Exact Enumeration and Sampling of Matrices with Specified Margins

We describe a dynamic programming algorithm for exact counting and exact uniform sampling of matrices with specified row and column sums. The algorithm runs in polynomial time when the column sums are bounded. Binary or non-negative integer matrices are handled. The method is distinguished by applicability to non-regular margins, tractability on large matrices, and the capacity for exact sampling

Exact sampling and counting for fixed-margin matrices

The uniform distribution on matrices with specified row and column sums is often a natural choice of null model when testing for structure in two-way tables (binary or nonnegative integer). Due to the difficulty of sampling from this distribution, many approximate methods have been developed. We will show that by exploiting certain symmetries, exact sampling and counting is in fact possible in many nontrivial real-world cases. We illustrate with real datasets including ecological co-occurrence matrices and contingency tables.Comment: Published in at http://dx.doi.org/10.1214/13-AOS1131 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org). arXiv admin note: text overlap with arXiv:1104.032

Inconsistency of Pitman-Yor process mixtures for the number of components

In many applications, a finite mixture is a natural model, but it can be difficult to choose an appropriate number of components. To circumvent this choice, investigators are increasingly turning to Dirichlet process mixtures (DPMs), and Pitman-Yor process mixtures (PYMs), more generally. While these models may be well-suited for Bayesian density estimation, many investigators are using them for inferences about the number of components, by considering the posterior on the number of components represented in the observed data. We show that this posterior is not consistent --- that is, on data from a finite mixture, it does not concentrate at the true number of components. This result applies to a large class of nonparametric mixtures, including DPMs and PYMs, over a wide variety of families of component distributions, including essentially all discrete families, as well as continuous exponential families satisfying mild regularity conditions (such as multivariate Gaussians).Comment: This is a general treatment of the problem discussed in our related article, "A simple example of Dirichlet process mixture inconsistency for the number of components", Miller and Harrison (2013) arXiv:1301.270

Editors' notes

No abstract.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/57347/1/279_ftp.pd

Accelerated return to sport after osteochondral autograft plug transfer

Background:Previous studies have reported varying return-to-sport protocols after knee cartilage restoration procedures.Purpose:To (1) evaluate the time for return to sport in athletes with an isolated chondral injury who underwent an accelerated return-to-sport protocol after osteochondral autograft plug transfer (OAT) and (2) evaluate clinical outcomes to assess for any consequences from the accelerated return to sport.Study Design:Case series; Level of evidence, 4.Methods:An institutional cohort of 152 OAT procedures was reviewed, of which 20 competitive athletes met inclusion and exclusion criteria. All patients underwent a physician-directed accelerated rehabilitation program after their procedure. Return to sport was determined for all athletes. Clinical outcomes were assessed using International Knee Documentation Committee (IKDC) and Tegner scores as well as assessment of level of participation on return to sport.Results:Return-to-sport data were available for all 20 athletes; 13 of 20 athletes (65%) were available for clinical evaluation at a mean 4.4-year follow-up. The mean time for return to sport for all 20 athletes was 82.9 ± 25 days (range, 38-134 days). All athletes were able to return to sport at their previous level and reported that they were satisfied or very satisfied with their surgical outcome and ability to return to sport. The mean postoperative IKDC score was 84.5 ± 9.5. The mean Tegner score prior to injury was 8.9 ± 1.7; it was 7.7 ± 1.9 at final follow-up.Conclusion:Competitive athletes with traumatic chondral defects treated with OAT managed using this protocol had reduced time to preinjury activity levels compared with what is currently reported, with excellent clinical outcomes and no serious long-term sequelae.</jats:sec

Composition Effects on Kilonova Spectra and Light Curves: I

The merger of neutron star binaries is believed to eject a wide range of heavy elements into the universe. By observing the emission from this ejecta, scientists can probe the ejecta properties (mass, velocity and composition distributions). The emission (a.k.a. kilonova) is powered by the radioactive decay of the heavy isotopes produced in the merger and this emission is reprocessed by atomic opacities to optical and infra-red wavelengths. Understanding the ejecta properties requires calculating the dependence of this emission on these opacities. The strong lines in the optical and infra-red in lanthanide opacities have been shown to significantly alter the light-curves and spectra in these wavelength bands, arguing that the emission in these wavelengths can probe the composition of this ejecta. Here we study variations in the kilonova emission by varying individual lanthanide (and the actinide uranium) concentrations in the ejecta. The broad forest of lanthanide lines makes it difficult to determine the exact fraction of individual lanthanides. Nd is an exception. Its opacities above 1 micron are higher than other lanthanides and observations of kilonovae can potentially probe increased abundances of Nd. Similarly, at early times when the ejecta is still hot (first day), the U opacity is strong in the 0.2-1 micron wavelength range and kilonova observations may also be able to constrain these abundances