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

A video analysis of head injuries satisfying the criteria for a head injury assessment in professional Rugby Union: a prospective cohort study

Objectives Concussion is the most common match injury in professional Rugby Union, accounting for 25% of match injuries. The primary prevention of head injuries requires that the injury mechanism be known so that interventions can be targeted to specifically overall incidence by focusing on characteristics with the greatest propensity to cause a head injury. Methods 611 head injury assessment (HIA) events in professional Rugby Union over a 3-year period were analysed, with specific reference to match events, position, time and nature of head contact. Results 464 (76%) of HIA events occur during tackles, with the tackler experiencing a significantly greater propensity for an HIA than the ball carrier (1.40 HIAs/1000 tackles for the tackler vs 0.54 HIAs/1000 tackles for the ball carrier, incidence rate ratio (IRR) 2.59). Propensity was significantly greater for backline players than forwards (IRR 1.54, 95%CI 1.28 to 1.84), but did not increase over the course of the match. Head to head contact accounted for the most tackler HIAs, with the greatest propensity. Conclusions By virtue of its high propensity and frequency, the tackle should be the focus for interventions that may include law change and technique education. A specific investigation of the characteristics of the tackle is warranted to refine the approach to preventative strategies

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

A detection pipeline for galactic binaries in LISA data

The Galaxy is suspected to contain hundreds of millions of binary white dwarf systems, a large fraction of which will have sufficiently small orbital period to emit gravitational radiation in band for space-based gravitational wave detectors such as the Laser Interferometer Space Antenna (LISA). LISA's main science goal is the detection of cosmological events (supermassive black hole mergers, etc.) however the gravitational signal from the galaxy will be the dominant contribution to the data -- including instrumental noise -- over approximately two decades in frequency. The catalogue of detectable binary systems will serve as an unparalleled means of studying the Galaxy. Furthermore, to maximize the scientific return from the mission, the data must be "cleansed" of the galactic foreground. We will present an algorithm that can accurately resolve and subtract >10000 of these sources from simulated data supplied by the Mock LISA Data Challenge Task Force. Using the time evolution of the gravitational wave frequency, we will reconstruct the position of the recovered binaries and show how LISA will sample the entire compact binary population in the Galaxy.Comment: 12 pages, 8 figure

Evaluation of Beam Quality Study of Arbitrary Beam Profiles from On-Wafer Vertical Cavity Surface Emitting Lasers

Vertical cavity surface emitting lasers (VCSELs) have found mainstream use in data centers and short-haul optical fiber communications. Along with the increase in the capacity of such systems comes an increase in the demand for greater power efficiency. System evaluation now includes an assessment of the energy required for each bit of data, a metric referred to as ‘joules per bit’. One source of loss for VCSELs is coupling loss, which is due to a mismatch in the mode profiles of the VCSELs and the optical fiber into which the VSCEL light is coupled. One way to reduce this loss is to develop single-mode VCSEL devices that are modally matched to optical fiber. Efficient development of these devices requires a technique for rapidly evaluating beam quality. This study investigates the use of a vertically mounted commercial beam profiling system and hardware interface software to quickly evaluate the beam quality of arbitrary beam profiles from on-wafer mounted VCSEL devices. This system captures the beam profile emitted from a VCSEL device at fixed locations along the vertical axis. Each image is evaluated within software along a predetermined axis, and the beam quality, or M2, is calculated according to international standards. This system is quantitatively compared against a commercial software package designed for determining beam quality across a fixed axis

Evaluation of Beam Quality Study of Arbitrary Beam Profiles from On-Wafer Vertical Cavity Surface Emitting Lasers

Vertical cavity surface emitting lasers (VCSELs) have found mainstream use in data centers and short-haul optical fiber communications. Along with the increase in the capacity of such systems comes an increase in the demand for greater power efficiency. System evaluation now includes an assessment of the energy required for each bit of data, a metric referred to as ‘joules per bit’. One source of loss for VCSELs is coupling loss, which is due to a mismatch in the mode profiles of the VCSELs and the optical fiber into which the VSCEL light is coupled. One way to reduce this loss is to develop single-mode VCSEL devices that are modally matched to optical fiber. Efficient development of these devices requires a technique for rapidly evaluating beam quality. This study investigates the use of a vertically mounted commercial beam profiling system and hardware interface software to quickly evaluate the beam quality of arbitrary beam profiles from on-wafer mounted VCSEL devices. This system captures the beam profile emitted from a VCSEL device at fixed locations along the vertical axis. Each image is evaluated within software along a predetermined axis, and the beam quality, or M2, is calculated according to international standards. This system is quantitatively compared against a commercial software package designed for determining beam quality across a fixed axis

