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. © 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 $\ell_1$-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 $\ell_p^q$ 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

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 2 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 – 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

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

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 $N$ 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