Binormal

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Talat Korpinar - One of the best experts on this subject based on the ideXlab platform.

Essin Turhan - One of the best experts on this subject based on the ideXlab platform.

Douglas Mossman - One of the best experts on this subject based on the ideXlab platform.

  • resampling techniques in the analysis of non Binormal roc data
    Medical Decision Making, 1995
    Co-Authors: Douglas Mossman
    Abstract:

    The methods most commonly used for analyzing receiver operating characteristic (ROC) data incorporate "Binormal" assumptions about the latent frequency distributions of test results. Although these assumptions have proved robust to a wide variety of actual frequency distributions, some data sets do not "fit" the Binormal model. In such cases, resampling techniques such as the jackknife and the bootstrap provide versatile, distribution-indepen dent, and more appropriate methods for hypothesis testing. This article describes the ap plication of resampling techniques to ROC data for which the Binormal assumptions are not appropriate, and suggests that the bootstrap may be especially helpful in determining con fidence intervals from small data samples. The widespread availability of ever-faster com puters has made resampling methods increasingly accessible and convenient tools for data analysis. Key words: receiver operating characteristic; ROC; resampling; jackknife; bootstrap; diagnostic testing; diagnostic...

  • roc curves and the Binormal assumption
    Journal of Neuropsychiatry and Clinical Neurosciences, 1991
    Co-Authors: Eugene Somoza, Douglas Mossman
    Abstract:

    : Previous articles in this series have described how receiver operating characteristic (ROC) graphs provide comprehensive graphic representations of the diagnostic performance of non-binary tests and have explained how one constructs "trapezoidal" ROC graphs in which discrete cutoff points are plotted and connected with line segments. In this article, we describe a set of mathematical assumptions that permit the generation of a continuous, smooth ROC curve for a given diagnostic test. These assumptions permit us to characterize a test's performance using a small number of parameters and also to explore properties of diagnostic tests. In this article, we describe a set of mathematical assumptions that can be used to link receiver operating characteristic (ROC) curves to the underlying distribution of values of the diagnostic variable being measured. We will illustrate these assumptions using a diagnostic test that distinguishes alcohol abusers from normal consumers of alcohol and abstainers.

Charles E Metz - One of the best experts on this subject based on the ideXlab platform.

  • an analytic expression for the Binormal partial area under the roc curve
    Academic Radiology, 2012
    Co-Authors: Stephen L Hillis, Charles E Metz
    Abstract:

    Rationale and Objectives The partial area under the receiver operating characteristic (ROC) curve (pAUC) is a useful summary measure for diagnostic studies. Unlike most summary measures that are functions of the ROC curve, researchers have not been aware of an analytic expression available for computing the pAUC for an ROC curve based on a latent Binormal model. Instead, the pAUC has been computed using numerical integration or a rational polynomial approximation. Our purpose is to provide analytic expressions for the two forms of pAUC. Materials and Methods We discuss the two fundamentally different types of pAUC. We present analytic expressions for both types, provide corresponding proofs, and illustrate their application with an example comparing the performances of spin echo and cine magnetic resonance imaging for detecting thoracic aortic dissection. Results We provide an example of using the pAUC as the outcome in a multireader multicase analysis. We find that using the pAUC results in a more significant finding. Conclusions We have provided analytic expressions for both types of pAUC, making it easier to compute the pAUCs corresponding to Binormal ROC curves.

  • a bayesian interpretation of the proper Binormal roc model using a uniform prior distribution for the area under the curve
    Medical Imaging 2007: Image Perception Observer Performance and Technology Assessment, 2007
    Co-Authors: Lorenzo Luigi Pesce, Yulei Jiang, Charles E Metz
    Abstract:

    Maximum likelihood estimation of receiver operating characteristic (ROC) curves using the "proper" Binormal model can be interpreted in terms of Bayesian estimation as assuming a flat joint prior distribution on the c and d a parameters. However, this is equivalent to assuming a non-flat prior distribution for the area under the curve (AUC) that peaks at AUC = 1.0. We hypothesize that this implicit prior on AUC biases the maximum likelihood estimate (MLE) of AUC. We propose a Bayesian implementation of the "proper" Binormal ROC curve-fitting model with a prior distribution that is marginally flat on AUC and conditionally flat over c . This specifies a non-flat joint prior for c and d a . We developed a Monte Carlo Markov chain (MCMC) algorithm to estimate the posterior distribution and the maximum a posteriori (MAP) estimate of AUC. We performed a simulation study using 500 draws of a small dataset (25 normal and 25 abnormal cases) with an underlying AUC value of 0.85. When the prior distribution was a flat joint prior on c and d a , the MLE and MAP estimates agreed, suggesting that the MCMC algorithm worked correctly. When the prior distribution was marginally flat on AUC, the MAP estimate of AUC appeared to be biased low. However, the MAP estimate of AUC for perfectly separable degenerate datasets did not appear to be biased. Further work is needed to validate the algorithm and refine the prior assumptions.

