Regression of ranked responses when raw responses are censored

We discuss semiparametric regression when only the ranks of responses are observed. The model is $Y_i = F (\mathbf{x}_i'{\boldsymbol\beta}_0 + \varepsilon_i)$, where $Y_i$ is the unobserved response, $F$ is a monotone increasing function, $\mathbf{x}_i$ is a known $p-$vector of covariates, ${\boldsymbol\beta}_0$ is an unknown $p$-vector of interest, and $\varepsilon_i$ is an error term independent of $\mathbf{x}_i$. We observe $\{(\mathbf{x}_i,R_n(Y_i)) : i = 1,\ldots ,n\}$, where $R_n$ is the ordinal rank function. We explore a novel estimator under Gaussian assumptions. We discuss the literature, apply the method to an Alzheimer's disease biomarker, conduct simulation studies, and prove consistency and asymptotic normality.Comment: 33 pages, 6 figure

The Bayesian Analysis of Complex, High-Dimensional Models: Can It Be CODA?

We consider the Bayesian analysis of a few complex, high-dimensional models and show that intuitive priors, which are not tailored to the fine details of the model and the estimated parameters, produce estimators which perform poorly in situations in which good, simple frequentist estimators exist. The models we consider are: stratified sampling, the partial linear model, linear and quadratic functionals of white noise and estimation with stopping times. We present a strong version of Doob's consistency theorem which demonstrates that the existence of a uniformly $\sqrt{n}$-consistent estimator ensures that the Bayes posterior is $\sqrt{n}$-consistent for values of the parameter in subsets of prior probability 1. We also demonstrate that it is, at least, in principle, possible to construct Bayes priors giving both global and local minimax rates, using a suitable combination of loss functions. We argue that there is no contradiction in these apparently conflicting findings.Comment: Published in at http://dx.doi.org/10.1214/14-STS483 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

The thermodynamic scale of inorganic crystalline metastability

The space of metastable materials offers promising new design opportunities for next-generation technological materials, such as complex oxides, semiconductors, pharmaceuticals, steels, and beyond. Although metastable phases are ubiquitous in both nature and technology, only a heuristic understanding of their underlying thermodynamics exists. We report a large-scale data-mining study of the Materials Project, a high-throughput database of density functional theory–calculated energetics of Inorganic Crystal Structure Database structures, to explicitly quantify the thermodynamic scale of metastability for 29,902 observed inorganic crystalline phases. We reveal the influence of chemistry and composition on the accessible thermodynamic range of crystalline metastability for polymorphic and phase-separating compounds, yielding new physical insights that can guide the design of novel metastable materials. We further assert that not all low-energy metastable compounds can necessarily be synthesized, and propose a principle of ‘remnant metastability’—that observable metastable crystalline phases are generally remnants of thermodynamic conditions where they were once the lowest free-energy phase.United States. Dept. of Energy. Office of Basic Energy Sciences (DE-AC02-05CH11231)United States. Dept. of Energy. Office of Basic Energy Sciences (contract UGA-0-41029-16/ER392000

Charting the complete elastic properties of inorganic crystalline compounds

The elastic constant tensor of an inorganic compound provides a complete description of the response of the material to external stresses in the elastic limit. It thus provides fundamental insight into the nature of the bonding in the material, and it is known to correlate with many mechanical properties. Despite the importance of the elastic constant tensor, it has been measured for a very small fraction of all known inorganic compounds, a situation that limits the ability of materials scientists to develop new materials with targeted mechanical responses. To address this deficiency, we present here the largest database of calculated elastic properties for inorganic compounds to date. The database currently contains full elastic information for 1,181 inorganic compounds, and this number is growing steadily. The methods used to develop the database are described, as are results of tests that establish the accuracy of the data. In addition, we document the database format and describe the different ways it can be accessed and analyzed in efforts related to materials discovery and design

An Analysis of Solution Properties of the Graph Coloring Problem

This paper concerns the analysis of solution properties of the Graph Coloring Problem. For this purpose, we introduce a property based on the notion of representative sets which are sets of vertices that are always colored the same in a set of solutions. Experimental results on well-studied DIMACS graphs show that many of them contain such sets and give interesting information about the diversity of the solutions. We also show how such an analysis may be used to improve a tabu search algorithm

Scatter Search for Graph Coloring

In this paper, we present a first scatter search approach for the Graph Coloring Problem (GCP). The evolutionary strategy scatter search operates on a set of configurations by combining two or more elements. New configurations are improved before replacing others according to their quality (fitness), and sometimes, to their diversity. Scatter search has been applied recently to some combinatorial optimization problems with promising results. Nevertheless, it seems that no attempt of scatter search has been published for the GCP. This paper presents such an investigation and reports experimental results on some wellstudied DIMACS graphs