Robust and Efficient Methods for Bayesian Finite Population Inference.

Bayesian model-based approaches provide data-driven estimates of population quantity of interest from complex survey data to achieve balance between bias correction and efficiency. We focus on the issue of accommodating sample weights equal to the inverse of the probabilities of inclusion. In settings with highly variable weights, weight "trimming" is often employed in an ad-hoc manner to decrease variance, while possibly increasing bias. We consider three model-based methods to provide principled bias-variance tradeoffs. Weighted estimators can be developed in a model-based framework by including interactions between the quantity of interest and the weights; weight pooling builds a variable selection model that drops interactions on various weight values; and estimation proceeds using the posterior distribution of model averages. The extension considers a weight pooling linear spline model that uses a linear spline to capture regression coefficient patterns for all strata, and collapses together the strata with minor differences. Our model achieves robustness when weights are needed to guard against model misspecification, and efficiency when weight-coefficient interactions could be ignored. We also model interactions between the weights and estimators of interest as random effects, reducing overall RMSEs by shrinking interactions toward zero when such shrinkage is supported by data. We adapt a flexible Laplace prior distribution to gain robustness against model misspecification. We find that weight smoothing models with Laplace priors approximate unweighted estimates when weighting is not necessary, and could greatly reduce the RMSE if strong pattern exists in data in linear model setting. Under logistic regression with same sample size, the estimates are still robust, but with less gain in efficiency. Finally, we adapt a Dirichlet process mixture (DPM) model that can approximat highly-skewed and multimodal distributions, often with few components. The extended weighted DPM version define the DP prior as a mixture of DP random basis measures that is a function of covariates, extends applications to regression, and creates a natural link to survey weights. We also investigate its application to provide a new approach for quantile regression inference with complex survey design. Simulation results suggest great reduction in RMSE from weighted DPM method under most of the scenarios.PhDBiostatisticsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/111372/1/xiaxi_1.pd

The Renaissance of Black Phosphorus

One hundred years after its first successful synthesis in the bulk form in 1914, black phosphorus (black P) was recently rediscovered from the perspective of a two-dimensional (2D) layered material, attracting tremendous interest from condensed matter physicists, chemists, semiconductor device engineers and material scientists. Similar to graphite and transition metal dichalcogenides (TMDs), black P has a layered structure but with a unique puckered single layer geometry. Because the direct electronic band gap of thin film black P can be varied from 0.3 to around 2 eV, depending on its film thickness, and because of its high carrier mobility and anisotropic in-plane properties, black P is promising for novel applications in nanoelectronics and nanophotonics different from graphene and TMDs. Black P as a nanomaterial has already attracted much attention from researchers within the past year. Here, we offer our opinions on this emerging material with the goal of motivating and inspiring fellow researchers in the 2D materials community and the broad readership of PNAS to discuss and contribute to this exciting new field. We also give our perspectives on future 2D and thin film black P research directions, aiming to assist researchers coming from a variety of disciplines who are desirous of working in this exciting research field.Comment: 23 pages, 6 figures, perspective article, appeared online in PNA

Difluoro­[2-(quinolin-2-yl)phenolato]borane

The title compound, C15H10BF2NO, was synthesized by the reaction of 2-(quinolin-2-yl)phenol and boron trifluoride etherate. The quinoline ring system and the benzene ring are twisted, making a dihedral angle of 8.3 (2)°. In the crystal, π–π inter­actions between the aromatic rings [centroid–centroid distance = 3.638 (9) Å] link the mol­ecules into chains propagating in [100]