Tests of Bayesian Model Selection Techniques for Gravitational Wave Astronomy

The analysis of gravitational wave data involves many model selection problems. The most important example is the detection problem of selecting between the data being consistent with instrument noise alone, or instrument noise and a gravitational wave signal. The analysis of data from ground based gravitational wave detectors is mostly conducted using classical statistics, and methods such as the Neyman-Pearson criteria are used for model selection. Future space based detectors, such as the \emph{Laser Interferometer Space Antenna} (LISA), are expected to produced rich data streams containing the signals from many millions of sources. Determining the number of sources that are resolvable, and the most appropriate description of each source poses a challenging model selection problem that may best be addressed in a Bayesian framework. An important class of LISA sources are the millions of low-mass binary systems within our own galaxy, tens of thousands of which will be detectable. Not only are the number of sources unknown, but so are the number of parameters required to model the waveforms. For example, a significant subset of the resolvable galactic binaries will exhibit orbital frequency evolution, while a smaller number will have measurable eccentricity. In the Bayesian approach to model selection one needs to compute the Bayes factor between competing models. Here we explore various methods for computing Bayes factors in the context of determining which galactic binaries have measurable frequency evolution. The methods explored include a Reverse Jump Markov Chain Monte Carlo (RJMCMC) algorithm, Savage-Dickie density ratios, the Schwarz-Bayes Information Criterion (BIC), and the Laplace approximation to the model evidence. We find good agreement between all of the approaches.Comment: 11 pages, 6 figure

The Faint End Slopes Of Galaxy Luminosity Functions In The COSMOS 2-Square Degree Field

We examine the faint-end slope of the rest-frame V-band luminosity function (LF), with respect to galaxy spectral type, of field galaxies with redshift z<0.5, using a sample of 80,820 galaxies with photometric redshifts in the Cosmic Evolution Survey (COSMOS) field. For all galaxy spectral types combined, the LF slope, alpha, ranges from -1.24 to -1.12, from the lowest redshift bin to the highest. In the lowest redshift bin (0.02<z<0.1), where the magnitude limit is M(V) ~ -13, the slope ranges from ~ -1.1 for galaxies with early-type spectral energy distributions (SEDs), to ~ -1.9 for galaxies with low-extinction starburst SEDs. In each galaxy SED category (Ell, Sbc, Scd/Irr, and starburst), the faint-end slopes grow shallower with increasing redshift; in the highest redshift bin (0.4<z<0.5), the slope is ~ -0.5 and ~ -1.3 for early-types and starbursts respectively. The steepness of alpha at lower redshift could be qualitatively explained by large numbers of faint dwarf galaxies, perhaps of low surface brightness, which are not detected at higher redshifts.Comment: 24 pages including 5 figures, accepted to ApJ

A Bayesian Approach to the Detection Problem in Gravitational Wave Astronomy

The analysis of data from gravitational wave detectors can be divided into three phases: search, characterization, and evaluation. The evaluation of the detection - determining whether a candidate event is astrophysical in origin or some artifact created by instrument noise - is a crucial step in the analysis. The on-going analyses of data from ground based detectors employ a frequentist approach to the detection problem. A detection statistic is chosen, for which background levels and detection efficiencies are estimated from Monte Carlo studies. This approach frames the detection problem in terms of an infinite collection of trials, with the actual measurement corresponding to some realization of this hypothetical set. Here we explore an alternative, Bayesian approach to the detection problem, that considers prior information and the actual data in hand. Our particular focus is on the computational techniques used to implement the Bayesian analysis. We find that the Parallel Tempered Markov Chain Monte Carlo (PTMCMC) algorithm is able to address all three phases of the anaylsis in a coherent framework. The signals are found by locating the posterior modes, the model parameters are characterized by mapping out the joint posterior distribution, and finally, the model evidence is computed by thermodynamic integration. As a demonstration, we consider the detection problem of selecting between models describing the data as instrument noise, or instrument noise plus the signal from a single compact galactic binary. The evidence ratios, or Bayes factors, computed by the PTMCMC algorithm are found to be in close agreement with those computed using a Reversible Jump Markov Chain Monte Carlo algorithm.Comment: 19 pages, 12 figures, revised to address referee's comment