  • proper Binormal roc curves theory and maximum likelihood estimation
    Journal of Mathematical Psychology, 1999
    Co-Authors: Charles E Metz
    Abstract:

    Abstract The conventional Binormal model, which assumes that a pair of latent normal decision-variable distributions underlies ROC data, has been used successfully for many years to fit smooth ROC curves. However, if the conventional Binormal model is used for small data sets or ordinal-category data with poorly allocated category boundaries, a “hook” in the fitted ROC may be evident near the upper-right or lower-left corner of the unit square. To overcome this curve-fitting artifact, we developed a “proper” Binormal model and a new algorithm for maximum-likelihood (ML) estimation of the corresponding ROC curves. Extensive simulation studies have shown the algorithm to be highly reliable. ML estimates of the proper and conventional Binormal ROC curves are virtually identical when the conventional Binormal ROC shows no “hook,” but the proper Binormal curves have monotonic slope for all data sets, including those for which the conventional model produces degenerate fits.

  • the proper Binormal model parametric receiver operating characteristic curve estimation with degenerate data
    Academic Radiology, 1997
    Co-Authors: Charles E Metz
    Abstract:

    Rationale and Objectives. The authors assessed the use of a “proper” Binormal model and a new algorithm for maximum-likelihood estimation of receiver operating characteristic (ROC) curves from degenerate data. Methods. The proper Binormal ROC model uses as its decision variable a monotonic transformation of the likelihood ratio that is associated with a pair of normal distributions, thereby ensuring fitted ROC curves with monotonic slope but maintaining a relationship with the conventional hinormal model. A computer program entitled PROPROC was used to fit proper ROC curves to data obtained from computer-simulated and real observer studies. Results. ROC indexes such as total area were estimated with proproc and compared with the corresponding values obtained from the conventional procedures. Conclusion. The proper Binormal ROC model overcomes the problem of degeneracy in ROC curve fitting, proproc is highly robust and yields ROC estimates with less bias and greater precision than those obtained with the conventional Binormal model.

Luis Vega - One of the best experts on this subject based on the ideXlab platform.

  • on the energy of critical solutions of the Binormal flow
    Communications in Partial Differential Equations, 2020
    Co-Authors: Valeria Banica, Luis Vega
    Abstract:

    The Binormal flow is a model for the dynamics of a vortex filament in a 3-D inviscid incompressible fluid. The flow is also related with the classical continuous Heisenberg model in ferromagnetism,...

  • evolution of polygonal lines by the Binormal flow
    arXiv: Analysis of PDEs, 2018
    Co-Authors: Valeria Banica, Luis Vega
    Abstract:

    The aim of this paper is threefold. First we display solutions of the cubic nonlinear Schr{\"o}dinger equation on R in link with initial data a sum of Dirac masses. Secondly we show a Talbot effect for the same equation. Finally we prove the existence of a unique solution of the Binormal flow with datum a polygonal line. This equation is used as a model for the vortex filaments dynamics in 3-D fluids and superfluids. We also construct solutions of the Binormal flow that present an intermittency phenomena. Finally, the solution we construct for the Binormal flow is continued for negative times, yielding a geometric way to approach the continuation after blow-up for the 1-D cubic nonlinear Schr{\"o}dinger equation.

  • Stability of the Self-similar Dynamics of a Vortex Filament
    Archive for Rational Mechanics and Analysis, 2013
    Co-Authors: Valeria Banica, Luis Vega
    Abstract:

    In this paper we continue our investigation of self-similar solutions of the vortex filament equation, also known as the Binormal flow or the localized induction equation. Our main result is the stability of the self-similar dynamics of small perturbations of a given self-similar solution. The proof relies on finding precise asymptotics in space and time for the tangent and the normal vectors of the perturbations. A main ingredient in the proof is the control of the evolution of weighted norms for a cubic one-dimensional Schrödinger equation, connected to the Binormal flow by Hasimoto’s transform.