Frequentist and Bayesian measures of confidence via multiscale bootstrap for testing three regions

A new computation method of frequentist $p$-values and Bayesian posterior probabilities based on the bootstrap probability is discussed for the multivariate normal model with unknown expectation parameter vector. The null hypothesis is represented as an arbitrary-shaped region. We introduce new parametric models for the scaling-law of bootstrap probability so that the multiscale bootstrap method, which was designed for one-sided test, can also computes confidence measures of two-sided test, extending applicability to a wider class of hypotheses. Parameter estimation is improved by the two-step multiscale bootstrap and also by including higher-order terms. Model selection is important not only as a motivating application of our method, but also as an essential ingredient in the method. A compromise between frequentist and Bayesian is attempted by showing that the Bayesian posterior probability with an noninformative prior is interpreted as a frequentist $p$-value of ``zero-sided'' test

The Utility of Trouble: Maximizing the Value of Our Human Services Dollars

Outlines recommendations to standardize service delivery areas and consolidate area offices of the state's seven largest human services agencies, as well as to close antiquated institutions. Projects benefits such as improved accessibility and savings

Discovery of a very X-ray luminous galaxy cluster at z=0.89 in the WARPS survey

We report the discovery of the galaxy cluster ClJ1226.9+3332 in the Wide Angle ROSAT Pointed Survey (WARPS). At z=0.888 and L_X=1.1e45 erg/s (0.5-2.0 keV, h_0=0.5) ClJ1226.9+3332 is the most distant X-ray luminous cluster currently known. The mere existence of this system represents a huge problem for Omega_0=1 world models. At the modest (off-axis) resolution of the ROSAT PSPC observation in which the system was detected, ClJ1226.9+3332 appears relaxed; an off-axis HRI observation confirms this impression and rules out significant contamination from point sources. However, in moderately deep optical images (R and I band) the cluster exhibits signs of substructure in its apparent galaxy distribution. A first crude estimate of the velocity dispersion of the cluster galaxies based on six redshifts yields a high value of 1650 km/s, indicative of a very massive cluster and/or the presence of substructure along the line of sight. While a more accurate assessment of the dynamical state of this system requires much better data at both optical and X-ray wavelengths, the high mass of the cluster has already been unambiguously confirmed by a very strong detection of the Sunyaev-Zel'dovich effect in its direction (Joy et al. 2001). Using ClJ1226.9+3332 and ClJ0152.7-1357 (z=0.835), the second-most distant X-ray luminous cluster currently known and also a WARPS discovery, we obtain a first estimate of the cluster X-ray luminosity function at 0.8<z<1.4 and L_X>5e44 erg/s. Using the best currently available data, we find the comoving space density of very distant, massive clusters to be in excellent agreement with the value measured locally (z<0.3), and conclude that negative evolution is not required at these luminosities out to z~1. (truncated)Comment: accepted for publication in ApJ Letters, 6 pages, 2 figures, uses emulateapj.st

The WARPS survey - IV: The X-ray luminosity-temperature relation of high redshift galaxy clusters

We present a measurement of the cluster X-ray luminosity-temperature relation out to high redshift (z~0.8). Combined ROSAT PSPC spectra of 91 galaxy clusters detected in the Wide Angle ROSAT Pointed Survey (WARPS) are simultaneously fit in redshift and luminosity bins. The resulting temperature and luminosity measurements of these bins, which occupy a region of the high redshift L-T relation not previously sampled, are compared to existing measurements at low redshift in order to constrain the evolution of the L-T relation. We find a best fit to low redshift (z1 keV, to be L proportional to T^(3.15\pm0.06). Our data are consistent with no evolution in the normalisation of the L-T relation up to z~0.8. Combining our results with ASCA measurements taken from the literature, we find eta=0.19\pm0.38 (for Omega_0=1, with 1 sigma errors) where L_Bol is proportional to (1 + z)^eta T^3.15, or eta=0.60\pm0.38 for Omega_0=0.3. This lack of evolution is considered in terms of the entropy-driven evolution of clusters. Further implications for cosmological constraints are also discussed.Comment: 11 pages, 7 figures, accepted for publication in MNRA

The WARPS Survey. VIII. Evolution of the Galaxy Cluster X-ray Luminosity Function

We present measurements of the galaxy cluster X-ray Luminosity Function (XLF) from the Wide Angle ROSAT Pointed Survey (WARPS) and quantify its evolution. WARPS is a serendipitous survey of the central region of ROSAT pointed observations and was carried out in two phases (WARPS-I and WARPS-II). The results here are based on a final sample of 124 clusters, complete above a flux limit of 6.5 10E-15 erg/s/cm2, with members out to redshift z ~ 1.05, and a sky coverage of 70.9 deg2. We find significant evidence for negative evolution of the XLF, which complements the majority of X-ray cluster surveys. To quantify the suggested evolution, we perform a maximum likelihood analysis and conclude that the evolution is driven by a decreasing number density of high luminosity clusters with redshift, while the bulk of the cluster population remains nearly unchanged out to redshift z ~ 1.1, as expected in a low density Universe. The results are found to be insensitive to a variety of sources of systematic uncertainty that affect the measurement of the XLF and determination of the survey selection function. We perform a Bayesian analysis of the XLF to fully account for uncertainties in the local XLF on the measured evolution, and find that the detected evolution remains significant at the 95% level. We observe a significant excess of clusters in the WARPS at 0.1 < z < 0.3 and LX ~ 2 10E42 erg/s compared with the reference low-redshift XLF, or our Bayesian fit to the WARPS data. We find that the excess cannot be explained by sample variance, or Eddington bias, and is unlikely to be due to problems with the survey selection function.Comment: 13 pages, 12 figures, accepted for publication in MNRA

