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

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

Wide Field Infrared Survey Telescope (WFIRST) Observatory Overview

NASA's Wide Field Infrared Survey Telescope (WFIRST) is being designed to deliver unprecedented capability in dark energy and exoplanet science, and to host a technology demonstration coronagraph for exoplanet imaging and spectroscopy. The observatory design has matured since 2013; we present a comprehensive description of the observatory configuration as refined during the WFIRST Phase-A study. The observatory is based on an existing, repurposed 2.4 meter space telescope coupled with a 288 megapixel near-infrared (0.6 to 2 microns) HgCdTe focal plane array with multiple imaging and spectrographic modes. Together they deliver a 0.28 square degree field of view, which is approximately 100 times larger than the Hubble Space Telescope, and a sensitivity that enables rapid science surveys. In addition, the coronagraph technology demonstration will prove the feasibility of new techniques for exoplanet discovery, imaging, and spectral analysis. A composite truss structure meters both instruments to the telescope assembly, and the instruments and the spacecraft are flight serviceable. We present configuration changes since 2013 that improved interfaces, improved testability, and reduced technical risk. We provide an overview of our Integrated Modeling results, performed at an unprecedented level for a phase-A study, to illustrate performance margins with respect to static wavefront error, jitter, and thermal drift

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

Sharp detection of low-dimensional structure in probability measures via dimensional logarithmic Sobolev inequalities

Identifying low-dimensional structure in high-dimensional probability measures is an essential pre-processing step for efficient sampling. We introduce a method for identifying and approximating a target measure $π$ as a perturbation of a given reference measure $μ$ along a few significant directions of $\mathbb{R}^{d}$. The reference measure can be a Gaussian or a nonlinear transformation of a Gaussian, as commonly arising in generative modeling. Our method extends prior work on minimizing majorizations of the Kullback--Leibler divergence to identify optimal approximations within this class of measures. Our main contribution unveils a connection between the \emph{dimensional} logarithmic Sobolev inequality (LSI) and approximations with this ansatz. Specifically, when the target and reference are both Gaussian, we show that minimizing the dimensional LSI is equivalent to minimizing the KL divergence restricted to this ansatz. For general non-Gaussian measures, the dimensional LSI produces majorants that uniformly improve on previous majorants for gradient-based dimension reduction. We further demonstrate the applicability of this analysis to the squared Hellinger distance, where analogous reasoning shows that the dimensional Poincaré inequality offers improved bounds