297 research outputs found
Compensation of domain modelling errors in the inverse source problem of the Poisson equation: Application in electroencephalographic imaging
Usability analysis of contending electronic health record systems
In this paper, we report measured usability of two leading EHR systems during procurement. A total of 18 users participated in paired-usability testing of three scenarios: ordering and managing medications by an outpatient physician, medicine administration by an inpatient nurse and scheduling of appointments by nursing staff. Data for audio, screen capture, satisfaction rating, task success and errors made was collected during testing. We found a clear difference between the systems for percentage of successfully completed tasks, two different satisfaction measures and perceived learnability when looking at the results over all scenarios. We conclude that usability should be evaluated during procurement and the difference in usability between systems could be revealed even with fewer measures than were used in our study. Ā© 2019 American Psychological Association Inc. All rights reserved.Peer reviewe
A TV-Gaussian prior for infinite-dimensional Bayesian inverse problems and its numerical implementations
Many scientific and engineering problems require to perform Bayesian
inferences in function spaces, in which the unknowns are of infinite dimension.
In such problems, choosing an appropriate prior distribution is an important
task. In particular we consider problems where the function to infer is subject
to sharp jumps which render the commonly used Gaussian measures unsuitable. On
the other hand, the so-called total variation (TV) prior can only be defined in
a finite dimensional setting, and does not lead to a well-defined posterior
measure in function spaces. In this work we present a TV-Gaussian (TG) prior to
address such problems, where the TV term is used to detect sharp jumps of the
function, and the Gaussian distribution is used as a reference measure so that
it results in a well-defined posterior measure in the function space. We also
present an efficient Markov Chain Monte Carlo (MCMC) algorithm to draw samples
from the posterior distribution of the TG prior. With numerical examples we
demonstrate the performance of the TG prior and the efficiency of the proposed
MCMC algorithm
Fast Gibbs sampling for high-dimensional Bayesian inversion
Solving ill-posed inverse problems by Bayesian inference has recently
attracted considerable attention. Compared to deterministic approaches, the
probabilistic representation of the solution by the posterior distribution can
be exploited to explore and quantify its uncertainties. In applications where
the inverse solution is subject to further analysis procedures, this can be a
significant advantage. Alongside theoretical progress, various new
computational techniques allow to sample very high dimensional posterior
distributions: In [Lucka2012], a Markov chain Monte Carlo (MCMC) posterior
sampler was developed for linear inverse problems with -type priors. In
this article, we extend this single component Gibbs-type sampler to a wide
range of priors used in Bayesian inversion, such as general priors
with additional hard constraints. Besides a fast computation of the
conditional, single component densities in an explicit, parameterized form, a
fast, robust and exact sampling from these one-dimensional densities is key to
obtain an efficient algorithm. We demonstrate that a generalization of slice
sampling can utilize their specific structure for this task and illustrate the
performance of the resulting slice-within-Gibbs samplers by different computed
examples. These new samplers allow us to perform sample-based Bayesian
inference in high-dimensional scenarios with certain priors for the first time,
including the inversion of computed tomography (CT) data with the popular
isotropic total variation (TV) prior.Comment: submitted to "Inverse Problems
On dimension reduction in Gaussian filters
A priori dimension reduction is a widely adopted technique for reducing the
computational complexity of stationary inverse problems. In this setting, the
solution of an inverse problem is parameterized by a low-dimensional basis that
is often obtained from the truncated Karhunen-Loeve expansion of the prior
distribution. For high-dimensional inverse problems equipped with smoothing
priors, this technique can lead to drastic reductions in parameter dimension
and significant computational savings.
