Seven Years with the Swift Supergiant Fast X-ray Transients Project

Supergiant Fast X-ray Transients (SFXTs) are HMXBs with OB supergiant companions. I review the results of the Swift SFXT Project, which since 2007 has been exploiting Swift's capabilities in a systematic study of SFXTs and supergiant X-ray binaries (SGXBs) by combining follow-ups of outbursts, when detailed broad-band spectroscopy is possible, with long-term monitoring campaigns, when the out-of-outburst fainter states can be observed. This strategy has led us to measure their duty cycles as a function of luminosity, to extract their differential luminosity distributions in the soft X-ray domain, and to compare, with unprecedented detail, the X-ray variability in these different classes of sources. I also discuss the "seventh year crisis", the challenges that the recent Swift observations are making to the prevailing models attempting to explain the SFXT behaviour.Comment: 12 pages, 9 figures, 1 table. Review paper for "Swift 10 Years of Discovery" conference. Accepted for Publication in the Journal of High Energy Astrophysic

Optimal testing of equivalence hypotheses

In this paper we consider the construction of optimal tests of equivalence hypotheses. Specifically, assume X_1,..., X_n are i.i.d. with distribution P_{\theta}, with \theta \in R^k. Let g(\theta) be some real-valued parameter of interest. The null hypothesis asserts g(\theta)\notin (a,b) versus the alternative g(\theta)\in (a,b). For example, such hypotheses occur in bioequivalence studies where one may wish to show two drugs, a brand name and a proposed generic version, have the same therapeutic effect. Little optimal theory is available for such testing problems, and it is the purpose of this paper to provide an asymptotic optimality theory. Thus, we provide asymptotic upper bounds for what is achievable, as well as asymptotically uniformly most powerful test constructions that attain the bounds. The asymptotic theory is based on Le Cam's notion of asymptotically normal experiments. In order to approximate a general problem by a limiting normal problem, a UMP equivalence test is obtained for testing the mean of a multivariate normal mean.Comment: Published at http://dx.doi.org/10.1214/009053605000000048 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Balmer Line Variations in the Radio-Loud AGN PG 1512+370

We present spectroscopic observations of the quasar PG~1512+370, covering the Hbeta line spectral range and collected at moderate resolution (2-7 A FWHM) from 1988 to 1996. The observations show that the blue wing of the Hbeta broad profile component has changed significantly in flux and shape between 1988 and 1990 and between 1995 and 1996. A displaced blue peak on the Hbeta profile, visible in 1988, but not in the 1990-1995 spectra, is revealed again in one of the spectra obtained in 1996. The blue peak (in both the 1988 and 1996 spectra) is centered at Delta v_r ~ -3000 +/- 500 km/s from the rest frame defined by the narrow component of Hbeta, and the OIII lambda4959,5007 lines. We discuss several conflicting interpretations of the data. We find that the variability of the Hbeta blue wing is consistent with Balmer line emission from regions whose motion is predominantly radial, if variations of the blue wing are a response to continuum changes. Alternatively, we note that observed Hbeta line profile variations are consistent with a variable line component as in a ``binary black hole'' scenario. More frequent observations of Hbeta are needed to distinguish among these hypotheses.Comment: 19 pages, 1 embedded figure (eps), to appear in ApJ 49

Explicit nonparametric confidence intervals for the variance with guaranteed coverage

In this paper, we provide a method for constructing confidence intervals for the variance that exhibit guaranteed coverage probability for any sample size, uniformly over a wide class of probability distributions. In contrast, standard methods achieve guaranteed coverage only in the limit for a fixed distribution or for any sample size over a very restrictive (parametric) class of probability distributions. Of course, it is impossible to construct effective confidence intervals for the variance without some restriction, due to a result of Bahadur and Savage (1956). However, it is possible if the observations lie in a fixed compact set. We also consider the case of lower confidence bounds without any support restriction. Our method is based on the behavior of the variance over distributions that lie within a Kolmogorov-Smirnov confidence band for the underlying distribution. The method is a generalization of an idea of Anderson (1967), who considered only the case of the mean; it applies to very general parameters, and particularly the variance. While typically it is not clear how to compute these intervals explicitly, for the special case of the variance we provide an algorithm to do so. Asymptotically, the length of the intervals is of order n -1/2 in probability), so that, while providing guaranteed coverage, they are not overly conservative. A small simulation study examines the finite sample behavior of the proposed intervals