Properties of Bayes Sequential Tests

Consider the problem of sequentially testing composite, contiguous hypotheses where the risk function is a linear combination of the probability of error in the terminal decision and the expected sample size. Assume that the common boundary of the closures of the null and the alternative hypothesis is compact. Observations are independent and identically distributed. We study properties of Bayes tests. One property is the exponential boundedness of the stopping time. Another property is continuity of the risk functions. The continuity property is used to establish complete class theorems as opposed to the essentially complete class theorems in Brown, Cohen and Strawderman

Bounded Stopping Times for a Class of Sequential Bayes Tests

Consider the problem of sequentially testing a null hypothesis vs an alternative hypothesis when the risk function is a linear combination of probability of error in the terminal decision and expected sample size (i.e., constant cost per observation.) Assume that the parameter space is the union of null and alternative, the parameter space is convex, the intersection of null and alternative is empty, and the common boundary of the closures of null and alternative is nonempty and compact. Assume further that observations are drawn from a p-dimensional exponential family with an open p-dimensional parameter space. Sufficient conditions for Bayes tests to have bounded stopping times are given

Microwave Components

Contains reports on two research projects

Optical/Near-Infrared Observations of GRO J1744-28

We present results from a series of optical (g and r-band) and near-infrared (K'-band) observations of the region of the sky including the entire XTE and ROSAT error circles for the ``Bursting Pulsar'' GRO J1744-28. These data were taken with the Astrophysical Research Consortium's 3.5-m telescope at Apache Point Observatory and with the 2.2-m telescope at the European Southern Observatory. We see no new object, nor any significant brightening of any known object, in these error circles, with the exception of an object detected in our 8 February 1996 image. This object has already been proposed as a near-infrared counterpart to GRO J1744-28. While it is seen in only two of our ten 8 February frames, there is no evidence that this is an instrumental artifact, suggesting the possibility of near-infrared flares from GRO J1744-28, similar to those that have been reported from the Rapid Burster. The distance to the ``Bursting Pulsar'' must be more than 2 kpc, and we suggest that it is more than 7 kpc.Comment: 21 pages, 5 JPEG plates, 2 postscript figures. This paper will appear in the May 1, 1997 edition of the Astrophysical Journa

The Black Hole-Bulge Relationship in Luminous Broad-Line Active Galactic Nuclei and Host Galaxies

We have measured the stellar velocity dispersions (\sigma_*) and estimated the central black hole (BH) masses for over 900 broad-line active galactic nuclei (AGNs) observed with the Sloan Digital Sky Survey. The sample includes objects which have redshifts up to z=0.452, high quality spectra, and host galaxy spectra dominated by an early-type (bulge) component. The AGN and host galaxy spectral components were decomposed using an eigenspectrum technique. The BH masses (M_BH) were estimated from the AGN broad-line widths, and the velocity dispersions were measured from the stellar absorption spectra of the host galaxies. The range of black hole masses covered by the sample is approximately 10^6 < M_BH < 10^9 M_Sun. The host galaxy luminosity-velocity dispersion relationship follows the well-known Faber-Jackson relation for early-type galaxies, with a power-law slope 4.33+-0.21. The estimated BH masses are correlated with both the host luminosities (L_{H}) and the stellar velocity dispersions (\sigma_*), similar to the relationships found for low-redshift, bulge-dominated galaxies. The intrinsic scatter in the correlations are large (~0.4 dex), but the very large sample size allows tight constraints to be placed on the mean relationships: M_BH ~ L_H^{0.73+-0.05} and M_BH ~ \sigma_*^{3.34+-0.24}. The amplitude of the M_BH-\sigma_* relation depends on the estimated Eddington ratio, such that objects with larger Eddington ratios have smaller black hole masses than expected at a given velocity dispersion.Comment: Accepted for publication in A

Direct retrieval of stratospheric CO_2 infrared cooling rate profiles from AIRS data

We expand upon methods for retrieving thermal infrared cooling rate profiles, originally developed by Liou and Xue (1988) through application to the inversion of the stratospheric cooling rate produced by carbon dioxide (CO_2) and a formal description of the associated error budget. Specifically, we infer lower- and mid-stratospheric cooling rates from the CO_2 ν_2 band on the basis of selected spectral channels and available data from the Atmospheric Infrared Sounder (AIRS). In order to establish the validity of our results, we compare our retrievals to those calculated from a forward radiative transfer program using retrieved temperature data from spectra taken by the Scanning High-Resolution Interferometer Sounder (S-HIS) on two aircraft campaigns: the Mixed-Phase Arctic Cloud Experiment (MPACE) and the Aura Validation Experiment (AVE) both in Fall, 2004. Reasonable and consistent comparisons are illustrated, revealing that spectral radiance data taken by high-resolution infrared sounders can be used to determine the vertical distribution of radiative cooling due to CO_2

A simplified method for determining regurgitant fraction by Doppler echocardiography in patients with aortic regurtitation

AbstractObjectives. This study attempted to develop and validate a simple method for calculating aortic regurgitant fraction by use of pulsed wave Doppler echocardiography.Background. Although several investigators have been able to determine aortic regurgitant fraction by Doppler echocardiography, the methods used require accurate determination of the cross-sectional areas of intracardiac sites at which the volumetric flow is calculated.Methods. Our concept was based on a constant relation that exists between the cross-sectional area of the left ventricular outflow tract and the mitral valve annulus in normal subjects. To verify this, we used Doppler echocardiography to measure the flow velocity integral of the left ventricular outflow tract and the mitral annulus in the apical view in 50 normal subjects (32 men, 18 women, mean age 34 years).Results. Close correlation (r = 0.95) was observed between the flow velocity integral (FVI) of the outflow tract (OT) and that of the mitral annulus (MA): FVIMA/FVIOT= 0.77. Because mitral flow equals aortic flow in normal subjects, the ratio of the cross-sectional area of the mitral annulus to that of the outflow tract was 1/0.77. In patients with aortic regurgitation, the regurgitant fraction (RF) = (Aortic flow − Mitral flow)/Aortic flow = 1 − Mitral flow/Aortic flow. Substituting 0.77 for the area component of flow, RF = 1 − (1/0.77) · (FVIMA/FVIOT). To evaluate the accuracy of this method, we compared the regurgitant fraction derived by Doppler echocardiography with that from catheterization findings in 20 patients with aortic regurgitation (an isolated lesion was found in 14). The regurgitant fraction by catheterization was the difference between total (angiographic) and forward (thermodilution) stroke volumes as a percent of total flow. Good correlation was observed between catheterization and Doppler regurgitant fraction (r = 0.88, SEE 9%, p < 0.01).Conclusions. Thus, regurgitant fraction can be estimated from Doppler echocardiography in patients with aortic regurgitation by a method that requires only measurements of the flow velocity integral from the mitral annulus and left ventricular outflow tract