THREE-DIMENSIONAL RADIATIVE TRANSFER SIMULATIONS OF THE SCATTERING POLARIZATION OF THE HYDROGEN LY alpha LINE IN A MAGNETOHYDRODYNAMIC MODEL OF THE CHROMOSPHERE-CORONA TRANSITION REGION
ASTROPHYSICAL JOURNAL
Authors: Stepan, J.; Trujillo Bueno, J.; Leenaarts, J.; Carlsson, M.
Abstract
Probing the magnetism of the upper solar chromosphere requires measuring and modeling the scattering polarization produced by anisotropic radiation pumping in UV spectral lines. Here we apply PORTA (a novel radiative transfer code) to investigate the hydrogen Ly alpha line in a three-dimensional model of the solar atmosphere resulting from a state of the art magnetohydrodynamic (MHD) simulation. At full spatial resolution the linear polarization signals are very significant all over the solar disk, with a large fraction of the field of view (FOV) showing line-center amplitudes well above the 1% level. Via the Hanle effect the line-center polarization signals are sensitive to the magnetic field of the model's transition region, even when its mean field strength is only 15 G. The breaking of the axial symmetry of the radiation field produces significant forward-scattering polarization in Ly alpha, without the need of an inclined magnetic field. Interestingly, the Hanle effect tends to decrease such forward-scattering polarization signals in most of the points of the FOV. When the spatial resolution is degraded, the line-center polarization of Ly alpha drops below the 1% level, reaching values similar to those previously found in one-dimensional (1D) semi-empirical models (i.e., up to about 0.5%). The center to limb variation (CLV) of the spatially averaged polarization signals is qualitatively similar to that found in 1D models, with the largest line-center amplitudes at mu = cos theta approximate to 0.4 (theta being the heliocentric angle). These results are important, both for designing the needed space-based instrumentation and for a reliable interpretation of future observations of the Ly alpha polarization.
Benefits of quantile regression for the analysis of customer lifetime value in a contractual setting: An application in financial services
EXPERT SYSTEMS WITH APPLICATIONS
Authors: Benoit, Dries F.; Van den Poel, Dirk
Abstract
The move towards a customer-centred approach to marketing, coupled with the increasing availability of customer transaction data, has led to an interest in understanding and estimating customer lifetime value (CLV). Several authors point out that, when evaluating customer profitability, profitable customers are rare compared to the unprofitable ones. In spite of this, most authors fail to recognize the implications of these skewed distributions on the performance of models they use. In this study, we propose analyzing CLV by means of quantile regression. In a financial services application, we show that this technique provides management more in-depth insights into the effects of the covariates that are missed with linear regression. Moreover, we show that in the common situation where interest is in a top-customer segment, quantile regression outperforms linear regression. The method also has the ability of constructing prediction intervals. Combining the CLV point estimate with the prediction intervals leads to a new segmentation scheme that is the first to account for uncertainty in the predictions. This segmentation is ideally suited for managing the portfolio of customers. (C) 2009 Published by Elsevier Ltd.