Brownian distance covariance

Distance correlation is a new class of multivariate dependence coefficients applicable to random vectors of arbitrary and not necessarily equal dimension. Distance covariance and distance correlation are analogous to product-moment covariance and correlation, but generalize and extend these classical bivariate measures of dependence. Distance correlation characterizes independence: it is zero if and only if the random vectors are independent. The notion of covariance with respect to a stochastic process is introduced, and it is shown that population distance covariance coincides with the covariance with respect to Brownian motion; thus, both can be called Brownian distance covariance. In the bivariate case, Brownian covariance is the natural extension of product-moment covariance, as we obtain Pearson product-moment covariance by replacing the Brownian motion in the definition with identity. The corresponding statistic has an elegantly simple computing formula. Advantages of applying Brownian covariance and correlation vs the classical Pearson covariance and correlation are discussed and illustrated.Comment: This paper discussed in: [arXiv:0912.3295], [arXiv:1010.0822], [arXiv:1010.0825], [arXiv:1010.0828], [arXiv:1010.0836], [arXiv:1010.0838], [arXiv:1010.0839]. Rejoinder at [arXiv:1010.0844]. Published in at http://dx.doi.org/10.1214/09-AOAS312 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

DISCO analysis: A nonparametric extension of analysis of variance

In classical analysis of variance, dispersion is measured by considering squared distances of sample elements from the sample mean. We consider a measure of dispersion for univariate or multivariate response based on all pairwise distances between-sample elements, and derive an analogous distance components (DISCO) decomposition for powers of distance in $(0,2]$. The ANOVA F statistic is obtained when the index (exponent) is 2. For each index in $(0,2)$, this decomposition determines a nonparametric test for the multi-sample hypothesis of equal distributions that is statistically consistent against general alternatives.Comment: Published in at http://dx.doi.org/10.1214/09-AOAS245 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

On the variational distance of two trees

A widely studied model for generating sequences is to ``evolve'' them on a tree according to a symmetric Markov process. We prove that model trees tend to be maximally ``far apart'' in terms of variational distance.Comment: Published at http://dx.doi.org/10.1214/105051606000000196 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

First description of myxozoans from Syria: novel records of hexactinomyxon, triactinomyxon and endocapsa actinospore types

Oligochaete worms collected in late March and early April 2005 from 3 freshwater biotopes in Syria were surveyed over an 11 wk period for myxosporean parasites (Myxozoa). Three types of novel actinospore stages were identified from 1 host species, Psammoryctides albicola. A hexactinomyxon was found in 6 P. albicola (7.5%) collected from a branch of the River Orontes, north of the city of Hama. A triactinomyxon and an endocapsa were found in single P. albicola specimens from the Al-Thaurah region of the Euphrates River (Lake Assad). No oligochaetes collected from Al-Ghab fish farm (Orontes region) released actinospores during the observation period. The present study is the first description of myxosporeans, including actinospore stages, from Syria. The 3 types described herein differ morphologically and molecularly (18S rDNA) from published records

Measuring and testing dependence by correlation of distances

Distance correlation is a new measure of dependence between random vectors. Distance covariance and distance correlation are analogous to product-moment covariance and correlation, but unlike the classical definition of correlation, distance correlation is zero only if the random vectors are independent. The empirical distance dependence measures are based on certain Euclidean distances between sample elements rather than sample moments, yet have a compact representation analogous to the classical covariance and correlation. Asymptotic properties and applications in testing independence are discussed. Implementation of the test and Monte Carlo results are also presented.Comment: Published in at http://dx.doi.org/10.1214/009053607000000505 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Discovery of the spectroscopic binary nature of three bright southern Cepheids

We present an analysis of spectroscopic radial velocity and photometric data of three bright Galactic Cepheids: LR Trianguli Australis (LR TrA), RZ Velorum (RZ Vel), and BG Velorum (BG Vel). Based on new radial velocity data, these Cepheids have been found to be members of spectroscopic binary systems. The ratio of the peak-to-peak radial velocity amplitude to photometric amplitude indicates the presence of a companion for LR TrA and BG Vel. IUE spectra indicate that the companions of RZ Vel and BG Vel cannot be hot stars. The analysis of all available photometric data revealed that the pulsation period of RZ Vel and BG Vel varies monotonically, due to stellar evolution. Moreover, the longest period Cepheid in this sample, RZ Vel, shows period fluctuations superimposed on the monotonic period increase. The light-time effect interpretation of the observed pattern needs long-term photometric monitoring of this Cepheid. The pulsation period of LR TrA has remained constant since the discovery of its brightness variation. Using statistical data, it is also shown that a large number of spectroscopic binaries still remain to be discovered among bright classical Cepheids.Comment: 9 pages, 14 figure

Discovery of the spectroscopic binary nature of six southern Cepheids

We present the analysis of photometric and spectroscopic data of six bright Galactic Cepheids: GH Carinae, V419 Centauri, V898 Centauri, AD Puppis, AY Sagittarii, and ST Velorum. Based on new radial velocity data (in some cases supplemented with earlier data available in the literature), these Cepheids have been found to be members in spectroscopic binary systems. V898 Cen turned out to have one of the largest orbital radial velocity amplitude (> 40 km/s) among the known binary Cepheids. The data are insufficient to determine the orbital periods nor other orbital elements for these new spectroscopic binaries. These discoveries corroborate the statement on the high frequency of occurrence of binaries among the classical Cepheids, a fact to be taken into account when calibrating the period-luminosity relationship for Cepheids. We have also compiled all available photometric data that revealed that the pulsation period of AD Pup, the longest period Cepheid in this sample, is continuously increasing with Delta P = 0.004567 d/century, likely to be caused by stellar evolution. The wave-like pattern superimposed on the parabolic O-C graph of AD Pup may well be caused by the light-time effect in the binary system. ST Vel also pulsates with a continuously increasing period. The other four Cepheids are characterised with stable pulsation periods in the last half century.Comment: accepted by the MNRAS, 11 pages, 16 figures, 18 tables, a part of the data can be downloaded from the online version of this articl

A photometric monitoring of bright high-amplitude delta Scuti stars. I. The double-mode pulsation of V567 Ophiuchi

We present the first results of an observational project, which addresses the period changing behaviour of a sample of high-amplitude delta Scuti stars. In this paper we discuss the double-mode nature of V567 Ophiuchi. It was observed on 15 nights in two consecutive years in order to resolve the long-standing ambiguity related to its secondary period. A frequency analysis of almost 5000 individual single-filtered CCD V measurements resulted in two independent frequencies (f_1=6.6879 c/d and f_2=11.8266 c/d) with a ratio of f_1/f_2=0.565. Earlier data taken from the literature were used to refine the dominant period, and the re-analysis supports the existence of the secondary period. Possible asteroseismological implications are briefly discussed