Stein-type covariance identities: Klaassen, Papathanasiou and Olkin-Shepp type bounds for arbitrary target distributions

In this paper, we present a minimal formalism for Stein operators which leads to different probabilistic representations of solutions to Stein equations. These in turn provide a wide family of Stein-Covariance identities which we put to use for revisiting the very classical topic of bounding the variance of functionals of random variables. Applying the Cauchy-Schwarz inequality yields first order upper and lower Klaassen-type variance bounds. A probabilistic representation of Lagrange's identity (i.e. Cauchy-Schwarz with remainder) leads to Papathanasiou-type variance expansions of arbitrary order. A matrix Cauchy-Schwarz inequality leads to Olkin-Shepp type covariance bounds. All results hold for univariate target distribution under very weak assumptions (in particular they hold for continuous and discrete distributions alike). Many concrete illustrations are provided

Co-variation between stressful events and rumination predicts depressive symptoms : an eighteen months prospective design in undergraduates

Rumination is a maladaptive form of emotion regulation and seems to be the cognitive mechanism linking stress to depressive symptoms. However, it remains to be investigated whether individuals' variation in rumination in relation to the occurrence of stressful events (e.g., phasic co-variation between stressful events and rumination) prospectively predict the experience of depressive symptoms in lengthy follow-up moments. In this eighteen months prospective design, a large unselected sample of undergraduates was tested before, during, and after a period with prominent naturally occurring stressful events. The multilevel results show that the co-variation of stressful events and ruminative thinking predicts the experience of depressive symptoms at 3 and 15 months follow up moments, also when statistically controlling for baseline depressive symptoms. Moreover, the data demonstrate that the phasic elevations of rumination in relation to the occurrence of stressful events are more predictive of depressive symptoms compared with the stable aspects of rumination measured at one occasion. At the clinical level, the current findings seem to suggest a process-oriented intervention to target the phasic ruminative cognitions where individuals need to learn to control rumination exactly at moments of stress. (C) 2016 Elsevier Ltd. All rights reserved

Robust detection techniques for multivariate spatial data

Spatial data are characterized by statistical units, with known geographical positions, on which non spatial attributes are measured. Two types of atypical observations can be defined: global and/or local outliers. The attribute values of a global outlier are outlying with respect to the values taken by the majority of the data points while the attribute values of a local outlier are extreme when compared to those of its neighbors. Classical outlier detection techniques may be used to find global outliers as the geographical positions of the data is not taken into account in this search. The detection of local outliers is more complex especially when there are more than one non spatial attribute. In this poster, two new procedures for local outliers detection are defined. The first approach is to adapt an existing technique using in particular a regularized estimator of the covariance matrix. The second technique measures outlyingness using depth function

Time resolved spectroscopy of dust and gas from extrasolar planetesimals orbiting WD 1145+017

Multiple long and variable transits caused by dust from possibly disintegrating asteroids were detected in light curves of WD 1145+017. We present time-resolved spectroscopic observations of this target with QUCAM CCDs mounted in the Intermediate dispersion Spectrograph and Imaging System at the 4.2-m William Herschel Telescope in two different spectral arms: the blue arm covering 3800-4025 {\AA} and the red arm covering 7000-7430 {\AA}. When comparing individual transits in both arms, our observations show with 20 {\sigma} significance an evident colour difference between the in- and out-of-transit data of the order of 0.05-0.1 mag, where transits are deeper in the red arm. We also show with > 6 {\sigma} significance that spectral lines in the blue arm are shallower during transits than out-of-transit. For the circumstellar lines it also appears that during transits the reduction in absorption is larger on the red side of the spectral profiles. Our results confirm previous findings showing the u'-band excess and a decrease in line absorption during transits. Both can be explained by an opaque body blocking a fraction of the gas disc causing the absorption, implying that the absorbing gas is between the white dwarf and the transiting objects. Our results also demonstrate the capability of EMCCDs to perform high-quality time resolved spectroscopy of relatively faint targets.Comment: 9 pages, 5 figures. Accepted to MNRA