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Reichert P.,Eawag - Swiss Federal Institute of Aquatic Science and Technology | Reichert P.,Statistical and Applied Mathematical science Institute SAMSI | White G.,North Carolina State University | White G.,Statistical and Applied Mathematical science Institute SAMSI | And 4 more authors.
Computational Statistics and Data Analysis | Year: 2011

Many model-based investigation techniques, such as sensitivity analysis, optimization, and statistical inference, require a large number of model evaluations to be performed at different input and/or parameter values. This limits the application of these techniques to models that can be implemented in computationally efficient computer codes. Emulators, by providing efficient interpolation between outputs of deterministic simulation models, can considerably extend the field of applicability of such computationally demanding techniques. So far, the dominant techniques for developing emulators have been priors in the form of Gaussian stochastic processes (GASP) that were conditioned with a design data set of inputs and corresponding model outputs. In the context of dynamic models, this approach has two essential disadvantages: (i) these emulators do not consider our knowledge of the structure of the model, and (ii) they run into numerical difficulties if there are a large number of closely spaced input points as is often the case in the time dimension of dynamic models. To address both of these problems, a new concept of developing emulators for dynamic models is proposed. This concept is based on a prior that combines a simplified linear state space model of the temporal evolution of the dynamic model with Gaussian stochastic processes for the innovation terms as functions of model parameters and/or inputs. These innovation terms are intended to correct the error of the linear model at each output step. Conditioning this prior to the design data set is done by Kalman smoothing. This leads to an efficient emulator that, due to the consideration of our knowledge about dominant mechanisms built into the simulation model, can be expected to outperform purely statistical emulators at least in cases in which the design data set is small. The feasibility and potential difficulties of the proposed approach are demonstrated by the application to a simple hydrological model. © 2010 Published by Elsevier B.V.


Lin X.,Rutgers University | Pham M.,Statistical and Applied Mathematical science Institute SAMSI | Ruszczynski A.,Rutgers University
Journal of Machine Learning Research | Year: 2014

We adapt the alternating linearization method for proximal decomposition to structured regularization problems, in particular, to the generalized lasso problems. The method is related to two well-known operator splitting methods, the Douglas-Rachford and the Peaceman-Rachford method, but it has descent properties with respect to the objective function. This is achieved by employing a special update test, which decides whether it is beneficial to make a Peaceman-Rachford step, any of the two possible Douglas-Rachford steps, or none. The convergence mechanism of the method is related to that of bundle methods of nonsmooth optimization. We also discuss implementation for very large problems, with the use of specialized algorithms and sparse data structures. Finally, we present numerical results for several synthetic and real-world examples, including a three-dimensional fused lasso problem, which illustrate the scalability, efficacy, and accuracy of the method. ©2014 Xiaodong Lin, Minh Pham and Andrzej Ruszczyński.


Lopiano K.K.,Statistical and Applied Mathematical science Institute SAMSI | Young L.J.,University of Florida | Gotway C.A.,Centers for Disease Control
Biostatistics | Year: 2013

In environmental studies, relationships among variables that aremisaligned in space are routinely assessed. Because the data are misaligned, kriging is often used to predict the covariate at the locations where the response is observed. Using kriging predictions to estimate regression parameters in linear regression models introduces a Berkson error, which induces a covariance structure that is challenging to estimate. In addition, if the parameters associated with kriging (e.g. trend surface parameters and spatial covariance parameters) are estimated, then an additional uncertainty is introduced.We characterize the total measurement error as part of a broader class of Berkson error models and develop an estimated generalized least squares estimator using estimated covariance parameters. In working with the induced model, we fully account for the error structure and estimate the covariance parameters using likelihood-based methods. We provide insight into when it is important to fully account for the covariance structure induced from the different error sources.We assess the performance of the estimators using simulation and illustrate the methodology using publicly available data from the US Environmental Protection Agency. © The Author 2013. Published by Oxford University Press. All rights reserved.


