Bayesian inverse problems with Gaussian priors

The posterior distribution in a nonparametric inverse problem is shown to contract to the true parameter at a rate that depends on the smoothness of the parameter, and the smoothness and scale of the prior. Correct combinations of these characteristics lead to the minimax rate. The frequentist coverage of credible sets is shown to depend on the combination of prior and true parameter, with smoother priors leading to zero coverage and rougher priors to conservative coverage. In the latter case credible sets are of the correct order of magnitude. The results are numerically illustrated by the problem of recovering a function from observation of a noisy version of its primitive.Comment: Published in at http://dx.doi.org/10.1214/11-AOS920 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

When Thinking Impairs Sleep : Trait, Daytime and Nighttime Repetitive Thinking in Insomnia

We like to thank Dorien van Baar, Lisette van Breen, Rachel Renet, Marlene Stone, Britt van Hest, and Noraly Dekkers for their help with the data acquisition.Peer reviewedPublisher PD

Niobium-based superconducting nano-devices fabrication using all-metal suspended masks

We report a novel method for the fabrication of superconducting nanodevices based on niobium. The well-known difficulties of lithographic patterning of high-quality niobium are overcome by replacing the usual organic resist mask by a metallic one. The quality of the fabrication procedure is demonstrated by the realization and characterization of long and narrow superconducting lines and niobium-gold-niobium proximity SQUIDs

Praktijkproeven blauwalgenbestrijding in Noord-Brabant

Overlast door blauwalgenbloei is een hardnekkig en veel voorkomend waterkwaliteitsprobleem. Het is niet alleen hinderlijk omdat het vaak in de woonomgeving of in zwemplassen voorkomt, maar er zijn ook risico’s voor dier- en volksgezondheid aan verbonden. Structurele bestrijding van blauwalgen blijkt in de praktijk een lastige opgave. Veel van de uitgevoerde bestrijdingsmaatregelen blijken onvoldoende effect te sorteren. Om de kennis van de effectiviteit, mogelijke neveneffecten en kosten van kansrijke maatregelen te vergroten, worden in Noord-Brabant praktijkproeven uitgevoerd. Maatregelen die worden onderzocht, zijn onder andere de recent beschikbaar gekomen Flock en Lock-methodiek, baggeren en actief biologisch beheer. De maatregelen worden in verschillende combinaties toegepast. De uitvoering van de eerste maatregelen begon in mei 2009. Het project loopt dit jaar in ieder geval door. In het onderzoek werken de Wageningen Universiteit, de waterschappen Brabantse Delta, Aa en Maas en De Dommel en STOWA same

Bayesian recovery of the initial condition for the heat equation

We study a Bayesian approach to recovering the initial condition for the heat equation from noisy observations of the solution at a later time. We consider a class of prior distributions indexed by a parameter quantifying "smoothness" and show that the corresponding posterior distributions contract around the true parameter at a rate that depends on the smoothness of the true initial condition and the smoothness and scale of the prior. Correct combinations of these characteristics lead to the optimal minimax rate. One type of priors leads to a rate-adaptive Bayesian procedure. The frequentist coverage of credible sets is shown to depend on the combination of the prior and true parameter as well, with smoother priors leading to zero coverage and rougher priors to (extremely) conservative results. In the latter case credible sets are much larger than frequentist confidence sets, in that the ratio of diameters diverges to infinity. The results are numerically illustrated by a simulated data example.Comment: 17 pages, 4 figures. Published in Comm. Statist. Theory Methods. This version differs from the original in pagination and typographic detail. arXiv admin note: text overlap with arXiv:1103.269