The Horseshoe Estimator: Posterior Concentration around Nearly Black Vectors

We consider the horseshoe estimator due to Carvalho, Polson and Scott (2010) for the multivariate normal mean model in the situation that the mean vector is sparse in the nearly black sense. We assume the frequentist framework where the data is generated according to a fixed mean vector. We show that if the number of nonzero parameters of the mean vector is known, the horseshoe estimator attains the minimax $\ell_2$ risk, possibly up to a multiplicative constant. We provide conditions under which the horseshoe estimator combined with an empirical Bayes estimate of the number of nonzero means still yields the minimax risk. We furthermore prove an upper bound on the rate of contraction of the posterior distribution around the horseshoe estimator, and a lower bound on the posterior variance. These bounds indicate that the posterior distribution of the horseshoe prior may be more informative than that of other one-component priors, including the Lasso.Comment: This version differs from the final published version in pagination and typographical detail; Available at http://projecteuclid.org/euclid.ejs/141813426

Horizontal activites. QLIF subproject 7: Horizontal activities

QLIF subproject 7 represents four horizontal activities common to the project, namely: • Environmental and sustainability audits • Cost-benefit analyses and socio-economic impact assessments • Dissemination and technology transfer • Training of graduate and postgraduate researchers Activities in the horizontal research have shown that organic crop production systems generally are more energy-efficient and have lower greenhouse gas emissions than the conventional production. In terms of dissemination the QLIF website has been central and the QLIF newsletter has attracted more than 1000 subscribers. Coupling of the website with the open access database Organic Eprints provides a prospective source of project information that can be accessed also by future stakeholders in organic and low-input systems. Training events arranged annually for students have contributed to proliferation of skills and knowledge gained in QLIF. Also, these events have served to mediate the attitude needed for research in organic and low-input farming

Direct control of the tunnel splitting in a one-electron double quantum dot

Quasi-static transport measurements are employed on a laterally defined tunnel-coupled double quantum dot. A nearby quantum point contact allows us to track the charge as added to the device. If charged with only up to one electron, the low-energy spectrum of the double quantum dot is characterized by its quantum mechanical interdot tunnel splitting. We directly measure its magnitude by utilizing particular anticrossing features in the stability diagram at finite source-drain bias. By modification of gate voltages defining the confinement potential as well as by variation of a perpendicular magnetic field we demonstrate the tunability of the coherent tunnel coupling.Comment: High resolution pdf file available at http://www2.nano.physik.uni-muenchen.de/~huettel/research/anticrossing.pd

BRDFs acquired by directional radiative measurements during EAGLE and AGRISAR

Radiation is the driving force for all processes and interactions between earth surface and atmosphere. The amount of measured radiation reflected by vegetation depends on its structure, the viewing angle and the solar angle. This angular dependence is usually expressed in the Bi-directional Reflectance Distribution Function (BRDF). This BRDF is not only different for different types of vegetation, but also different for different stages of the growth. The BRDF therefore has to be measured at ground level before any satellite imagery can be used the calculate surface-atmosphere interaction. The objective of this research is to acquire the BRDFs for agricultural crop types. A goniometric system is used to acquire the BRDFs. This is a mechanical device capable of a complete hemispherical rotation. The radiative directional measurements are performed with different sensors that can be attached to this system. The BRDFs are calculated from the measured radiation. In the periods 10 June - 18 June 2006 and 2 July - 10 July 2006 directional radiative measurements were performed at three sites: Speulderbos site, in the Netherlands, the Cabauw site, in the Netherlands, and an agricultural test site in Goermin, Germany. The measurements were performed over eight different crops: forest, grass, pine tree, corn, wheat, sugar beat and barley. The sensors covered the spectrum from the optical to the thermal domain. The measured radiance is used to calculate the BRDFs or directional thermal signature. This contribution describes the measurements and calculation of the BRDFs of forest, grassland, young corn, mature corn, wheat, sugar beat and barley during the EAGLE2006 and AGRISAR 2006 fieldcampaigns. Optical BRDF have been acquired for all crops except barley. Thermal angular signatures are acquired for all the crop