Brown University Center for Statistical Sciences Seminar
Abstract: Advances in technology provide new diagnostic tests for early detection of disease. Frequently, these tests have continuous outcomes. One popular method to summarize the accuracy of such a test is the Receiver Operating Characteristic (ROC) curve. Methods for estimating ROC curves have long been available. To examine covariate effects, Pepe (1997, 2000) and Alonzo and Pepe (2002) proposed distribution free approaches based on a parametric regression model for the ROC curve. In this research, we extend the parametric ROC regression model by allowing an arbitrary non-parametric baseline function and propose two approaches to the estimation of the unknown parameters in the semi-parametric model. The proposed methods will be illustrated with dataset from a prostate cancer biomarker study. Simulation studies suggest that the extra flexibility inherent in the semi-parametric method is gained with little loss in statistical efficiency.
Scientific Computing Seminar
Abstract: Motivated by applications to inertial confinement fusion and astrophysics we investigate the evolution of instabilities generated by a shock interacting with a perturbed interface (the Richmyer-Meshkov instability) using the formally high order weighted essentially non-oscillatory (WENO) shock-capturing method. The vorticicity deposited on the interface by the shock drives the evolution of the instability and a mixing layer develops.
First, we report comprehensive numerical simulations of the mixing layer growth corresponding to a Mach 1.2 shock and a single-mode perturbation.The mixing layer growth and other quantites are investigated and compared to the predictions of analytical models both before and after re-shock.
Second, we report simulations for the case when the interface and the plane of the shock are not normal. In this case, the development of shear is observed after the shock, and the interplay of the Richtmyer-Meshkov and Kelvin-Helholtz instability drives the evolution of the mixing layer. An analysis of the mixing and a systematic discussion of the effects of the numerical method are presented. Results using different formal order of accuracy and spatial resolutions are compared.
The simulation results suggest that the WENO shock-capturing method is an excellent choice for the investigation of the evolution of complex hydrodynamic flows induced by shock-interface interactions.
Pop Coding Seminar
PDE Seminar
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