Localization for MCMC: sampling high-dimensional posterior distributions with local structure

We investigate how ideas from covariance localization in numerical weather prediction can be used in Markov chain Monte Carlo (MCMC) sampling of high-dimensional posterior distributions arising in Bayesian inverse problems. To localize an inverse problem is to enforce an anticipated "local" structure by (i) neglecting small off-diagonal elements of the prior precision and covariance matrices; and (ii) restricting the influence of observations to their neighborhood. For linear problems we can specify the conditions under which posterior moments of the localized problem are close to those of the original problem. We explain physical interpretations of our assumptions about local structure and discuss the notion of high dimensionality in local problems, which is different from the usual notion of high dimensionality in function space MCMC. The Gibbs sampler is a natural choice of MCMC algorithm for localized inverse problems and we demonstrate that its convergence rate is independent of dimension for localized linear problems. Nonlinear problems can also be tackled efficiently by localization and, as a simple illustration of these ideas, we present a localized Metropolis-within-Gibbs sampler. Several linear and nonlinear numerical examples illustrate localization in the context of MCMC samplers for inverse problems.Comment: 33 pages, 5 figure

Diffeomorphic random sampling using optimal information transport

In this article we explore an algorithm for diffeomorphic random sampling of nonuniform probability distributions on Riemannian manifolds. The algorithm is based on optimal information transport (OIT)---an analogue of optimal mass transport (OMT). Our framework uses the deep geometric connections between the Fisher-Rao metric on the space of probability densities and the right-invariant information metric on the group of diffeomorphisms. The resulting sampling algorithm is a promising alternative to OMT, in particular as our formulation is semi-explicit, free of the nonlinear Monge--Ampere equation. Compared to Markov Chain Monte Carlo methods, we expect our algorithm to stand up well when a large number of samples from a low dimensional nonuniform distribution is needed.Comment: 8 pages, 3 figure

An approximate empirical Bayesian method for large-scale linear-Gaussian inverse problems

We study Bayesian inference methods for solving linear inverse problems, focusing on hierarchical formulations where the prior or the likelihood function depend on unspecified hyperparameters. In practice, these hyperparameters are often determined via an empirical Bayesian method that maximizes the marginal likelihood function, i.e., the probability density of the data conditional on the hyperparameters. Evaluating the marginal likelihood, however, is computationally challenging for large-scale problems. In this work, we present a method to approximately evaluate marginal likelihood functions, based on a low-rank approximation of the update from the prior covariance to the posterior covariance. We show that this approximation is optimal in a minimax sense. Moreover, we provide an efficient algorithm to implement the proposed method, based on a combination of the randomized SVD and a spectral approximation method to compute square roots of the prior covariance matrix. Several numerical examples demonstrate good performance of the proposed method

Nano-probing station incorporating MEMS probes for 1D device RF on-wafer characterization

International audienc

SUSCEPTIBILITY OF DESERT LOCUST, SCHISTOCERCA GREGARIA (ORTHOPTERA: ACRIDIDAE) TO BACILLUS CEREUS ISOLATED FROM EGYPT

Examination was done at preliminary bracketing bioassay on one old 4th nymphal instar of desert locust. Results showed that two isolates, namely NDL1 and NDL2 were having highly potentiality as entomopathogenic bioagents. Thirty isolates were isolated from dead/ infected nymphs of desert locust occurred in raring cages at Department of Locust and Grasshoppers Research, Plant Protection Research Institute, Agricultural Research Center, Dokki, Giza, Egypt. Molecular identification of isolated bacteria was done using universal primers of 16s rRNA, followed by DNA sequencing. Nucleotides were blasted at (https://www.ncbi. nlm.nih.gov /genbank/) to recognize that NDL1 and NDL2 isolates were two different isolates of Bacillus cereus with a high similarity (100%).  Susceptibility of 4th nymphal instar of Schistocerca gregaria (Forskal) to the isolated B. cereus was determined using two bioassay procedures, Leaf-dip and per os. The insecticidal activity of both isolates against locust nymph in leaf dipping showed that NDL2 was more efficient than NDL1. However, the opposite trend was observed in using per os.  Both Isolates have the potential to be a successful biocidal agent to control desert locust

Composición del aceite de la semilla del pistacho (Pistacia vera): efectos de la situación geográfica y de la variedad

