Brown University Center for Statistical Sciences Seminar
|
Abstract: Nonignorable (NI) missing data can result in biased inference when standard methods are applied. Analysts currently assess nonignorability by performing sensitivity analyses using models with and without a NI component. This is computationally intensive, so a simple diagnostic tool is desirable, to determine the presence and scope of NI missing data. We propose a measure based on the simple proportion of missing data, and called the Sensitivity of the Probability Interval to Nonignorability, or SPIN. The usual likelihood assuming missing at random (MAR) data is first augmented by a fixed amount for each missing value. The interval in question is then the Bayesian posterior probability interval around the parameter of interest, conditional on the augmented likelihood. The posterior probability content is easily computed, and divergence from the nominal probability level indicates susceptibility of the inference to nonignorability. SPIN is the second derivative of this probability content, and is a function of both the proportion of missing data and the quantity used to augment the likelihood. Large values of SPIN indicate that inference is highly sensitive. The framework is still that of a sensitivity analysis, but the computations are trivial. Some examples and simulation results will be presented.
*Authors: Andrea B. Troxel, Daniel F. Heitjan
Center for Fluid Mechanics Seminar
Abstract: An alternative approach to RANS turbulence modeling is discussed where the primary modeled quantities are the scalar and vector potentials of the turbulent body force - the divergence of the Reynolds stress tensor. The physical significance of these turbulent potentials is discussed and transport equations for the evolution of the potentials are proposed. The model equations have the attractive property that no constitutive relation between the mean flow and the turbulence is required allowing non-equilibrium flows to be accurately captured. However, the computational cost and complexity of the model are comparable to advanced two-equation models. Predictions for a number of basic turbulent flows are presented including: zero pressure gradient boundary layers, adverse pressure gradient boundary layers, backward facing steps, and an impinging jet.
PDE Seminar
Abstract: With mild restrictions on the initial data, we show well-posedness of the initial value problem for systems of conservation laws in one space variable with real and equal characteristic speeds and a deficiency of one eigenvector. The obtained weak solutions assume values as Borel measures on each time after a smooth solution ceases to exist. The concept of entropy density/flux functions is extended to such systems. Finally, we show that systems with well-posed initial value problems, admitting weak solutions of this type, necessarily satisfy these structural assumptions.
Joint Seminar -- Fluids, Thermal and Chemical Processes and The Center for Fluid Mechanics
National Academy of Sciences, Kiev, Ukraine | |
If you would like to meet with Dr. Nina F. Yurchenko, please contact Madeline Brewster at 863-1414. |
Abstract: Streamwise vortices are studied as a feature of fluid motion intrinsic to the vast variety of flow types. The studies are focused on mechanisms of the vortical structure evolution both under natural and controlled conditions of its formation. Special attention is paid to practical applications of the fundamental knowledge and advantages of this structure for flow control. Experimental and numerical results reveal peculiarities of the vortex scale transformation and possibilities to favorably modify the vortical structure, in particular, for heat transfer enhancement.
Brown Analysis Seminar
Scientific Computing Seminar
Abstract: The problem of determining a current distribution confined to a volume from measurements of the magnetic field it induces exterior to that volume is known to have nonunique solutions. This is, for example, the inverse problem of magnetoencephalography (MEG). Presently, MEG inversion is restricted to localized multipole currents, typically involving few dipoles and quadrupoles.
Orthogonality relationships have proven beneficial in the analogous problem of gravimetry by determining classes of mass distributions which can be uniquely inverted from measurements of the exterior gravitational potential.
We propose an orthogonality relationship applicable to the inverse MEG problem and demonstrate its use by proving uniqueness of inversion for the case of a current confined to a star-shaped shell.
PDE Seminar
Department of Mathematics Colloquium
<--- 2000 Index