Asymptotic properties of the sequential empirical ROC, PPV and NPV curves under case-control sampling

The receiver operating characteristic (ROC) curve, the positive predictive value (PPV) curve and the negative predictive value (NPV) curve are three measures of performance for a continuous diagnostic biomarker. The ROC, PPV and NPV curves are often estimated empirically to avoid assumptions about the distributional form of the biomarkers. Recently, there has been a push to incorporate group sequential methods into the design of diagnostic biomarker studies. A thorough understanding of the asymptotic properties of the sequential empirical ROC, PPV and NPV curves will provide more flexibility when designing group sequential diagnostic biomarker studies. In this paper, we derive asymptotic theory for the sequential empirical ROC, PPV and NPV curves under case-control sampling using sequential empirical process theory. We show that the sequential empirical ROC, PPV and NPV curves converge to the sum of independent Kiefer processes and show how these results can be used to derive asymptotic results for summaries of the sequential empirical ROC, PPV and NPV curves.Comment: Published in at http://dx.doi.org/10.1214/11-AOS937 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Correlation length and negative phase velocity in isotropic dielectric-magnetic materials

A composite material comprising randomly distributed spherical particles of two different isotropic dielectric-magnetic materials is homogenized using the second-order strong-property-fluctuation theory in the long-wavelength approximation. Whereas neither of the two constituent materials by itself supports planewave propagation with negative phase velocity (NPV), the homogenized composite material (HCM) can. The propensity of the HCM to support NPV propagation is sensitive to the distributional statistics of the constituent material particles, as characterized by a two--point covariance function and its associated correlation length. The scope for NPV propagation diminishes as the correlation length increases

Global and local perspectives of gravitationally assisted negative-phase-velocity propagation of electromagnetic waves in vacuum

Consistently with the Einstein equivalence principle and using an electromagnetic formulation first suggested by Tamm, we show that a local observer cannot observe negative-phase-velocity (NPV) propagation of electromagnetic waves in vacuum, whereas a global observer can appreciate that phenomenon. Using the specific example of the Kerr metric, we also demonstrate the possibility of NPV propagation within the ergosphere of a rotating black hole

Uncertainty of net present value calculations and the impact on applying integrated maintenance approaches to the UK rail industry

The Public performance indicator (PPI) is an important Key Performance Indicator for Network Rail and monitored carefully by the organisation and their external stakeholders. Condition monitoring is of increasing interest within network rail as a suitable method for increasing asset reliability and improving the PPI metric. As condition monitoring methods are identified each will need assessment to establish the cost and benefit. Benefit can be measured in cost savings as poor PPI performance results in fines. Within many industries Net Present Value (NPV) calculations are used to determine how quickly investments will break-even. Cost-risk is a term that is used to describe the financial impact of an unexpected event (a risk). This paper outlines a more detailed approach to calculating NPV which considers the cost-risk effect of changes of the denial of service charging rate. NPV prediction is of importance when assessing when to deploy different fault detection strategies to maintenance issues, and therefore the cost-risk of the NPV calculation should be used to support asset management decisions

Anomalies in net present value calculations. A solution

The so-called anomalies that arise in the computation and interpretation of the Net Present Value (NPV) and the Internal Rate of Return (IRR) can be easily overcome if the properties of the NPV function are taken into account and it is clearly defined what is an investment and what is a credit. All the roots of the NPV function have economic meaning and, when there is at least one IRR, the NPV and the IRR criteria agree.Net Present Value; Internal Rate of Return; Investment Analysis; Project Evaluation.

Scheduling Markovian PERT networks with maximum-NPV objective.

We examine project scheduling with net-present-value objective and exponential activity durations, using a continuous-time Markov decision chain. Based on a judicious partitioning of the state space, we achieve a significant performance improvement compared to the existing algorithms.Project scheduling; Net present value; Stochastic activity durations; Exponential distribution;

Diffraction gratings of isotropic negative phase-velocity materials

Diffraction of electromagnetic plane waves by the gratings made by periodically corrugating the exposed planar boundaries of homogeneous, isotropic, linear dielectric--magnetic half--spaces is examined. The phase velocity vector in the diffracting material can be either co-parallel or anti-parallel to the time-averaged Poynting vector, thereby allowing for the material to be classified as of either the positive or the negative negative phase-velocity (PPV or NPV) type. Three methods used for analyzing dielectric gratings - the Rayleigh-hypothesis method, a perturbative approach, and the C formalism - are extended here to encompass NPV gratings by a careful consideration of field representation inside the refracting half--space. Corrugations of both symmetric as well as asymmetric shapes are studied, as also the diversity of grating response to the linear polarization states of the incident plane wave. The replacement of PPV grating by its NPV analog affects only nonspecular diffraction efficiencies when the corrugations are shallow, and the effect on specular diffraction efficiencies intensifies as the corrugations deepen. Whether the type of the refracting material is NPV or PPV is shown to affect surface wave propagation as well as resonant excitation of surface waves.Comment: 28 pages, 10 figures in 27 file