Random template banks and relaxed lattice coverings

Template-based searches for gravitational waves are often limited by the computational cost associated with searching large parameter spaces. The study of efficient template banks, in the sense of using the smallest number of templates, is therefore of great practical interest. The "traditional" approach to template-bank construction requires every point in parameter space to be covered by at least one template, which rapidly becomes inefficient at higher dimensions. Here we study an alternative approach, where any point in parameter space is covered only with a given probability < 1. We find that by giving up complete coverage in this way, large reductions in the number of templates are possible, especially at higher dimensions. The prime examples studied here are "random template banks", in which templates are placed randomly with uniform probability over the parameter space. In addition to its obvious simplicity, this method turns out to be surprisingly efficient. We analyze the statistical properties of such random template banks, and compare their efficiency to traditional lattice coverings. We further study "relaxed" lattice coverings (using Zn and An* lattices), which similarly cover any signal location only with probability < 1. The relaxed An* lattice is found to yield the most efficient template banks at low dimensions (n < 10), while random template banks increasingly outperform any other method at higher dimensions.Comment: 13 pages, 10 figures, submitted to PR

Targeted search for continuous gravitational waves: Bayesian versus maximum-likelihood statistics

We investigate the Bayesian framework for detection of continuous gravitational waves (GWs) in the context of targeted searches, where the phase evolution of the GW signal is assumed to be known, while the four amplitude parameters are unknown. We show that the orthodox maximum-likelihood statistic (known as F-statistic) can be rediscovered as a Bayes factor with an unphysical prior in amplitude parameter space. We introduce an alternative detection statistic ("B-statistic") using the Bayes factor with a more natural amplitude prior, namely an isotropic probability distribution for the orientation of GW sources. Monte-Carlo simulations of targeted searches show that the resulting Bayesian B-statistic is more powerful in the Neyman-Pearson sense (i.e. has a higher expected detection probability at equal false-alarm probability) than the frequentist F-statistic.Comment: 12 pages, presented at GWDAW13, to appear in CQ

Building a stochastic template bank for detecting massive black hole binaries

Coalescence of two massive black holes is the strongest and most promising source for LISA. In fact, gravitational signal from the end of inspiral and merger will be detectable throughout the Universe. In this article we describe the first step in the two-step hierarchical search for gravitational wave signal from the inspiraling massive BH binaries. It is based on the routinely used in the ground base gravitational wave astronomy method of filtering the data through the bank of templates. However we use a novel Monte-Carlo based (stochastic) method to lay a grid in the parameter space, and we use the likelihood maximized analytically over some parameters, known as F-statistic, as a detection statistic. We build a coarse template bank to detect gravitational wave signals and to make preliminary parameter estimation. The best candidates will be followed up using Metropolis-Hasting stochastic search to refine the parameter estimation. We demonstrate the performance of the method by applying it to the Mock LISA data challenge 1B (training data set).Comment: revtex4, 8 figure

Gravitational wave background from rotating neutron stars

The background of gravitational waves produced by the ensemble of rotating neutron stars (which includes pulsars, magnetars and gravitars) is investigated. A formula for \Omega(f) (commonly used to quantify the background) is derived, properly taking into account the time evolution of the systems since their formation until the present day. Moreover, the formula allows one to distinguish the different parts of the background: the unresolvable (which forms a stochastic background) and the resolvable. Several estimations of the background are obtained, for different assumptions on the parameters that characterize neutron stars and their population. In particular, different initial spin period distributions lead to very different results. For one of the models, with slow initial spins, the detection of the background can be rejected. However, other models do predict the detection of the background by the future ground-based gravitational wave detector ET. A robust upper limit for the background of rotating neutron stars is obtained; it does not exceed the detection threshold of two cross-correlated Advanced LIGO interferometers. If gravitars exist and constitute more than a few percent of the neutron star population, then they produce an unresolvable background that could be detected by ET. Under the most reasonable assumptions on the parameters characterizing a neutron star, the background is too faint. Previous papers have suggested neutron star models in which large magnetic fields (like the ones that characterize magnetars) induce big deformations in the star, which produce a stronger emission of gravitational radiation. Considering the most optimistic (in terms of the detection of gravitational waves) of these models, an upper limit for the background produced by magnetars is obtained; it could be detected by ET, but not by BBO or DECIGO.Comment: 25 pages, 15 figure

A hierarchical search for gravitational waves from supermassive black hole binary mergers

We present a method to search for gravitational waves from coalescing supermassive binary black holes in LISA data. The search utilizes the $\mathcal{F}$-statistic to maximize over, and determine the values of, the extrinsic parameters of the binary system. The intrinsic parameters are searched over hierarchically using stochastically generated multi-dimensional template banks to recover the masses and sky locations of the binary. We present the results of this method applied to the mock LISA data Challenge 1B data set.Comment: 11 pages, 2 figures, for GWDAW-12 proceedings edition of CQ

Random template placement and prior information

In signal detection problems, one is usually faced with the task of searching a parameter space for peaks in the likelihood function which indicate the presence of a signal. Random searches have proven to be very efficient as well as easy to implement, compared e.g. to searches along regular grids in parameter space. Knowledge of the parameterised shape of the signal searched for adds structure to the parameter space, i.e., there are usually regions requiring to be densely searched while in other regions a coarser search is sufficient. On the other hand, prior information identifies the regions in which a search will actually be promising or may likely be in vain. Defining specific figures of merit allows one to combine both template metric and prior distribution and devise optimal sampling schemes over the parameter space. We show an example related to the gravitational wave signal from a binary inspiral event. Here the template metric and prior information are particularly contradictory, since signals from low-mass systems tolerate the least mismatch in parameter space while high-mass systems are far more likely, as they imply a greater signal-to-noise ratio (SNR) and hence are detectable to greater distances. The derived sampling strategy is implemented in a Markov chain Monte Carlo (MCMC) algorithm where it improves convergence.Comment: Proceedings of the 8th Edoardo Amaldi Conference on Gravitational Waves. 7 pages, 4 figure

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

The Mock LISA Data Challenges: from Challenge 3 to Challenge 4

The Mock LISA Data Challenges are a program to demonstrate LISA data-analysis capabilities and to encourage their development. Each round of challenges consists of one or more datasets containing simulated instrument noise and gravitational waves from sources of undisclosed parameters. Participants analyze the datasets and report best-fit solutions for the source parameters. Here we present the results of the third challenge, issued in Apr 2008, which demonstrated the positive recovery of signals from chirping Galactic binaries, from spinning supermassive--black-hole binaries (with optimal SNRs between ~ 10 and 2000), from simultaneous extreme-mass-ratio inspirals (SNRs of 10-50), from cosmic-string-cusp bursts (SNRs of 10-100), and from a relatively loud isotropic background with Omega_gw(f) ~ 10^-11, slightly below the LISA instrument noise.Comment: 12 pages, 2 figures, proceedings of the 8th Edoardo Amaldi Conference on Gravitational Waves, New York, June 21-26, 200

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