A geometric characterization of cc-optimal designs for heteroscedastic regression

We consider the common nonlinear regression model where the variance, as well as the mean, is a parametric function of the explanatory variables. The $c$-optimal design problem is investigated in the case when the parameters of both the mean and the variance function are of interest. A geometric characterization of $c$-optimal designs in this context is presented, which generalizes the classical result of Elfving [Ann. Math. Statist. 23 (1952) 255--262] for $c$-optimal designs. As in Elfving's famous characterization, $c$-optimal designs can be described as representations of boundary points of a convex set. However, in the case where there appear parameters of interest in the variance, the structure of the Elfving set is different. Roughly speaking, the Elfving set corresponding to a heteroscedastic regression model is the convex hull of a set of ellipsoids induced by the underlying model and indexed by the design space. The $c$-optimal designs are characterized as representations of the points where the line in direction of the vector $c$ intersects the boundary of the new Elfving set. The theory is illustrated in several examples including pharmacokinetic models with random effects.Comment: Published in at http://dx.doi.org/10.1214/09-AOS708 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

A geometric characterization of c-optimal designs for heteroscedastic regression

We consider the common nonlinear regression model where the variance as well as the mean is a parametric function of the explanatory variables. The c-optimal design problem is investigated in the case when the parameters of both the mean and the variance function are of interest. A geometric characterization of c-optimal designs in this context is presented, which generalizes the classical result of Elfving (1952) for c-optimal designs. As in Elfving's famous characterization c-optimal designs can be described as representations of boundary points of a convex set. However, in the case where there appear parameters of interest in the variance, the structure of the Elfving set is different. Roughly speaking the Elfving set corresponding to a heteroscedastic regression model is the convex hull of a set of ellipsoids induced by the underlying model and indexed by the design space. The c-optimal designs are characterized as representations of the points where the line in direction of the vector c intersects the boundary of the new Elfving set. The theory is illustrated in several examples including pharmacokinetic models with random effects. --c-optimal design,heteroscedastic regression,Elfving's theorem,pharmacokinetic models,random effects,locally optimal design,geometric characterization

Optimal designs for random effect models with correlated errors with applications in population pharmacokinetics

We consider the problem of constructing optimal designs for population pharmacokinetics which use random effect models. It is common practice in the design of experiments in such studies to assume uncorrelated errors for each subject. In the present paper a new approach is introduced to determine efficient designs for nonlinear least squares estimation which addresses the problem of correlation between observations corresponding to the same subject. We use asymptotic arguments to derive optimal design densities, and the designs for finite sample sizes are constructed from the quantiles of the corresponding optimal distribution function. It is demonstrated that compared to the optimal exact designs, whose determination is a hard numerical problem, these designs are very efficient. Alternatively, the designs derived from asymptotic theory could be used as starting designs for the numerical computation of exact optimal designs. Several examples of linear and nonlinear models are presented in order to illustrate the methodology. In particular, it is demonstrated that naively chosen equally spaced designs may lead to less accurate estimation.Comment: Published in at http://dx.doi.org/10.1214/09-AOAS324 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Removing sky contributions from SCUBA data

The Submillimetre Common-User Bolometer Array (SCUBA) is a new continuum camera operating on the James Clerk Maxwell Telescope (JCMT) on Mauna Kea, Hawaii. It consists of two arrays of bolometric detectors; a 91 pixel 350/450 micron array and a 37 pixel 750/850 micron array. Both arrays can be used simultaneously and have a field-of-view of approximately 2.4 arcminutes in diameter on the sky. Ideally, performance should be limited solely by the photon noise from the sky background at all wavelengths of operation. However, observations at submillimetre wavelengths are hampered by ``sky-noise'' which is caused by spatial and temporal fluctuations in the emissivity of the atmosphere above the telescope. These variations occur in atmospheric cells that are larger than the array diameter, and so it is expected that the resultant noise will be correlated across the array and, possibly, at different wavelengths. In this paper we describe our initial investigations into the presence of sky-noise for all the SCUBA observing modes, and explain our current technique for removing it from the data.Comment: 11 pages, 16 figures, Proc SPIE vol 335

Extinction correction and on-sky calibration of SCUBA-2

Commissioning of SCUBA-2 included a program of skydips and observations of calibration sources intended to be folded into regular observing as standard methods of source flux calibration and to monitor the atmospheric opacity and stability. During commissioning, it was found that these methods could also be utilised to characterise the fundamental instrument response to sky noise and astronomical signals. Novel techniques for analysing on-sky performance and atmospheric conditions are presented, along with results from the calibration observations and skydips.Comment: 10 pages, 7 figure

