomatic statements can provide a proof of its own consistency. Such a proof requires the use of statements belonging to another (higher) level system. In the case of economics or business theory and practice these ‘higher level' statements are value judgments. By stressing the importance of ethics and moral philosophy for daily life, Caritas in Veritate strongly reminds us that neither economy nor business are self-sufficient either in organisational and social, practical or moral term

A likelihood method to cross-calibrate air-shower detectors

We present a detailed statistical treatment of the energy calibration of hybrid air-shower detectors, which combine a surface detector array and a fluorescence detector, to obtain an unbiased estimate of the calibration curve. The special features of calibration data from air showers prevent unbiased results, if a standard least-squares fit is applied to the problem. We develop a general maximum-likelihood approach, based on the detailed statistical model, to solve the problem. Our approach was developed for the Pierre Auger Observatory, but the applied principles are general and can be transferred to other air-shower experiments, even to the cross-calibration of other observables. Since our general likelihood function is expensive to compute, we derive two approximations with significantly smaller computational cost. In the recent years both have been used to calibrate data of the Pierre Auger Observatory. We demonstrate that these approximations introduce negligible bias when they are applied to simulated toy experiments, which mimic realistic experimental conditions.Comment: 10 pages, 7 figure

Effects of Microbial DNA on Human Forensic DNA Profiles

poster abstractMost biological evidence obtained from crimes scenes is found in non-sterile environments, and therefore there is an opportunity for the forensic samples to become contaminated with environmental DNA. In particular, the effects of microbial species that may contaminate forensic samples have not been extensively studied. This type of information could be especially important in cases where decomposition has occurred and microbes are in abundance. We investigated the environmental effects on DNA samples via contamination from microbial sources by intentionally spiking human DNA samples with known concentrations of DNA from 17 common microbe species associated with human decomposition. Quantitation and amplification was performed using the Quantifiler® Human DNA quantitation kit (Thermo Fisher Scientific, Inc.) and PowerPlex® 16 HS system (Promega Corp.), respectively. Single species of microbial DNA were added in varying quantities (1, 50, 100 ng) to a standard 1 ng human DNA sample. Results indicate that there was little to no effect on quantitation of the human DNA samples. However during genotyping, two species, Bacillus subtilis and Mycobacterium smegmatis, produced an artifact peak at the TPOX locus. The same artifact was still amplified when the DNA of the two species was tested in the absence of human DNA. This type of data will impact the forensic community as it demonstrates that microbial contamination may affect the development and interpretation of a human DNA profile. As most forensic genotyping kits are developed to be human specific, these results indicate that caution should still be used in interpreting the human DNA profile, especially in cases of decomposition in which there would be higher levels of microbial contamination

Perspektiven der Europäischen Sicherheits- und Verteidigungspolitik

Mit der Entscheidung, die Aufgaben der Krisenbewältigung in die eigene Hand zu nehmen, erschließt die EU ein ganz neues Feld der Zusammenarbeit und hat dadurch bereits jetzt die Machtkonstellation in Europa und gegenüber den transatlantischen Partnern verändert. Doch noch sind viele Fragen offen, die Zielsetzungen teilweise gar widersprüchlich: Wie könnte eine mögliche Arbeitsteilung zwischen NATO und ESVP aussehen? Sollte sich die EU auf Krisenbewältigung beschränken oder auch die Verantwortung für die kollektive Verteidigung ihrer Außengrenzen übernehmen und auf welche Bedrohungsszenarien muss sich Europa in diesem Zusammenhang einstellen? Wie sollen die Anteile von zivilen und militärischen Instrumenten gewichtet sein? Wie lässt sich das Spannungsverhältnis zwischen regionalen und globalen Prinzipien nicht zuletzt gegenüber den Vereinten Nationen, wie das zwischen Legitimität und Effektivität innerhalb der Gemeinschaft auflösen? Diesen Fragen und den sich daraus ergebenden Interessenkonflikten innerhalb Europas und des transatlantischen Bündnisses geht der Autor nach, zeigt Entwicklungspotentiale auf und plädiert für eine angemessene, aber bescheidene Rolle der Europäischen Sicherheits- und Verteidigungspolitik: So sollte die EU nicht den Anspruch erheben, Weltmacht zu werden

Potential for measuring the longitudinal and lateral profile of muons in TeV air showers with IACTs

Muons are copiously produced within hadronic extensive air showers (EAS) occurring in the Earth's atmosphere, and are used by particle air shower detectors as a means of identifying the primary cosmic ray which initiated the EAS. Imaging Atmospheric Cherenkov Telescopes (IACTs), designed for the detection of gamma-ray initiated EAS for the purposes of Very High Energy (VHE) gamma-ray astronomy, are subject to a considerable background signal due to hadronic EAS. Although hadronic EAS are typically rejected for gamma-ray analysis purposes, single muons produced within such showers generate clearly identifiable signals in IACTs and muon images are routinely retained and used for calibration purposes. For IACT arrays operating with a stereoscopic trigger, when a muon triggers one telescope, other telescopes in IACT arrays usually detect the associated hadronic EAS. We demonstrate for the first time the potential of IACT arrays for competitive measurements of the muon content of air showers, their lateral distribution and longitudinal profile of production slant heights in the TeV energy range. Such information can provide useful input to hadronic interaction models.Comment: 15 pages, 11 figures, 2 tables, accepted for publication in Astroparticle Physic