Model-robust regression and a Bayesian ``sandwich'' estimator

We present a new Bayesian approach to model-robust linear regression that leads to uncertainty estimates with the same robustness properties as the Huber--White sandwich estimator. The sandwich estimator is known to provide asymptotically correct frequentist inference, even when standard modeling assumptions such as linearity and homoscedasticity in the data-generating mechanism are violated. Our derivation provides a compelling Bayesian justification for using this simple and popular tool, and it also clarifies what is being estimated when the data-generating mechanism is not linear. We demonstrate the applicability of our approach using a simulation study and health care cost data from an evaluation of the Washington State Basic Health Plan.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS362 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Hydrogen solubility in zirconium intermetallic second phase particles

The enthalpies of solution of H in Zr binary intermetallic compounds formed with Cu, Cr, Fe, Mo, Ni, Nb, Sn and V were calculated by means of density functional theory simulations and compared to that of H in {\alpha}-Zr. It is predicted that all Zr-rich phases (formed with Cu, Fe, Ni and Sn), and those phases formed with Nb and V, offer lower energy, more stable sites for H than {\alpha}-Zr. Conversely, Mo and Cr containing phases do not provide preferential solution sites for H. In all cases the most stable site for H are those that offer the highest coordination fraction of Zr atoms. Often these are four Zr tetrahedra but not always. Implications with respect to H-trapping properties of commonly observed ternary phases such as Zr(Cr,Fe)2, Zr2(Fe,Ni) and Zr(Nb,Fe)2 are also discussed.Comment: manuscript accepted for publication in Journal of Nuclear Materials (2013

Trading Bias for Precision: Decision Theory for Intervals and Sets

Interval- and set-valued decisions are an essential part of statistical inference. Despite this, the justification behind them is often unclear, leading in practice to a great deal of confusion about exactly what is being presented. In this paper we review and attempt to unify several competing methods of interval-construction, within a formal decision-theoretic framework. The result is a new emphasis on interval-estimation as a distinct goal, and not as an afterthought to point estimation. We also see that representing intervals as trade-offs between measures of precision and bias unifies many existing approaches -- as well as suggesting interpretable criteria to calibrate this trade-off. The novel statistical arguments produced allow many extensions, and we apply these to resolve several outstanding areas of disagreement between Bayesians and frequentists

Model-Robust Bayesian Regression and the Sandwich Estimator

PLEASE NOTE THAT AN UPDATED VERSION OF THIS RESEARCH IS AVAILABLE AS WORKING PAPER 338 IN THE UNIVERSITY OF WASHINGTON BIOSTATISTICS WORKING PAPER SERIES (http://www.bepress.com/uwbiostat/paper338). In applied regression problems there is often sufficient data for accurate estimation, but standard parametric models do not accurately describe the source of the data, so associated uncertainty estimates are not reliable. We describe a simple Bayesian approach to inference in linear regression that recovers least-squares point estimates while providing correct uncertainty bounds by explicitly recognizing that standard modeling assumptions need not be valid. Our model-robust development parallels frequentist estimating equations and leads to intervals with the same robustness properties as the ’sandwich’ estimator

Direct numerical simulations of statistically steady, homogeneous, isotropic fluid turbulence with polymer additives

We carry out a direct numerical simulation (DNS) study that reveals the effects of polymers on statistically steady, forced, homogeneous, isotropic fluid turbulence. We find clear manifestations of dissipation-reduction phenomena: On the addition of polymers to the turbulent fluid, we obtain a reduction in the energy dissipation rate, a significant modification of the fluid energy spectrum, especially in the deep-dissipation range, a suppression of small-scale intermittency, and a decrease in small-scale vorticity filaments. We also compare our results with recent experiments and earlier DNS studies of decaying fluid turbulence with polymer additives.Comment: consistent with the published versio

Toward a structural understanding of turbulent drag reduction: nonlinear coherent states in viscoelastic shear flows

Nontrivial steady flows have recently been found that capture the main structures of the turbulent buffer layer. We study the effects of polymer addition on these "exact coherent states" (ECS) in plane Couette flow. Despite the simplicity of the ECS flows, these effects closely mirror those observed experimentally: Structures shift to larger length scales, wall-normal fluctuations are suppressed while streamwise ones are enhanced, and drag is reduced. The mechanism underlying these effects is elucidated. These results suggest that the ECS are closely related to buffer layer turbulence.Comment: 5 pages, 3 figures, published version, Phys. Rev. Lett. 89, 208301 (2002

Cognitive Organization, Perceptions of Parenting and Depression Symptoms in Early Adolescence

Despite its strong relation to depression and theorized development across childhood and adolescence, cognitive schema organization has not been explored in early adolescence, a sensitive developmental period for first depression onset. Schema organization is theorized to derive from childhood cognitive internalizations of caregiving relationships, such as critical parenting experiences (e.g., Young et al. in Schema therapy: a practitioner’s guide. Guilford Press, New York, 2003). Thus, the current investigation considers the organization of positive and negative schemas with youth’s perceptions of parental warmth and psychological control and self-reported emotional functioning. Participants were 198 boys and girls aged 9–14 years who completed the Psychological Distance Scaling Task, measures of perceptions of parenting behaviors, anxiety symptoms and depression symptoms. Consistent with hypotheses, higher depression, but not anxiety symptoms were associated with a loosely-interconnected positive schema organization and a tightly-interconnected negative schema organization. Parental responsiveness emerged as the strongest predictor of negative schema structure. Implications for cognitive-developmental theories of depression and early identification of depression risk are discussed

Universal long-time properties of Lagrangian statistics in the Batchelor regime and their application to the passive scalar problem

We consider transport of dynamically passive quantities in the Batchelor regime of smooth in space velocity field. For the case of arbitrary temporal correlations of the velocity we formulate the statistics of relevant characteristics of Lagrangian motion. This allows to generalize many results obtained previously for the delta-correlated in time strain, thus answering the question of universality of these results.Comment: 11 pages, revtex; added references, typos correcte