Modelling national HIV/AIDS epidemics: revised approach in the UNAIDS Estimation and Projection Package 2011

Objective: United Nations Programme on HIV/AIDS reports regularly on estimated levels and trends in HIV/AIDS epidemics, which are evaluated using an epidemiological model within the Estimation and Projection Package (EPP). The relatively simple four-parameter model of HIV incidence used in EPP through the previous round of estimates has encountered challenges when attempting to fit certain data series on prevalence over time, particularly in settings with long running epidemics where prevalence has increased recently. To address this, the most recent version of the modelling package (EPP 2011) includes a more flexible epidemiological model that allows HIV infection risk to vary over time. This paper describes the technical details of this flexible approach to modelling HIV transmission dynamics within EPP 2011. Methodology For the flexible modelling approach, the force of infection parameter, r, is allowed to vary over time through a random walk formulation, and an informative prior distribution is used to improve short-term projections beyond the last year of data. Model parameters are estimated using a Bayesian estimation approach in which models are fit to HIV seroprevalence data from surveillance sites. Results: This flexible model can yield better estimates of HIV prevalence over time in situations where the classic EPP model has difficulties, such as in Uganda, where prevalence is no longer falling. Based on formal out-of-sample projection tests, the flexible modelling approach also improves predictions and CIs for extrapolations beyond the last observed data point. Conclusions: We recommend use of a flexible modelling approach where data are sufficient (eg, where at least 5 years of observations are available), and particularly where an epidemic is beyond its peak

Risk factors for head injury events in professional rugby union: a video analysis of 464 head injury events to inform proposed injury prevention strategies

OBJECTIVES: The tackle is responsible for the majority of head injuries during rugby union. In order to address head injury risk, risk factors during the tackle must first be identified. This study analysed tackle characteristics in the professional game in order to inform potential interventions. METHODS: 464 tackles resulting in a head injury assessment (HIA) were analysed in detail, with tackle type, direction, speed, acceleration, nature of head contact and player body position the characteristics of interest. RESULTS: Propensity to cause an HIA was significantly greater for active shoulder tackles, front-on tackles, high speeder tackles and an accelerating tackler. Head contact between a tackler's head and ball carrier's head or shoulder was significantly more likely to cause an HIA than contact below the level of the shoulder (incident rate ratio (IRR) 4.25, 95%-CI 3.38 to 5.35). The tackler experiences the majority (78%) of HIAs when head-to-head contact occurs. An upright tackler was 1.5 times more likely to experience an HIA than a bent at the waist tackler (IRR 1.44, 95% CI 1.18 to 1.76). CONCLUSIONS: This study confirms that energy transfer in the tackle is a risk factor for head injury, since direction, type and speed all influence HIA propensity. The study provides evidence that body position and the height of tackles should be a focus for interventions, since lowering height and adopting a bent at the waist body position is associated with reduced risk for both tacklers and ball carriers. To this end, World Rugby has implemented law change based on the present data

A Link to the Past: Using Markov Chain Monte Carlo Fitting to Constrain Fundamental Parameters of High-Redshift Galaxies

We have a developed a new method for fitting spectral energy distributions (SEDs) to identify and constrain the physical properties of high-redshift (4 < z < 8) galaxies. Our approach uses an implementation of Bayesian based Markov Chain Monte Carlo (PiMC^2) that allows us to compare observations to arbitrarily complex models and to compute 95% credible intervals that provide robust constraints for the model parameters. The work is presented in 2 sections. In the first, we test PiMC^2 using simulated SEDs to not only confirm the recovery of the known inputs but to assess the limitations of the method and identify potential hazards of SED fitting when applied specifically to high redshift (z>4) galaxies. Our tests reveal five critical results: 1) the ability to confidently constrain metallicity, population ages, and Av all require photometric accuracy better than what is currently achievable (i.e. less than a few percent); 2) the ability to confidently constrain stellar masses (within a factor of two) can be achieved without the need for high-precision photometry; 3) the addition of IRAC photometry does not guarantee that tighter constraints of the stellar masses and ages can be defined; 4) different assumptions about the star formation history can lead to significant biases in mass and age estimates; and 5) we are able to constrain stellar age and Av of objects that are both young and relatively dust free. In the second part of the paper we apply PiMC^2 to 17 4<z<8 objects, including the GRAPES Ly alpha sample (4<z<6), supplemented by HST/WFC3 near-IR observations, and several broad band selected z>6 galaxies. Using PiMC^2, we are able to constrain the stellar mass of these objects and in some cases their stellar age and find no evidence that any of these sources formed at a redshift much larger than z_f=8, a time when the Universe was ~ 0.6 Gyr old.Comment: Submitted to ApJ (Full abstract, 47 pages, 17 figures, 7 tables