Maximum-a-posteriori estimation with Bayesian confidence regions

Solutions to inverse problems that are ill-conditioned or ill-posed may have significant intrinsic uncertainty. Unfortunately, analysing and quantifying this uncertainty is very challenging, particularly in high-dimensional problems. As a result, while most modern mathematical imaging methods produce impressive point estimation results, they are generally unable to quantify the uncertainty in the solutions delivered. This paper presents a new general methodology for approximating Bayesian high-posterior-density credibility regions in inverse problems that are convex and potentially very high-dimensional. The approximations are derived by using recent concentration of measure results related to information theory for log-concave random vectors. A remarkable property of the approximations is that they can be computed very efficiently, even in large-scale problems, by using standard convex optimisation techniques. In particular, they are available as a by-product in problems solved by maximum-a-posteriori estimation. The approximations also have favourable theoretical properties, namely they outer-bound the true high-posterior-density credibility regions, and they are stable with respect to model dimension. The proposed methodology is illustrated on two high-dimensional imaging inverse problems related to tomographic reconstruction and sparse deconvolution, where the approximations are used to perform Bayesian hypothesis tests and explore the uncertainty about the solutions, and where proximal Markov chain Monte Carlo algorithms are used as benchmark to compute exact credible regions and measure the approximation error

CrocoPat 2.1 Introduction and Reference Manual

CrocoPat is an efficient, powerful and easy-to-use tool for manipulating relations of arbitrary arity, including directed graphs. This manual provides an introduction to and a reference for CrocoPat and its programming language RML. It includes several application examples, in particular from the analysis of structural models of software systems.Comment: 19 pages + cover, 2 eps figures, uses llncs.cls and cs_techrpt_cover.sty, for downloading the source code, binaries, and RML examples, see http://www.software-systemtechnik.de/CrocoPat

IGA-based Multi-Index Stochastic Collocation for random PDEs on arbitrary domains

This paper proposes an extension of the Multi-Index Stochastic Collocation (MISC) method for forward uncertainty quantification (UQ) problems in computational domains of shape other than a square or cube, by exploiting isogeometric analysis (IGA) techniques. Introducing IGA solvers to the MISC algorithm is very natural since they are tensor-based PDE solvers, which are precisely what is required by the MISC machinery. Moreover, the combination-technique formulation of MISC allows the straight-forward reuse of existing implementations of IGA solvers. We present numerical results to showcase the effectiveness of the proposed approach.Comment: version 3, version after revisio

Detection of REM Sleep Behaviour Disorder by Automated Polysomnography Analysis

Evidence suggests Rapid-Eye-Movement (REM) Sleep Behaviour Disorder (RBD) is an early predictor of Parkinson's disease. This study proposes a fully-automated framework for RBD detection consisting of automated sleep staging followed by RBD identification. Analysis was assessed using a limited polysomnography montage from 53 participants with RBD and 53 age-matched healthy controls. Sleep stage classification was achieved using a Random Forest (RF) classifier and 156 features extracted from electroencephalogram (EEG), electrooculogram (EOG) and electromyogram (EMG) channels. For RBD detection, a RF classifier was trained combining established techniques to quantify muscle atonia with additional features that incorporate sleep architecture and the EMG fractal exponent. Automated multi-state sleep staging achieved a 0.62 Cohen's Kappa score. RBD detection accuracy improved by 10% to 96% (compared to individual established metrics) when using manually annotated sleep staging. Accuracy remained high (92%) when using automated sleep staging. This study outperforms established metrics and demonstrates that incorporating sleep architecture and sleep stage transitions can benefit RBD detection. This study also achieved automated sleep staging with a level of accuracy comparable to manual annotation. This study validates a tractable, fully-automated, and sensitive pipeline for RBD identification that could be translated to wearable take-home technology.Comment: 20 pages, 3 figure

Research and Education in Computational Science and Engineering

Over the past two decades the field of computational science and engineering (CSE) has penetrated both basic and applied research in academia, industry, and laboratories to advance discovery, optimize systems, support decision-makers, and educate the scientific and engineering workforce. Informed by centuries of theory and experiment, CSE performs computational experiments to answer questions that neither theory nor experiment alone is equipped to answer. CSE provides scientists and engineers of all persuasions with algorithmic inventions and software systems that transcend disciplines and scales. Carried on a wave of digital technology, CSE brings the power of parallelism to bear on troves of data. Mathematics-based advanced computing has become a prevalent means of discovery and innovation in essentially all areas of science, engineering, technology, and society; and the CSE community is at the core of this transformation. However, a combination of disruptive developments---including the architectural complexity of extreme-scale computing, the data revolution that engulfs the planet, and the specialization required to follow the applications to new frontiers---is redefining the scope and reach of the CSE endeavor. This report describes the rapid expansion of CSE and the challenges to sustaining its bold advances. The report also presents strategies and directions for CSE research and education for the next decade.Comment: Major revision, to appear in SIAM Revie

An Assessment of PIER Electric Grid Research 2003-2014 White Paper

This white paper describes the circumstances in California around the turn of the 21st century that led the California Energy Commission (CEC) to direct additional Public Interest Energy Research funds to address critical electric grid issues, especially those arising from integrating high penetrations of variable renewable generation with the electric grid. It contains an assessment of the beneficial science and technology advances of the resultant portfolio of electric grid research projects administered under the direction of the CEC by a competitively selected contractor, the University of California’s California Institute for Energy and the Environment, from 2003-2014