Robust Bayes-Like Estimation: Rho-Bayes estimation

We consider the problem of estimating the joint distribution $P$ of $n$ independent random variables within the Bayes paradigm from a non-asymptotic point of view. Assuming that $P$ admits some density $s$ with respect to a given reference measure, we consider a density model $\overline S$ for $s$ that we endow with a prior distribution $\pi$ (with support $\overline S$) and we build a robust alternative to the classical Bayes posterior distribution which possesses similar concentration properties around $s$ whenever it belongs to the model $\overline S$. Furthermore, in density estimation, the Hellinger distance between the classical and the robust posterior distributions tends to 0, as the number of observations tends to infinity, under suitable assumptions on the model and the prior, provided that the model $\overline S$ contains the true density $s$. However, unlike what happens with the classical Bayes posterior distribution, we show that the concentration properties of this new posterior distribution are still preserved in the case of a misspecification of the model, that is when $s$ does not belong to $\overline S$ but is close enough to it with respect to the Hellinger distance.Comment: 68 page

Detecting Cage Crossing and Filling Clusters of Magnesium and Carbon Atoms in Zeolite SSZ-13 with Atom Probe Tomography

The conversion of methanol to valuable hydrocarbon molecules is of great commercial interest, as the process serves as a sustainable alternative for the production of, for instance, the base chemicals for plastics. The reaction is catalyzed by zeolite materials. By the introduction of magnesium as a cationic metal, the properties of the zeolite, and thereby the catalytic performance, are changed. With atom probe tomography (APT), nanoscale relations within zeolite materials can be revealed: i.e., crucial information for a fundamental mechanistic understanding. We show that magnesium forms clusters within the cages of zeolite SSZ-13, while the framework elements are homogeneously distributed. These clusters of just a few nanometers were analyzed and visualized in 3-D. Magnesium atoms seem to initially be directed to the aluminum sites, after which they aggregate and fill one or two cages in the zeolite SSZ-13 structure. The presence of magnesium in zeolite SSZ-13 increases the lifetime as well as the propylene selectivity. By using operando UV-vis spectroscopy and X-ray diffraction techniques, we are able to show that these findings are related to the suppression of aromatic intermediate products, while maintaining the formation of polyaromatic compounds. Further nanoscale analysis of the spent catalysts showed indications of magnesium redistribution after catalysis. Unlike zeolite H-SSZ-13, for which only a homogeneous distribution of carbon was found, carbon can be either homogeneously or heterogeneously distributed within zeolite Mg-SSZ-13 crystals as the magnesium decreases the coking rate. Carbon clusters were isolated, visualized, and analyzed and were assumed to be polyaromatic compounds. Small one-cage-filling polyaromatic compounds were identified; furthermore, large-cage-crossing aromatic molecules were found by isolating large coke clusters, demonstrating the unique coking mechanism in zeolite SSZ-13. Short-length-scale evidence for the formation of polyaromatic compounds at acid sites is discovered, as clear nanoscale relations between aluminum and carbon atoms exist

Schnakenburg's Dorpater Kalender für das Jahr 1889

http://www.ester.ee/record=b3577681*es

Detecting Cage Crossing and Filling Clusters of Magnesium and Carbon Atoms in Zeolite SSZ-13 with Atom Probe Tomography

The conversion of methanol to valuable hydrocarbon molecules is of great commercial interest, as the process serves as a sustainable alternative for the production of, for instance, the base chemicals for plastics. The reaction is catalyzed by zeolite materials. By the introduction of magnesium as a cationic metal, the properties of the zeolite, and thereby the catalytic performance, are changed. With atom probe tomography (APT), nanoscale relations within zeolite materials can be revealed: i.e., crucial information for a fundamental mechanistic understanding. We show that magnesium forms clusters within the cages of zeolite SSZ-13, while the framework elements are homogeneously distributed. These clusters of just a few nanometers were analyzed and visualized in 3-D. Magnesium atoms seem to initially be directed to the aluminum sites, after which they aggregate and fill one or two cages in the zeolite SSZ-13 structure. The presence of magnesium in zeolite SSZ-13 increases the lifetime as well as the propylene selectivity. By using operando UV-vis spectroscopy and X-ray diffraction techniques, we are able to show that these findings are related to the suppression of aromatic intermediate products, while maintaining the formation of polyaromatic compounds. Further nanoscale analysis of the spent catalysts showed indications of magnesium redistribution after catalysis. Unlike zeolite H-SSZ-13, for which only a homogeneous distribution of carbon was found, carbon can be either homogeneously or heterogeneously distributed within zeolite Mg-SSZ-13 crystals as the magnesium decreases the coking rate. Carbon clusters were isolated, visualized, and analyzed and were assumed to be polyaromatic compounds. Small one-cage-filling polyaromatic compounds were identified; furthermore, large-cage-crossing aromatic molecules were found by isolating large coke clusters, demonstrating the unique coking mechanism in zeolite SSZ-13. Short-length-scale evidence for the formation of polyaromatic compounds at acid sites is discovered, as clear nanoscale relations between aluminum and carbon atoms exist