This study was aimed at characterizing four Tunisian pistachio cultivations (Pistacia vera) from the Mateur (North), Nabeul (North-East), Kairouan (Middle) and Sfax (Middle- East) regions and two varieties, Mateur and Ohadi, considering fatty acid composition and main lipid class contents (polar lipids, diacylglycerols, triacylglycerols and free fatty acids) in ripe seeds. Lipid classes were separated using thin layer chromatography, and fatty acid methyl esters (FAMEs) were analyzed by gas chromatography. Oleic acid (C18:1 Δ9) was the major fatty acid for all samples; those of the Mateur region (the northern region) differed significantly with the lowest content in C18:1 (54.2 % of total fatty acids) and the highest in C18:2 (24.1 %). The total amount of fatty acids (TFA) in the seeds of Ohadi variety was significantly lower than that of the Mateur variety from the Sfax region. Triacylglycerols were most abundant in pistachio seeds from Nabeul (98.5% of total glycerolipids).Este estudio tiene como objetivo caracterizar cuatro cultivos de pistacho (Pistacia vera) de Túnez, de las regiones de Mateur (Norte), Nabeul (Nordeste), Kairouan (Centro) y Sfax (Centro-Este) y dos variedades, Mateur and Ohadi, considerando la composición en ácidos grasos y de lípidos mayoritarios (lípidos polares, diglicéridos, triglicéridos y ácidos grasos libres) de semillas maduras. Los lípidos se separaron mediante cromatografía en capa fina, y los ésteres metílicos de los ácidos grasos (FAMEs) se analizaron por cromatografía de gases. El ácido oleico (C18:1 Δ9) fue el mayoritario en todas las muestras; las de la región de Mateur (Norte) fueron significativamente distintas, presentando el contenido más bajo de C18:1 (54.2 % del total de ácidos grasos) y más alto de C18:2 (24.1 %). La cantidad total de ácidos grasos (TFA) en las semillas de la variedad Ohadi fue significativamente más bajo que el de la variedad Mateur de la región de Sfax. Los triglicéridos fueron el componente más importante en la semillas de pistacho de Nabeul (98.5% del total de glicerolípidos)

Inference of Experimental Radial Impurity Transport on Alcator C-Mod: Bayesian Parameter Estimation and Model Selection

We present a fully Bayesian approach for the inference of radial profiles of impurity transport coefficients and compare its results to neoclassical, gyrofluid and gyrokinetic modeling. Using nested sampling, the Bayesian Impurity Transport InferencE (BITE) framework can handle complex parameter spaces with multiple possible solutions, offering great advantages in interpretative power and reliability with respect to previously demonstrated methods. BITE employs a forward model based on the pySTRAHL package, built on the success of the well-known STRAHL code [Dux, IPP Report, 2004], to simulate impurity transport in magnetically-confined plasmas. In this paper, we focus on calcium (Ca, Z=20) Laser Blow-Off injections into Alcator C-Mod plasmas. Multiple Ca atomic lines are diagnosed via high-resolution X-ray Imaging Crystal Spectroscopy and Vacuum Ultra-Violet measurements. We analyze a sawtoothing I-mode discharge for which neoclassical and turbulent (quasilinear and nonlinear) predictions are also obtained. We find good agreement in diffusion across the entire radial extent, while turbulent convection and density profile peaking are estimated to be larger in experiment than suggested by theory. Efforts and challenges associated with the inference of experimental pedestal impurity transport are discussed.Comment: 38 pages, 19 figures, submitted for publication in Nuclear Fusio

Fabrication and characterization of dual function nanoscale pH-scanning ion conductance microscopy (SICM) probes for high resolution pH mapping

The easy fabrication and use of nanoscale dual function pH-scanning ion conductance microscopy (SICM) probes is reported. These probes incorporate an iridium oxide coated carbon electrode for pH measurement and an SICM barrel for distance control, enabling simultaneous pH and topography mapping. These pH-SICM probes were fabricated rapidly from laser pulled theta quartz pipets, with the pH electrode prepared by in situ carbon filling of one of the barrels by the pyrolytic decomposition of butane, followed by electrodeposition of a thin layer of hydrous iridium oxide. The other barrel was filled with an electrolyte solution and Ag/AgCl electrode as part of a conductance cell for SICM. The fabricated probes, with pH and SICM sensing elements typically on the 100 nm scale, were characterized by scanning electron microscopy, energy-dispersive X-ray spectroscopy, and various electrochemical measurements. They showed a linear super-Nernstian pH response over a range of pH (pH 2–10). The capability of the pH-SICM probe was demonstrated by detecting both pH and topographical changes during the dissolution of a calcite microcrystal in aqueous solution. This system illustrates the quantitative nature of pH-SICM imaging, because the dissolution process changes the crystal height and interfacial pH (compared to bulk), and each is sensitive to the rate. Both measurements reveal similar dissolution rates, which are in agreement with previously reported literature values measured by classical bulk methods