The faint-end slopes of galaxy luminosity functions in the COSMOS field

We examine the faint-end slope of the rest-frame V-band luminosity function (LF), with respect to galaxy spectral type, of field galaxies with redshift z < 0.5, using a sample of 80,820 galaxies with photometric redshifts in the 2 deg^2 Cosmic Evolution Survey (COSMOS) field. For all galaxy spectral types combined, the LF slope ranges from –1.24 to –1.12, from the lowest redshift bin to the highest. In the lowest redshift bin (0.02 < z < 0.1), where the magnitude limit is MV ≾ − 13, the slope ranges from α ~ − 1.1 for galaxies with early-type spectral energy distributions (SEDs) to α ~ − 1.9 for galaxies with low-extinction starburst SEDs. In each galaxy SED category (early-type, Sbc, Scd+Irr, and starburst), the faint-end slopes grow shallower with increasing redshift; in the highest redshift bin (0.4 < z < 0.5), α ~ − 0.5 and –1.3 for early types and starbursts, respectively. The steepness of α at lower redshifts could be qualitatively explained by LF evolution, or by large numbers of faint dwarf galaxies, perhaps of low surface brightness, that are not detected at higher redshifts

Comparison of MRI- and TRUS-Informed Prostate Biopsy for Prostate Cancer Diagnosis in Biopsy-Naive Men: A Systematic Review and Meta-Analysis.

PURPOSE: Multiparametric magnetic resonance imaging (mpMRI) with informed targeted biopsies (TGBX) has changed the paradigm of prostate cancer (PCa) diagnosis. Randomized studies have demonstrated a diagnostic benefit of Clinically significant (CS) for TGBX compared to standard systematic biopsies (SBX). We aimed to evaluate whether mpMRI-informed TGBX has superior diagnosis rates of any-, CS-, high-grade (HG)-, and clinically insignificant (CI)-PCa compared to SBX in biopsy-naive men. METHODS: Data was searched in Medline, Embase, Web of Science, and Evidence-based medicine reviews-Cochrane Database of systematic reviews from database inception until 2019. Studies were selected by two authors independently, with disagreements resolved by consensus with a third author. Overall 1951 unique references were identified, and 100 manuscripts underwent full-text review. Data were pooled using random-effects models. The meta-analysis is reported according to the PRISMA statement. The study protocol is registered with PROSPERO (CRD42019128468). RESULTS: Overall 29 studies (13,845 patients) were analyzed. Compared to SBX, use of mpMRI-informed TGBX was associated with a 15% higher rate of any PCa diagnosis (95% CI 10-20%, p\u3c0.00001). This relationship was not affected by the study methodology (p=0.11). Diagnosis of CS and HG PCa were more common in the mpMRI-informed TGBX group (risk difference of 11%, 95% CI 0-20%, p=0.05, and 2%, 95% CI 1-4%; p=0.005, respectively) while there was no difference in diagnosis of CI PCa (risk difference of 0, 95% CI -3-3%, p=0.96). Notably, the exclusion of SBX in the mpMRI-informed TGBX arm significantly modified the association between a mpMRI strategy and lower rates of CI PCa diagnosis (p=0.01) without affecting the diagnosis rates of CS- or HG-PCa. CONCLUSIONS: In comparison to SBX, a mpMRI-informed TGBX strategy results in a significantly higher diagnosis rate of any-, CS-, and HG-PCa. Excluding SBX from mpMRI-informed TGBX was associated with decreased rates of CI-PCa diagnosis without affecting diagnosis of CS- or HG-PCa

Strategic intent, high-performance HRM, and the role of the HR director: an investigation into attitudes and practices in the country of Jordan