Is the core of M87 the source of its TeV emission? Implications for unified schemes

M87 has been recently shown to be a TeV source which is likely to be variable. Based on this, and on contemporaneous optical and X-ray monitoring, we argue that the source of the TeV emission is the core of M87 and not one of two jet knots (HST-1 and A) with X-ray brightness comparable to that of the core. We model the TeV emission in the core as inverse Compton (IC) emission from the base of the jet. Homogeneous models fail to reproduce the spectral energy distribution (SED) and, in particular, the TeV flux. They also fail to comply with the unified scheme of BL Lacertae (BL) objects and FR I radio galaxies. A jet that decelerates from a Lorentz factor Gamma ~ 20 down to Gamma \~ 5 over a length of ~ 0.1 pc reproduces the observed SED of the M87 core, and, when aligned to the line of sight, produces a SED similar to those of TeV BLs. The TeV flux in the decelerating jet model is successfully reproduced as upstream Compton (UC) scattering, a recently identified emission mechanism, in which energetic electrons of the upstream faster flow upscatter the low energy photons produced in the slower downstream part of the flow.Comment: accepted to ApJ Letter

The WARPS survey: III. The discovery of an X-ray luminous galaxy cluster at z=0.833 and the impact of X-ray substructure on cluster abundance measurements

The WARPS team reviews the properties and history of discovery of ClJ0152.7-1357, an X-ray luminous, rich cluster of galaxies at z=0.833. At L_X = 8 x 10^44 h^(-2) erg/s (0.5-2.0 keV) ClJ0152.7-1357 is the most X-ray luminous cluster known at redshifts z>0.55. The high X-ray luminosity of the system suggests that massive clusters may begin to form at redshifts considerably greater than unity. This scenario is supported by the high degree of optical and X-ray substructure in ClJ0152.7-1357, which is similarly complex as that of other X-ray selected distant clusters and consistent with the picture of cluster formation by mass infall along large-scale filaments. X-ray emission from ClJ0152.7-1357 was detected already in 1980 with the EINSTEIN IPC. However, because the complex morphology of the emission caused its significance to be underestimated, the corresponding source was not included in the EMSS cluster sample and hence not previously identified. Simulations of the EMSS source detection and selection procedure suggest a general bias of the EMSS against X-ray luminous clusters with pronounced substructure. If highly unrelaxed, merging clusters are common at high redshift, they could create a bias in some samples as the morphological complexity of mergers may cause them to fall below the flux limit of surveys that assume a unimodal spatial source geometry. Conversely, the enhanced X-ray luminosity of mergers might cause them to, temporarily, rise above the flux limit. Either effect could lead to erroneous conclusions about the evolution of the comoving cluster space density. A high fraction of morphologically complex clusters at high redshift would also call into question the validity of cosmological studies that assume that the systems under investigation are virialized.Comment: 17 pages, 7 figures; revised to focus on possible detection biases caused by substructure in clusters; accepted for publication in ApJ; uses emulateapj.sty; eps files of figures 1 and 2 can be obtained from ftp://hubble.ifa.hawaii.edu/pub/ebeling/warp

Polarization Diagnostics for Cool Core Cluster Emission Lines

The nature of the interaction between low-excitation gas filaments at ~104 K, seen in optical line emission, and diffuse X-ray emitting coronal gas at ~107 K in the centers of galaxy clusters remains a puzzle. The presence of a strong, empirical correlation between the two gas phases is indicative of a fundamental relationship between them, though as yet of undetermined cause. The cooler filaments, originally thought to have condensed from the hot gas, could also arise from a merger or the disturbance of cool circumnuclear gas by nuclear activity. Here, we have searched for intrinsic line emission polarization in cool core galaxy clusters as a diagnostic of fundamental transport processes. Drawing on developments in solar astrophysics, direct energetic particle impact induced polarization holds the promise to definitively determine the role of collisional processes such as thermal conduction in the ISM physics of galaxy clusters, while providing insight into other highly anisotropic excitation mechanisms such as shocks, intense radiation fields, and suprathermal particles. Under certain physical conditions, theoretical calculations predict of the order of 10% polarization. Our observations of the filaments in four nearby cool core clusters place stringent upper limits ( 0.1%) on the presence of emission line polarization, requiring that if thermal conduction is operative, the thermal gradients are not in the saturated regime. This limit is consistent with theoretical models of the thermal structure of filament interfacesPeer reviewe

Existence of Large Scale Synchrotron X-ray Jets in Radio-loud Active Galactic Nuclei

In this paper, analytical arguments are presented that there exists a synchrotron X-ray jet on large scales in most radio-loud AGNs, based on the knowledge of the nature and physics of blazars. In blue blazars and blue-blazar-like radio galaxies, the large scale X-ray jet may get faint along the jet, while in most red blazars and red-blazar-like radio galaxies, the X-ray jet is bright on 10 kpc scales whether the jet is highly relativistic on large scales or not. In extreme red blazars in which the jet is still highly relativistic on large scales and the synchrotron peak of the inner jet lies in the infrared bands, the X-ray jet may get fainter along the jet from 10 kpc to 100 kpc scales while the optical and IR jet gets brighter. The predictions can be tested with the ongoing observations of the Chandra X-ray Observatory.Comment: 4 pages, accepted by ApJ Letter