Efficient algorithms for calculating optimal designs in pharmacokinetics and dose finding studies

Random effects models are widely used in population pharmacokinetics and dose finding studies. In such models the presence of correlated observations (due to shared random effects and possibly residual serial correlation) usually makes the explicit determination of optimal designs diffcult. In this paper we develop a class of multiplicative algorithms for the numerical calculation of optimal experimental designs in such situations. In particular we demonstrate its application in a concrete example of a cross-over dose finding trial. Additionally, we show that the methodology can be modified to determine optimal designs where there exist some requirements regarding the minimal number of treatments for several (in some cases all) experimental conditions. AMS Subject Classi cation: 62K0

Worlds Apart? Reassessing von Uexküll’s Umwelt in Embodied Cognition with Canguilhem, Merleau-Ponty, and Deleuze

Jakob von Uexküll’s (1864-1944) account of Umwelt has been proposed as a mediating concept to bridge the gap between ecological psychology’s realism about environmental information and enactivism’s emphasis on the organism’s active role in constructing the meaningful world it inhabits. If successful, this move would constitute a significant step towards establishing a single ecological-enactive framework for cognitive science. However, Uexküll’s thought itself contains different perspectives that are in tension with each other, and the concept of Umwelt is developed in representationalist terms that conflict with the commitments of both enactivism and ecological psychology. One central issue shared by all these approaches is the problem of how a living being experiences its environment. In this paper, we will look at Uexküll’s reception in French philosophy and highlight the different ways in which the concept of Umwelt functions in the work of Georges Canguilhem, Maurice Merleau-Ponty, and Gilles Deleuze. This analysis helps clarify different aspects of Uexküll’s thought and the deeper philosophical implications of importing his concepts into embodied cognitive science. This paper is part of a recent trend in which enactivism engages with continental philosophy in a way that both deepens and transcends the traditional links to phenomenology, including most recently the thought of Georg W. F. Hegel and Gilbert Simondon. However, no more than a brief outline and introduction to the potentials and challenges of this complex conceptual intersection can be given here. Our hope is that it serves to make more explicit the philosophical issues that are at stake for cognitive science in the question of experienced environments, while charting a useful course for future research

SCUBA - A submillimetre camera operating on the James Clerk Maxwell Telescope

The Submillimetre Common-User Bolometer Array (SCUBA) is one of a new generation of cameras designed to operate in the submillimetre waveband. The instrument has a wide wavelength range covering all the atmospheric transmission windows between 300 and 2000 microns. In the heart of the instrument are two arrays of bolometers optimised for the short (350/450 microns) and long (750/850 microns) wavelength ends of the submillimetre spectrum. The two arrays can be used simultaneously, giving a unique dual-wavelength capability, and have a 2.3 arc-minute field of view on the sky. Background-limited performance is achieved by cooling the arrays to below 100 mK. SCUBA has now been in active service for over a year, and has already made substantial breakthroughs in many areas of astronomy. In this paper we present an overview of the performance of SCUBA during the commissioning phase on the James Clerk Maxwell Telescope (JCMT).Comment: 14 pages, 13 figures (1 JPEG), Proc SPIE vol 335

A geometric characterization of c-optimal designs for regression models with correlated observations

We consider the problem of optimal design of experiments for random effects models, especially population models, where a small number of correlated observations can be taken on each individual, while the observations corresponding to different individuals can be assumed to be uncorrelated. We focus on c-optimal design problems and show that the classical equivalence theorem and the famous geometric characterization of Elfving (1952) from the case of uncorrelated data can be adapted to the problem of selecting optimal sets of observations for the n individual patients. The theory is demonstrated in a linear model with correlated observations and a nonlinear random effects population model, which is commonly used in pharmacokinetics

Bridging Opportunities in Human Health Services

The Campus to Community project aims to develop facilitated, in-depth site visits for VCU faculty and staff interested in exploring human health services opportunities in the Richmond community. The site visit experience will provide exposure to various community organizations specializing in human health, essentially creating a “bridge” between VCU’s campus and these facilities. This initiative is intended to motivate employees to action within the Richmond community by enabling them to observe first-hand the services that these organizations provide, learn more about the organizations’ missions, and engage in meaningful interactions with representatives on site. Likewise, it will allow Richmond community organizations to discuss unique needs and opportunities for partnerships with VCU