There is an implicit undercurrent in the HRM literature that the role of present day HR director has become ‘strategic’ as opposed to ‘routine’, as in the past. In this paper, we empirically test these assertions in the context of the country of Jordan—a context within which little past research into HRM has been undertaken. The design includes a detailed survey instrument sent to all financial firms within the country. We find that the reliance on routine functions has indeed fallen for HR directors surveyed; however, there is only weak evidence to support that the perceived importance of strategic functions has increased substantially. Results show that male HR directors and those longer serving, with higher qualifications, and those working for companies with lower employee turnover, are more likely to rate as ‘high’ the importance of the most strategic HR functions. Neither company size nor years of establishment moderated this relationship. The empirical evidence from this study—as one of a few conducted in non-Western environment—adds to the literature with some interesting implications and avenues for future work. Importantly, implications from our findings for strategic HRM and the role of the HR director are considered in conclusion

US Cosmic Visions: New Ideas in Dark Matter 2017: Community Report

This white paper summarizes the workshop "U.S. Cosmic Visions: New Ideas in Dark Matter" held at University of Maryland on March 23-25, 2017.Comment: 102 pages + reference

The Sorcerer II Global Ocean Sampling Expedition: Metagenomic Characterization of Viruses within Aquatic Microbial Samples

Viruses are the most abundant biological entities on our planet. Interactions between viruses and their hosts impact several important biological processes in the world's oceans such as horizontal gene transfer, microbial diversity and biogeochemical cycling. Interrogation of microbial metagenomic sequence data collected as part of the Sorcerer II Global Ocean Expedition (GOS) revealed a high abundance of viral sequences, representing approximately 3% of the total predicted proteins. Cluster analyses of the viral sequences revealed hundreds to thousands of viral genes encoding various metabolic and cellular functions. Quantitative analyses of viral genes of host origin performed on the viral fraction of aquatic samples confirmed the viral nature of these sequences and suggested that significant portions of aquatic viral communities behave as reservoirs of such genetic material. Distributional and phylogenetic analyses of these host-derived viral sequences also suggested that viral acquisition of environmentally relevant genes of host origin is a more abundant and widespread phenomenon than previously appreciated. The predominant viral sequences identified within microbial fractions originated from tailed bacteriophages and exhibited varying global distributions according to viral family. Recruitment of GOS viral sequence fragments against 27 complete aquatic viral genomes revealed that only one reference bacteriophage genome was highly abundant and was closely related, but not identical, to the cyanomyovirus P-SSM4. The co-distribution across all sampling sites of P-SSM4-like sequences with the dominant ecotype of its host, Prochlorococcus supports the classification of the viral sequences as P-SSM4-like and suggests that this virus may influence the abundance, distribution and diversity of one of the most dominant components of picophytoplankton in oligotrophic oceans. In summary, the abundance and broad geographical distribution of viral sequences within microbial fractions, the prevalence of genes among viral sequences that encode microbial physiological function and their distinct phylogenetic distribution lend strong support to the notion that viral-mediated gene acquisition is a common and ongoing mechanism for generating microbial diversity in the marine environment

How to Detect an Astrophysical Nanohertz Gravitational-Wave Background

Analysis of pulsar timing data have provided evidence for a stochastic gravitational wave background in the nHz frequency band. The most plausible source of such a background is the superposition of signals from millions of supermassive black hole binaries. The standard statistical techniques used to search for such a background and assess its significance make several simplifying assumptions, namely: i) Gaussianity; ii) isotropy; and most often iii) a power-law spectrum. However, a stochastic background from a finite collection of binaries does not exactly satisfy any of these assumptions. To understand the effect of these assumptions, we test standard analysis techniques on a large collection of realistic simulated datasets. The dataset length, observing schedule, and noise levels were chosen to emulate the NANOGrav 15-year dataset. Simulated signals from millions of binaries drawn from models based on the Illustris cosmological hydrodynamical simulation were added to the data. We find that the standard statistical methods perform remarkably well on these simulated datasets, despite their fundamental assumptions not being strictly met. They are able to achieve a confident detection of the background. However, even for a fixed set of astrophysical parameters, different realizations of the universe result in a large variance in the significance and recovered parameters of the background. We also find that the presence of loud individual binaries can bias the spectral recovery of the background if we do not account for them.Comment: 14 pages, 8 figure