A Bayesian approach to the follow-up of candidate gravitational wave signals

Ground-based gravitational wave laser interferometers (LIGO, GEO-600, Virgo and Tama-300) have now reached high sensitivity and duty cycle. We present a Bayesian evidence-based approach to the search for gravitational waves, in particular aimed at the followup of candidate events generated by the analysis pipeline. We introduce and demonstrate an efficient method to compute the evidence and odds ratio between different models, and illustrate this approach using the specific case of the gravitational wave signal generated during the inspiral phase of binary systems, modelled at the leading quadrupole Newtonian order, in synthetic noise. We show that the method is effective in detecting signals at the detection threshold and it is robust against (some types of) instrumental artefacts. The computational efficiency of this method makes it scalable to the analysis of all the triggers generated by the analysis pipelines to search for coalescing binaries in surveys with ground-based interferometers, and to a whole variety of signal waveforms, characterised by a larger number of parameters.Comment: 9 page

Studying stellar binary systems with the Laser Interferometer Space Antenna using Delayed Rejection Markov chain Monte Carlo methods

Bayesian analysis of LISA data sets based on Markov chain Monte Carlo methods has been shown to be a challenging problem, in part due to the complicated structure of the likelihood function consisting of several isolated local maxima that dramatically reduces the efficiency of the sampling techniques. Here we introduce a new fully Markovian algorithm, a Delayed Rejection Metropolis-Hastings Markov chain Monte Carlo method, to efficiently explore these kind of structures and we demonstrate its performance on selected LISA data sets containing a known number of stellar-mass binary signals embedded in Gaussian stationary noise.Comment: 12 pages, 4 figures, accepted in CQG (GWDAW-13 proceedings

Negative Quasi-Probability as a Resource for Quantum Computation

A central problem in quantum information is to determine the minimal physical resources that are required for quantum computational speedup and, in particular, for fault-tolerant quantum computation. We establish a remarkable connection between the potential for quantum speed-up and the onset of negative values in a distinguished quasi-probability representation, a discrete analog of the Wigner function for quantum systems of odd dimension. This connection allows us to resolve an open question on the existence of bound states for magic-state distillation: we prove that there exist mixed states outside the convex hull of stabilizer states that cannot be distilled to non-stabilizer target states using stabilizer operations. We also provide an efficient simulation protocol for Clifford circuits that extends to a large class of mixed states, including bound universal states.Comment: 15 pages v4: This is a major revision. In particular, we have added a new section detailing an explicit extension of the Gottesman-Knill simulation protocol to deal with positively represented states and measurement (even when these are non-stabilizer). This paper also includes significant elaboration on the two main results of the previous versio

Parameterized tests of the strong-field dynamics of general relativity using gravitational wave signals from coalescing binary black holes: Fast likelihood calculations and sensitivity of the method

Thanks to the recent discoveries of gravitational wave signals from binary black hole mergers by Advanced Laser Interferometer Gravitational Wave Observatory and Advanced Virgo, the genuinely strong-field dynamics of spacetime can now be probed, allowing for stringent tests of general relativity (GR). One set of tests consists of allowing for parametrized deformations away from GR in the template waveform models and then constraining the size of the deviations, as was done for the detected signals in previous work. In this paper, we construct reduced-order quadratures so as to speed up likelihood calculations for parameter estimation on future events. Next, we explicitly demonstrate the robustness of the parametrized tests by showing that they will correctly indicate consistency with GR if the theory is valid. We also check to what extent deviations from GR can be constrained as information from an increasing number of detections is combined. Finally, we evaluate the sensitivity of the method to possible violations of GR.Comment: 19 pages, many figures. Matches PRD versio

Compensation of Strong Thermal Lensing in High Optical Power Cavities

In an experiment to simulate the conditions in high optical power advanced gravitational wave detectors such as Advanced LIGO, we show that strong thermal lenses form in accordance with predictions and that they can be compensated using an intra-cavity compensation plate heated on its cylindrical surface. We show that high finesse ~1400 can be achieved in cavities with internal compensation plates, and that the cavity mode structure can be maintained by thermal compensation. It is also shown that the measurements allow a direct measurement of substrate optical absorption in the test mass and the compensation plate.Comment: 8 page