Gordon-Wright R.,North Carolina State University | Gremaud P.A.,Statistical and Applied Mathematical science Institute SAMSI | Martens E.G.H.J.,TU Eindhoven | Novak V.,Beth Israel Deaconess Medical Center
1st International Workshop on Innovative Simulation for Health Care, IWISH 2012, Held at the International Multidisciplinary Modeling and Simulation Multiconference, I3M 2012 | Year: 2012

There is a pressing need for noninvasive and continuous measurements of cerebral blood flow (CBF) in several areas of medicine. Transcranial Doppler (TCD) technology is clinically used for measurements of blood flow velocities (BFV). It is assumed that perfusion and vasoreactivity in a vascular territory can be inferred from BFV measurements in the corresponding stem artery. However, only very modest correlations have been found between TCD-based and magnetic resonance imaging (MRI)-based CBF measurements. Several factors, whose values are uncertain, such as vessel diameter, hematocrit and insonation angle, affect the BFV - CBF relationship. Their influence on CBF and vasoreactivity estimates has not been rigorously analyzed but cannot be ignored. We present initial work toward a subject specific computational and experimental model to both quantify and reduce the uncertainty attached to CBF and vasoreactivity estimates based on Doppler ultrasound.


Thai D.H.,University of Gottingen | Thai D.H.,Statistical and Applied Mathematical Science Institute SAMSI | Gottschlich C.,University of Gottingen
Eurasip Journal on Image and Video Processing | Year: 2016

We consider the task of image decomposition, and we introduce a new model coined directional global three-part decomposition (DG3PD) for solving it. As key ingredients of the DG3PD model, we introduce a discrete multi-directional total variation norm and a discrete multi-directional G-norm. Using these novel norms, the proposed discrete DG3PD model can decompose an image into two or three parts. Existing models for image decomposition by Vese and Osher (J. Sci. Comput. 19(1–3):553–572, 2003), by Aujol and Chambolle (Int. J. Comput. Vis. 63(1):85–104, 2005), by Starck et al. (IEEE Trans. Image Process. 14(10):1570–1582, 2005), and by Thai and Gottschlich are included as special cases in the new model. Decomposition of an image by DG3PD results in a cartoon image, a texture image, and a residual image. Advantages of the DG3PD model over existing ones lie in the properties enforced on the cartoon and texture images. The geometric objects in the cartoon image have a very smooth surface and sharp edges. The texture image yields oscillating patterns on a defined scale which are both smooth and sparse. Moreover, the DG3PD method achieves the goal of perfect reconstruction by summation of all components better than the other considered methods. Relevant applications of DG3PD are a novel way of image compression as well as feature extraction for applications such as latent fingerprint processing and optical character recognition. © 2016, Thai and Gottschlich.


Srivastava S.,Duke University | Srivastava S.,Statistical and Applied Mathematical science Institute SAMSI | Cevher V.,Ecole Polytechnique Federale de Lausanne | Tran-Dinh Q.,Ecole Polytechnique Federale de Lausanne | Dunson D.B.,Duke University
Journal of Machine Learning Research | Year: 2015

The promise of Bayesian methods for big data sets has not fully been realized due to the lack of scalable computational algorithms. For massive data, it is necessary to store and process subsets on different machines in a distributed manner. We propose a simple, general, and highly efficient approach, which first runs a posterior sampling algorithm in parallel on different machines for subsets of a large data set. To combine these subset posteriors, we calculate the Wasserstein barycenter via a highly efficient linear program. The resulting estimate for the Wasserstein posterior (WASP) has an atomic form, facilitating straightforward estimation of posterior summaries of functionals of interest. The WASP approach allows posterior sampling algorithms for smaller data sets to be trivially scaled to huge data. We provide theoretical justification in terms of posterior consistency and algorithm efficiency. Examples are provided in complex settings including Gaussian process regression and nonparametric Bayes mixture models. Copyright 2015 by the authors.


