Modeling the variability of rankings

For better or for worse, rankings of institutions, such as universities, schools and hospitals, play an important role today in conveying information about relative performance. They inform policy decisions and budgets, and are often reported in the media. While overall rankings can vary markedly over relatively short time periods, it is not unusual to find that the ranks of a small number of "highly performing" institutions remain fixed, even when the data on which the rankings are based are extensively revised, and even when a large number of new institutions are added to the competition. In the present paper, we endeavor to model this phenomenon. In particular, we interpret as a random variable the value of the attribute on which the ranking should ideally be based. More precisely, if $p$ items are to be ranked then the true, but unobserved, attributes are taken to be values of $p$ independent and identically distributed variates. However, each attribute value is observed only with noise, and via a sample of size roughly equal to $n$, say. These noisy approximations to the true attributes are the quantities that are actually ranked. We show that, if the distribution of the true attributes is light-tailed (e.g., normal or exponential) then the number of institutions whose ranking is correct, even after recalculation using new data and even after many new institutions are added, is essentially fixed. Formally, $p$ is taken to be of order $n^C$ for any fixed $C>0$, and the number of institutions whose ranking is reliable depends very little on $p$.Comment: Published in at http://dx.doi.org/10.1214/10-AOS794 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Evaluation of Variability Concepts for Simulink in the Automotive Domain

Modeling variability in Matlab/Simulink becomes more and more important. We took the two variability modeling concepts already included in Matlab/Simulink and our own one and evaluated them to find out which one is suited best for modeling variability in the automotive domain. We conducted a controlled experiment with developers at Volkswagen AG to decide which concept is preferred by developers and if their preference aligns with measurable performance factors. We found out that all existing concepts are viable approaches and that the delta approach is both the preferred concept as well as the objectively most efficient one, which makes Delta-Simulink a good solution to model variability in the automotive domain.Comment: 10 pages, 7 figures, 6 tables, Proceedings of 48th Hawaii International Conference on System Sciences (HICSS), pp. 5373-5382, Kauai, Hawaii, USA, IEEE Computer Society, 201

Natural Variability in Projections of Climate Change Impacts on Fine Particulate Matter Pollution

Variations in meteorology associated with climate change can impact fine particulate matter (PM2.5) pollution by affecting natural emissions, atmospheric chemistry, and pollutant transport. However, substantial discrepancies exist among model-based projections of PM2.5 impacts driven by anthropogenic climate change. Natural variability can significantly contribute to the uncertainty in these estimates. Using a large ensemble of climate and atmospheric chemistry simulations, we evaluate the influence of natural variability on projections of climate change impacts on PM2.5 pollution in the United States. We find that natural variability in simulated PM2.5 can be comparable or larger than reported estimates of anthropogenic-induced climate impacts. Relative to mean concentrations, the variability in projected PM2.5 climate impacts can also exceed that of ozone impacts. Based on our projections, we recommend that analyses aiming to isolate the effect climate change on PM2.5 use 10 years or more of modeling to capture the internal variability in air quality and increase confidence that the anthropogenic-forced effect is differentiated from the noise introduced by natural variability. Projections at a regional scale or under greenhouse gas mitigation scenarios can require additional modeling to attribute impacts to climate change. Adequately considering natural variability can be an important step toward explaining the inconsistencies in estimates of climate-induced impacts on PM2.5. Improved treatment of natural variability through extended modeling lengths or initial condition ensembles can reduce uncertainty in air quality projections and improve assessments of climate policy risks and benefits

Gait variability: methods, modeling and meaning

The study of gait variability, the stride-to-stride fluctuations in walking, offers a complementary way of quantifying locomotion and its changes with aging and disease as well as a means of monitoring the effects of therapeutic interventions and rehabilitation. Previous work has suggested that measures of gait variability may be more closely related to falls, a serious consequence of many gait disorders, than are measures based on the mean values of other walking parameters. The Current JNER series presents nine reports on the results of recent investigations into gait variability. One novel method for collecting unconstrained, ambulatory data is reviewed, and a primer on analysis methods is presented along with a heuristic approach to summarizing variability measures. In addition, the first studies of gait variability in animal models of neurodegenerative disease are described, as is a mathematical model of human walking that characterizes certain complex (multifractal) features of the motor control's pattern generator. Another investigation demonstrates that, whereas both healthy older controls and patients with a higher-level gait disorder walk more slowly in reduced lighting, only the latter's stride variability increases. Studies of the effects of dual tasks suggest that the regulation of the stride-to-stride fluctuations in stride width and stride time may be influenced by attention loading and may require cognitive input. Finally, a report of gait variability in over 500 subjects, probably the largest study of this kind, suggests how step width variability may relate to fall risk. Together, these studies provide new insights into the factors that regulate the stride-to-stride fluctuations in walking and pave the way for expanded research into the control of gait and the practical application of measures of gait variability in the clinical setting