Improving response rates using a monetary incentive for patient completion of questionnaires: an observational study

Background: Poor response rates to postal questionnaires can introduce bias and reduce the statistical power of a study. To improve response rates in our trial in primary care we tested the effect of introducing an unconditional direct payment of 5 pound for the completion of postal questionnaires. Methods: We recruited patients in general practice with knee problems from sites across the United Kingdom. An evidence-based strategy was used to follow-up patients at twelve months with postal questionnaires. This included an unconditional direct payment of 5 pound to patients for the completion and return of questionnaires. The first 105 patients did not receive the 5 pound incentive, but the subsequent 442 patients did. We used logistic regression to analyse the effect of introducing a monetary incentive to increase the response to postal questionnaires. Results: The response rate following reminders for the historical controls was 78.1% ( 82 of 105) compared with 88.0% ( 389 of 442) for those patients who received the 5 pound payment (diff = 9.9%, 95% CI 2.3% to 19.1%). Direct payments significantly increased the odds of response ( adjusted odds ratio = 2.2, 95% CI 1.2 to 4.0, P = 0.009) with only 12 of 442 patients declining the payment. The incentive did not save costs to the trial - the extra cost per additional respondent was almost 50 pound. Conclusion: The direct payment of 5 pound significantly increased the completion of postal questionnaires at negligible increase in cost for an adequately powered study

Report on the first round of the Mock LISA Data Challenges

The Mock LISA Data Challenges (MLDCs) have the dual purpose of fostering the development of LISA data analysis tools and capabilities, and demonstrating the technical readiness already achieved by the gravitational-wave community in distilling a rich science payoff from the LISA data output. The first round of MLDCs has just been completed: nine data sets containing simulated gravitational wave signals produced either by galactic binaries or massive black hole binaries embedded in simulated LISA instrumental noise were released in June 2006 with deadline for submission of results at the beginning of December 2006. Ten groups have participated in this first round of challenges. Here we describe the challenges, summarise the results, and provide a first critical assessment of the entries.Comment: Proceedings report from GWDAW 11. Added author, added reference, clarified some text, removed typos. Results unchanged; Removed author, minor edits, reflects submitted versio

A Bayesian parameter estimation approach to pulsar time-of-arrival analysis

The increasing sensitivities of pulsar timing arrays to ultra-low frequency (nHz) gravitational waves promises to achieve direct gravitational wave detection within the next 5-10 years. While there are many parallel efforts being made in the improvement of telescope sensitivity, the detection of stable millisecond pulsars and the improvement of the timing software, there are reasons to believe that the methods used to accurately determine the time-of-arrival (TOA) of pulses from radio pulsars can be improved upon. More specifically, the determination of the uncertainties on these TOAs, which strongly affect the ability to detect GWs through pulsar timing, may be unreliable. We propose two Bayesian methods for the generation of pulsar TOAs starting from pulsar "search-mode" data and pre-folded data. These methods are applied to simulated toy-model examples and in this initial work we focus on the issue of uncertainties in the folding period. The final results of our analysis are expressed in the form of posterior probability distributions on the signal parameters (including the TOA) from a single observation.Comment: 16 pages, 4 figure

Compact Binary Coalescences in the Band of Ground-based Gravitational-Wave Detectors

As the ground-based gravitational-wave telescopes LIGO, Virgo, and GEO 600 approach the era of first detections, we review the current knowledge of the coalescence rates and the mass and spin distributions of merging neutron-star and black-hole binaries. We emphasize the bi-directional connection between gravitational-wave astronomy and conventional astrophysics. Astrophysical input will make possible informed decisions about optimal detector configurations and search techniques. Meanwhile, rate upper limits, detected merger rates, and the distribution of masses and spins measured by gravitational-wave searches will constrain astrophysical parameters through comparisons with astrophysical models. Future developments necessary to the success of gravitational-wave astronomy are discussed.Comment: Replaced with version accepted by CQG