Exact Post-Selection Inference for Sequential Regression Procedures

We propose new inference tools for forward stepwise regression, least angle regression, and the lasso. Assuming a Gaussian model for the observation vector y, we first describe a general scheme to perform valid inference after any selection event that can be characterized as y falling into a polyhedral set. This framework allows us to derive conditional (post-selection) hypothesis tests at any step of forward stepwise or least angle regression, or any step along the lasso regularization path, because, as it turns out, selection events for these procedures can be expressed as polyhedral constraints on y. The p-values associated with these tests are exactly uniform under the null distribution, in finite samples, yielding exact type I error control. The tests can also be inverted to produce confidence intervals for appropriate underlying regression parameters. The R package "selectiveInference", freely available on the CRAN repository, implements the new inference tools described in this paper.Comment: 26 pages, 5 figure

Optimal Ensemble Length of Mixed Separable States

The optimal (pure state) ensemble length of a separable state, A, is the minimum number of (pure) product states needed in convex combination to construct A. We study the set of all separable states with optimal (pure state) ensemble length equal to k or fewer. Lower bounds on k are found below which these sets have measure 0 in the set of separable states. In the bipartite case and the multiparticle case where one of the particles has significantly more quantum numbers than the rest, the lower bound for non-pure state ensembles is sharp. A consequence of our results is that for all two particle systems, except possibly those with a qubit or those with a nine dimensional Hilbert space, and for all systems with more than two particles the optimal pure state ensemble length for a randomly picked separable state is with probability 1 greater than the state's rank. In bipartite systems with probability 1 it is greater than 1/4 the rank raised to the 3/2 power and in a system with p qubits with probability 1 it is greater than (2^2p)/(1+2p), which is almost the square of the rank.Comment: 8 page

Rejoinder: "A significance test for the lasso"

Rejoinder of "A significance test for the lasso" by Richard Lockhart, Jonathan Taylor, Ryan J. Tibshirani, Robert Tibshirani [arXiv:1301.7161].Comment: Published in at http://dx.doi.org/10.1214/14-AOS1175REJ the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org). With Correctio

Referencing Sources of Molecular Spectroscopic Data in the Era of Data Science: Application to the HITRAN and AMBDAS Databases

The application described has been designed to create bibliographic entries in large databases with diverse sources automatically, which reduces both the frequency of mistakes and the workload for the administrators. This new system uniquely identifies each reference from its digital object identifier (DOI) and retrieves the corresponding bibliographic information from any of several online services, including the SAO/NASA Astrophysics Data Systems (ADS) and CrossRef APIs. Once parsed into a relational database, the software is able to produce bibliographies in any of several formats, including HTML and BibTeX, for use on websites or printed articles. The application is provided free-of-charge for general use by any scientific database. The power of this application is demonstrated when used to populate reference data for the HITRAN and AMBDAS databases as test cases. HITRAN contains data that is provided by researchers and collaborators throughout the spectroscopic community. These contributors are accredited for their contributions through the bibliography produced alongside the data returned by an online search in HITRAN. Prior to the work presented here, HITRAN and AMBDAS created these bibliographies manually, which is a tedious, time-consuming and error-prone process. The complete code for the new referencing system can be found at \url{https://github.com/hitranonline/refs}.Comment: 11 pages, 5 figures, already published online at https://doi.org/10.3390/atoms802001

Crown Radius and Diameter at Breast Height Relationships for Six Bottomland Hardwood Species

The relationship between a tree\u27s crown radius and diameter at breast height (DBH) has a variety of uses including forest competition studies, tree crown densities, spacing and stocking relationships, wildlife habitat suitability models, and tree volume estimations. Estimating DBH from mean crown radius (MCR) is of interest to natural resource managers because MCR can be estimated from high resolution digital imagery using remote sensing techniques. DBH is a common tree dimensional characteristic that is used to quantify tree and stand structure. This research presents MCR/DBH and DBH/MCR relationships for boxelder (Acer negundo L.), sweet pecan (Carya illinoensis (Wang) K.Koch), sugarberry (Celtis laevigata Willd.), green ash (Fraxinus pennsylvanica Marsh.), Nuttall oak (Quercus nuttallii Palmer), and American elm (Ulmus americana L.). The linear model, y =a+b * x, provided the best model fit with adjusted r values of 0.567 to 0.855 for the 6 species. Crown radius can be determined from digital imagery and then used to predict DBH

Rejoinder to “A Significance Test for the Lasso”

We would like to thank the editors and referees for their considerable efforts that improved our paper, and all of the discussants for their feedback, and their thoughtful and stimulating comments. Linear models are central in applied statistics, and inference for adaptive linear modeling is an important active area of research. Our paper is clearly not the last word on the subject! Several of the discussants introduce novel proposals for this problem; in fact, many of the discussions are interesting “mini-papers ” on their own, and we will not attempt to reply to all of the points that they raise. Our hope is that our paper and the excellent accompanying discussions will serve as a helpful resource for researchers interested in this topic. Since the writing of our original paper, we have (with many our of graduate students) extended the work considerably. Before responding to the discussants, we will first summarize this new work because it will be relevant to our responses. • As mentioned in the last section of the paper, we have derived a “spacing ” test of the global null hypothesis, β ∗ = 0, which takes the for

A first-in-human study of AMG 208, an oral MET inhibitor, in adult patients with advanced solid tumors.

BackgroundThis first-in-human study evaluated AMG 208, a small-molecule MET inhibitor, in patients with advanced solid tumors.MethodsThree to nine patients were enrolled into one of seven AMG 208 dose cohorts (25, 50, 100, 150, 200, 300, and 400 mg). Patients received AMG 208 orally on days 1 and days 4-28 once daily. The primary objectives were to evaluate the safety, tolerability, pharmacokinetics, and maximum tolerated dose (MTD) of AMG 208.ResultsFifty-four patients were enrolled. Six dose-limiting toxicities were observed: grade 3 increased aspartate aminotransferase (200 mg), grade 3 thrombocytopenia (200 mg), grade 4 acute myocardial infarction (300 mg), grade 3 prolonged QT (300 mg), and two cases of grade 3 hypertension (400 mg). The MTD was not reached. The most frequent grade ≥3 treatment-related adverse event was anemia (n = 3) followed by hypertension, prolonged QT, and thrombocytopenia (two patients each). AMG 208 exposure increased linearly with dose; mean plasma half-life estimates were 21.4-68.7 hours. One complete response (prostate cancer) and three partial responses (two in prostate cancer, one in kidney cancer) were observed.ConclusionsIn this study, AMG 208 had manageable toxicities and showed evidence of antitumor activity, particularly in prostate cancer

Conceptual Basis for an Index of Forest Integrity for Upland Coastal Plain Ecosystems

Following the recent trend to manage natural resources for sustainability, ecologists, resource managers and policymakers are beginning to think of the management of forest ecosystems in terms of ecosystem health or ecosystem integrity. Biologists are increasingly recognizing that use of chemical assays in assessing the condition of an ecosystem has limited value, and that biological factors, e.g., species diversity and composition, can be useful characters in the analysis of biotic integrity. An index of biotic integrity (IBI) has been developed for riverine ecosystems in the Midwest U.S., using fish species diversity, indicator population analysis, trophic structure assessment, and physiological abnormalities in fish as measurable surrogates for biotic integrity . This paper explores the development of an analogous index of forest integrity (IFI) to be applied to the upland coastal plain forests of southern Arkansas and northern Louisiana. The IFI developed here includes sampling and analysis of population trends of dominant plant taxa, plant species diversity, and horizontal and vertical vegetative structure at midstory, shrub and detritus levels