Collins J.,North Carolina State University | Gremaud P.,North Carolina State University | Gremaud P.,Statistical and Applied Mathematical science Institute SAMSI
Mathematics and Computers in Simulation | Year: 2011

A simple mathematical model of laser drilling is proposed. Assuming axi-symmetry of the process around the axis of the laser beam, a one-dimensional formulation is obtained after cross-sectional averaging. The novelty of the approach relies on the fact that even after dimension reduction, the shape of the hole can still be described. The model is derived, implemented and validated for drilling using lasers with intensities in the GW/cm2 range and microsecond pulses. © 2010 IMACS.


Aristotelous A.C.,Statistical and Applied Mathematical science Institute SAMSI | Aristotelous A.C.,Duke University | Haider M.A.,North Carolina State University
International Journal for Numerical Methods in Biomedical Engineering | Year: 2014

Macroscopic models accounting for cellular effects in natural or engineered tissues may involve unknown constitutive terms that are highly dependent on interactions at the scale of individual cells. Hybrid discrete models, which represent cells individually, were used to develop and apply techniques for modeling diffusive nutrient transport and cellular uptake to identify a nonlinear nutrient loss term in a macroscopic reaction-diffusion model of the system. Flexible and robust numerical methods were used, based on discontinuous Galerkin finite elements in space and a Crank-Nicolson temporal discretization. Scales were bridged via averaging operations over a complete set of subdomains yielding data for identification of a macroscopic nutrient loss term that was accurately captured via a fifth-order polynomial. Accuracy of the identified macroscopic model was demonstrated by direct, quantitative comparisons of the tissue and cellular scale models in terms of three error norms computed on a mesoscale mesh. © 2014 John Wiley & Sons, Ltd.


Liu B.,Statistical and Applied Mathematical science Institute SAMSI | Liu B.,Duke University | Ji C.,Duke University | Zhang Y.,University College London | And 2 more authors.
IET Radar, Sonar and Navigation | Year: 2010

For multi-target tracking (MTT) in the presence of clutters, both issues of state estimation and data association are crucial. This study tackles them jointly by Sequential Monte Carlo methods, a.k.a. particle filters. A number of novel particle algorithms are devised. The first one, which we term Monte-Carlo data association (MCDA), is a direct extension of the classical sequential importance resampling (SIR) algorithm. The second one is called maximum predictive particle filter (MPPF), in which the measurement combination with the maximum predictive likelihood is used to update the estimate of the multi-target's posterior. The third, called proportionally weighting particle filter (PWPF), weights all feasible measurement combinations according to their predictive likelihoods, and uses them proportionally in the importance sampling framework. We demonstrate the efficiency and superiority of our methods over conventional approaches through simulations. © 2010 The Institution of Engineering and Technology.


Thai D.H.,University of Gottingen | Thai D.H.,Statistical and Applied Mathematical Science Institute SAMSI | Huckemann S.,University of Gottingen | Gottschlich C.,University of Gottingen
PLoS ONE | Year: 2016

Fingerprint recognition plays an important role in many commercial applications and is used by millions of people every day, e.g. for unlocking mobile phones. Fingerprint image segmentation is typically the first processing step of most fingerprint algorithms and it divides an image into foreground, the region of interest, and background. Two types of error can occur during this step which both have a negative impact on the recognition performance: 'true' foreground can be labeled as background and features like minutiae can be lost, or conversely 'true' background can be misclassified as foreground and spurious features can be introduced. The contribution of this paper is threefold: firstly, we propose a novel factorized directional bandpass (FDB) segmentation method for texture extraction based on the directional Hilbert transform of a Butterworth bandpass (DHBB) filter interwoven with soft-thresholding. Secondly, we provide a manually marked ground truth segmentation for 10560 images as an evaluation benchmark. Thirdly, we conduct a systematic performance comparison between the FDB method and four of the most often cited fingerprint segmentation algorithms showing that the FDB segmentation method clearly outperforms these four widely used methods. The benchmark and the implementation of the FDB method are made publicly available. © 2016 Thai et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

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