Measuring is more than assigning numbers

'Measurement is fundamental to research-related activities in social science (hence this Handbook). In my own field of education research, perhaps the most discussed element of education lies in test scores. Examination results are measurements, the number of students attaining a particular standard in a test is a measurement; indeed the standard of a test is a measurement. The allocation of places at school, college or university, student:teacher ratios, funding plans, school timetables, staff workloads, adult participation rates, and the stratification of educational outcomes by sex, social class, ethnicity or geography for example, are all based on measurements. Good and careful work has been done in all of these areas (Nuttall 1987). However, the concept of measurement itself remains under-examined, and is often treated in an uncritical way. In saying this I mean more than the usual lament about qualitative:quantitative schism or the supposed reluctance of social scientists to engage with numeric analysis (Gorard et al. 2004a). I mean that even where numeric analysis is being conducted, the emphasis is on collecting, collating, analysing, and reporting the kinds of data generated by measurement, with the process of measurement and the rigor of the measurement instrument being somewhat taken for granted by many commentators. Issues that are traditionally considered by social scientists include levels of measurement, reliability, validity, and the creation of complex indices (as illustrated in some of the chapters contained in this volume). But these matters are too often dealt with primarily as technical matters – such as how to assess reliability or which statistical test to use with which combination of levels of measurement. The process of quantification itself is just assumed'

Supporting User-Defined Functions on Uncertain Data

Uncertain data management has become crucial in many sensing and scientific applications. As user-defined functions (UDFs) become widely used in these applications, an important task is to capture result uncertainty for queries that evaluate UDFs on uncertain data. In this work, we provide a general framework for supporting UDFs on uncertain data. Specifically, we propose a learning approach based on Gaussian processes (GPs) to compute approximate output distributions of a UDF when evaluated on uncertain input, with guaranteed error bounds. We also devise an online algorithm to compute such output distributions, which employs a suite of optimizations to improve accuracy and performance. Our evaluation using both real-world and synthetic functions shows that our proposed GP approach can outperform the state-of-the-art sampling approach with up to two orders of magnitude improvement for a variety of UDFs. 1

Bayesian astrostatistics: a backward look to the future

This perspective chapter briefly surveys: (1) past growth in the use of Bayesian methods in astrophysics; (2) current misconceptions about both frequentist and Bayesian statistical inference that hinder wider adoption of Bayesian methods by astronomers; and (3) multilevel (hierarchical) Bayesian modeling as a major future direction for research in Bayesian astrostatistics, exemplified in part by presentations at the first ISI invited session on astrostatistics, commemorated in this volume. It closes with an intentionally provocative recommendation for astronomical survey data reporting, motivated by the multilevel Bayesian perspective on modeling cosmic populations: that astronomers cease producing catalogs of estimated fluxes and other source properties from surveys. Instead, summaries of likelihood functions (or marginal likelihood functions) for source properties should be reported (not posterior probability density functions), including nontrivial summaries (not simply upper limits) for candidate objects that do not pass traditional detection thresholds.Comment: 27 pp, 4 figures. A lightly revised version of a chapter in "Astrostatistical Challenges for the New Astronomy" (Joseph M. Hilbe, ed., Springer, New York, forthcoming in 2012), the inaugural volume for the Springer Series in Astrostatistics. Version 2 has minor clarifications and an additional referenc