In this paper, we extend the concept of a priori dimension reduction to
non-stationary inverse problems, in which the goal is to sequentially infer the
state of a dynamical system. Our approach proceeds in an offline-online
fashion. We first identify a low-dimensional subspace in the state space before
solving the inverse problem (the offline phase), using either the method of
"snapshots" or regularized covariance estimation. Then this subspace is used to
reduce the computational complexity of various filtering algorithms - including
the Kalman filter, extended Kalman filter, and ensemble Kalman filter - within
a novel subspace-constrained Bayesian prediction-and-update procedure (the
online phase). We demonstrate the performance of our new dimension reduction
approach on various numerical examples. In some test cases, our approach
reduces the dimensionality of the original problem by orders of magnitude and
yields up to two orders of magnitude in computational savings
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
Ambient pressure x-ray photoelectron spectroscopy setup for synchrotron-based in situ and operando atomic layer deposition research
An ambient pressure cell is described for conducting synchrotron-based x-ray photoelectron spectroscopy (XPS) measurements during atomic layer deposition (ALD) processes. The instrument is capable of true in situ and operando experiments in which it is possible to directly obtain elemental and chemical information from the sample surface using XPS as the deposition process is ongoing. The setup is based on the ambient pressure XPS technique, in which sample environments with high pressure (several mbar) can be created without compromising the ultrahigh vacuum requirements needed for the operation of the spectrometer and the synchrotron beamline. The setup is intended for chemical characterization of the surface intermediates during the initial stages of the deposition processes. The SPECIES beamline and the ALD cell provide a unique experimental platform for obtaining new information on the surface chemistry during ALD half-cycles at high temporal resolution. Such information is valuable for understanding the ALD reaction mechanisms and crucial in further developing and improving ALD processes. We demonstrate the capabilities of the setup by studying the deposition of TiO2 on a SiO2 surface by using titanium(IV) tetraisopropoxide and water as precursors. Multiple core levels and the valence band of the substrate surface were followed during the film deposition using ambient pressure XPS.Peer reviewe
Retrieval of process rate parameters in the general dynamic equation for aerosols using Bayesian state estimation: BAYROSOL1.0
The uncertainty in the radiative forcing caused by aerosols and its effect on climate change calls for research to improve knowledge of the aerosol
particle formation and growth processes. While experimental research has
provided a large amount of high-quality data on aerosols over the last 2Ā decades, the inference of the process rates is still inadequate, mainly due to
limitations in the analysis of data. This paper focuses on developing
computational methods to infer aerosol process rates from size distribution
measurements. In the proposed approach, the temporal evolution of aerosol
size distributions is modeled with the general dynamic equation (GDE) equipped with
stochastic terms that account for the uncertainties of the process rates. The
time-dependent particle size distribution and the rates of the underlying
formation and growth processes are reconstructed based on time series of
particle analyzer data using Bayesian state estimation ā which not only
provides (point) estimates for the process rates but also enables quantification of
their uncertainties. The feasibility of the proposed computational framework
is demonstrated by a set of numerical simulation studies.</p
Fisher Information for Inverse Problems and Trace Class Operators
This paper provides a mathematical framework for Fisher information analysis
for inverse problems based on Gaussian noise on infinite-dimensional Hilbert
space. The covariance operator for the Gaussian noise is assumed to be trace
class, and the Jacobian of the forward operator Hilbert-Schmidt. We show that
the appropriate space for defining the Fisher information is given by the
Cameron-Martin space. This is mainly because the range space of the covariance
operator always is strictly smaller than the Hilbert space. For the Fisher
information to be well-defined, it is furthermore required that the range space
of the Jacobian is contained in the Cameron-Martin space. In order for this
condition to hold and for the Fisher information to be trace class, a
sufficient condition is formulated based on the singular values of the Jacobian
as well as of the eigenvalues of the covariance operator, together with some
regularity assumptions regarding their relative rate of convergence. An
explicit example is given regarding an electromagnetic inverse source problem
with "external" spherically isotropic noise, as well as "internal" additive
uncorrelated noise.Comment: Submitted to Journal of Mathematical Physic
Sparse Deterministic Approximation of Bayesian Inverse Problems
We present a parametric deterministic formulation of Bayesian inverse
problems with input parameter from infinite dimensional, separable Banach
spaces. In this formulation, the forward problems are parametric, deterministic
elliptic partial differential equations, and the inverse problem is to
determine the unknown, parametric deterministic coefficients from noisy
observations comprising linear functionals of the solution.
We prove a generalized polynomial chaos representation of the posterior
density with respect to the prior measure, given noisy observational data. We
analyze the sparsity of the posterior density in terms of the summability of
the input data's coefficient sequence. To this end, we estimate the
fluctuations in the prior. We exhibit sufficient conditions on the prior model
in order for approximations of the posterior density to converge at a given
algebraic rate, in terms of the number of unknowns appearing in the
parameteric representation of the prior measure. Similar sparsity and
approximation results are also exhibited for the solution and covariance of the
elliptic partial differential equation under the posterior. These results then
form the basis for efficient uncertainty quantification, in the presence of
data with noise
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