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

Observation of polarization domain wall solitons in weakly birefringent cavity fiber lasers

We report on the experimental observation of two types of phase-locked vector soliton in weakly birefringent cavity erbium-doped fiber lasers. While a phase-locked dark-dark vector soliton was only observed in fiber lasers of positive dispersion, a phase-locked dark-bright vector soliton was obtained in fiber lasers of either positive or negative dispersion. Numerical simulations confirmed the experimental observations, and further showed that the observed vector solitons are the two types of phase-locked polarization domain-wall solitons theoretically predicted.Comment: 14 pages, 4 Figure

Physical Electronics

Contains reports on four research projects

Physical Electronics

Contains reports on three research projects

A Note on Frame Dragging

The measurement of spin effects in general relativity has recently taken centre stage with the successfully launched Gravity Probe B experiment coming toward an end, coupled with recently reported measurements using laser ranging. Many accounts of these experiments have been in terms of frame-dragging. We point out that this terminology has given rise to much confusion and that a better description is in terms of spin-orbit and spin-spin effects. In particular, we point out that the de Sitter precession (which has been mesured to a high accuracy) is also a frame-dragging effect and provides an accurate benchmark measurement of spin-orbit effects which GPB needs to emulate

“Doctor my eyes” : A natural experiment on the demand for eye care services

This paper is dedicated to our friend Divine Ikenwilo, who passed away on the 27th November 2015. Divine was a gifted researcher who was taken from us too early and will be sorely missed by everyone in the team. Our thoughts are with his family. This research was funded by a research grant (CGZ/2/533) from the Chief Scientist Office of the Scottish Government. The Health Economics Research Unit is funded by the Scottish Government Health and Social Care Directorate. The usual disclaimer applies.Peer reviewedPostprin

Physical Electronics

Contains reports on four research projects

The Millennium Arecibo 21-CM Absorption Line Survey. II. Properties of the Warm and Cold Neutral Media

We use the Gaussian-fit results of Paper I to investigate the properties of interstellar HI in the Solar neighborhood. The Warm and Cold Neutral Media (WNM and CNM) are physically distinct components. The CNM spin temperature histogram peaks at about 40 K. About 60% of all HI is WNM. At z=0, we derive a volume filling fraction of about 0.50 for the WNM; this value is very rough. The upper-limit WNM temperatures determined from line width range upward from about 500 K; a minimum of about 48% of the WNM lies in the thermally unstable region 500 to 5000 K. The WNM is a prominent constituent of the interstellar medium and its properties depend on many factors, requiring global models that include all relevant energy sources, of which there are many. We use Principal Components Analysis, together with a form of least squares fitting that accounts for errors in both the independent and dependent parameters, to discuss the relationships among the four CNM Gaussian parameters. The spin temperature T_s and column density N(HI) are, approximately, the two most important eigenvectors; as such, they are sufficient, convenient, and physically meaningful primary parameters for describing CNM clouds. The Mach number of internal macroscopic motions for CNM clouds is typically 2.5, but there are wide variations. We discuss the historical tau-T_s relationship in some detail and show that it has little physical meaning. We discuss CNM morphology using the CNM pressure known from UV stellar absorption lines. Knowing the pressure allows us to show that CNM structures cannot be isotropic but instead are sheetlike, with length-to-thickness aspect ratios ranging up to about 280. We present large-scale maps of two regions where CNM lies in very large ``blobby sheets''.Comment: Revised submission to Ap.J. Changes include: (1) correction of turbulent Mach number in equation 16 and figure 12; the new typical value is 1.3 versus the old, incorrect value 2.5. (2) smaller typeface for the astro-ph version to conserve paper. 60 pages, 16 figure

Detection of OH absorption against PSR B1849+00

We have searched for OH absorption against seven pulsars using the Arecibo telescope. In both OH mainlines (at 1665 and 1667 MHz), deep and narrow absorption features were detected toward PSR B1849+00. In addition, we have detected several absorption and emission features against B33.6+0.1, a nearby supernova remnant (SNR). The most interesting result of this study is that a pencil-sharp absorption sample against the PSR differs greatly from the large-angle absorption sample observed against the SNR. If both the PSR and the SNR probe the same molecular cloud then this finding has important implications for absorption studies of the molecular medium, as it shows that the statistics of absorbing OH depends on the size of the background source. We also show that the OH absorption against the PSR most likely originates from a small (<30 arcsec) and dense (>10^5 cm^-3) molecular clump.Comment: 12 pages, 8 figures. Accepted for publication in Ap