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Authors: John T. Whelan, Reinhard Prix, Deepak Khurana

Date: 14 May 2008

Abstract: We report on our F-statistic search for white-dwarf binary signals in the Mock LISA Data Challenge 1B (MLDC1B). We focus in particular on the improvements in our search pipeline since MLDC1, namely refinements in the search pipeline and the use of a more accurate detector response (rigid adiabatic approximation). The search method employs a hierarchical template-grid based exploration of the parameter space, using a coincidence step to distinguish between primary (‘true’) and secondary maxima, followed by a final (multi-TDI) ‘zoom’ stage to provide an accurate parameter estimation of the final candidates.

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Authors: E. L. Robinson, J. D. Romano, A. Vecchio

Date: 25 Apr 2008

Abstract: The analysis method currently proposed to search for isotropic stochastic radiation of primordial or astrophysical origin with the Laser Interferometer Space Antenna (LISA) relies on the combined use of two LISA channels, one of which is insensitive to gravitational waves, such as the symmetrised Sagnac. For this method to work, it is essential to know how the instrumental noise power in the two channels are related to one another; however, no quantitative estimates of this key information are available to date. The purpose of our study is to assess the performance of the symmetrised Sagnac method for different levels of prior information regarding the instrumental noise. We develop a general approach in the framework of Bayesian inference and an end-to-end analysis algorithm based on Markov Chain Monte Carlo methods to compute the posterior probability density functions of the relevant model parameters. We apply this method to data released as part of the second round of the Mock LISA Data Challenges. For the selected (and somewhat idealised) cases considered here, we find that a prior uncertainty of a factor ~2 in the ratio between the power of the instrumental noise contributions in the two channels allows for the detection of isotropic stochastic radiation. More importantly, we provide a framework for more realistic studies of LISA's performance and development of analysis techniques in the context of searches for stochastic signals.

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Authors: N. J. Cornish

Date: 21 Apr 2008

Abstract: The capture of compact stellar remnants by galactic black holes provides a unique laboratory for exploring the near horizon geometry of the Kerr spacetime. The gravitational radiation produced by these Extreme Mass Ratio Inspirals (EMRIs) encodes a detailed map of the black hole geometry, and the detection and characterization of these signals is a major science driver for the LISA observatory. The waveforms produced are very complex, and the signals need to be coherently tracked for hundreds to thousands of cycles to produce a detection, making EMRI signals one of the most challenging data analysis problems in all of gravitational wave astronomy. Estimates for the number of templates required to perform an optimal matched-filter search for these signals are astronomically large, and far out of reach of current computational resources. Here a sub-optimal, hierarchical approach to the EMRI detection problem is developed that employs a directed-stochastic search technique. The algorithm, dubbed Metropolis Hastings Monte Carlo (MHMC), is a close cousin of Markov Chain Monte Carlo and genetic algorithms. The utility of the MHMC approach is demonstrated using simulated data sets from the Mock LISA Data Challenge.

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Authors: Miquel Trias, Alberto Vecchio, John Veitch

Date: 24 Apr 2008

Abstract: We are developing a Bayesian approach based on Markov chain Monte Carlo techniques to search for and extract information about white dwarf binary systems with the Laser Interferometer Space Antenna (LISA). Here we present results obtained by applying an initial implementation of this method to some of the data sets released in Round 1B of the Mock LISA Data Challenges. For Challenges 1B.1.1a and 1b the signals were recovered with parameters lying within the 95.5% posterior probability interval and the correlation between the true and recovered waveform is in excess of 99%. Results were not submitted for Challenge 1B.1.1c due to some convergence problems of the algorithms, despite the signal was detected in a search over a 2 mHz band.

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Authors: Jonathan R. Gair, Stanislav Babak, Edward K. Porter, Leor Barack

Date: 21 Apr 2008

Abstract: We describe a search for the EMRI sources in the Round 1B Mock LISA Data Challenge data sets. The search algorithm is a Monte-Carlo search based on the Metropolis-Hastings algorithm, but also incorporates simulated, thermostated and time annealing, plus a harmonic identification stage designed to reduce the chance of the chain locking onto secondary maxima. In this paper, we focus on describing the algorithm that we have been developing. We give the results of the search of the Round 1B data, although parameter recovery has improved since that deadline. Finally, we describe several modifications to the search pipeline that we are currently investigating for incorporation in future searches.

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Authors: I.W. Harry, S. Fairhurst, B.S. Sathyaprakash

Date: 21 Apr 2008

Abstract: 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.

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Authors: Jonathan R Gair, Ilya Mandel, Linqing Wen

Date: 7 Apr 2008

Abstract: The planned Laser Interferometer Space Antenna (LISA) is expected to detect gravitational wave signals from ~100 extreme-mass-ratio inspirals (EMRIs) of stellar-mass compact objects into massive black holes. The long duration and large parameter space of EMRI signals makes data analysis for these signals a challenging problem. One approach to EMRI data analysis is to use time-frequency methods. This consists of two steps: (i) searching for tracks from EMRI sources in a time-frequency spectrogram, and (ii) extracting parameter estimates from the tracks. In this paper we discuss the results of applying these techniques to the latest round of the Mock LISA Data Challenge, Round 1B. This analysis included three new techniques not used in previous analyses: (i) a new Chirp-based Algorithm for Track Search for track detection; (ii) estimation of the inclination of the source to the line of sight; (iii) a Metropolis-Hastings Monte Carlo over the parameter space in order to find the best fit to the tracks.

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Authors: Stanislav Babak

Date: 26 Jan 2008

Abstract: 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).

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Authors: Jonathan R Gair, Ilya Mandel, Linqing Wen

Date: 27 Oct 2007

Abstract: Extreme-mass-ratio inspirals (EMRIs) of ~ 1-10 solar-mass compact objects into ~ million solar-mass massive black holes can serve as excellent probes of strong-field general relativity. The Laser Interferometer Space Antenna (LISA) is expected to detect gravitational wave signals from apprxomiately one hundred EMRIs per year, but the data analysis of EMRI signals poses a unique set of challenges due to their long duration and the extensive parameter space of possible signals. One possible approach is to carry out a search for EMRI tracks in the time-frequency domain. We have applied a time-frequency search to the data from the Mock LISA Data Challenge (MLDC) with promising results. Our analysis used the Hierarchical Algorithm for Clusters and Ridges to identify tracks in the time-frequency spectrogram corresponding to EMRI sources. We then estimated the EMRI source parameters from these tracks. In these proceedings, we discuss the results of this analysis of the MLDC round 1.3 data.

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Authors: Christian Röver, Alexander Stroeer, Ed Bloomer, Nelson Christensen, James Clark, Martin Hendry, Chris Messenger, Renate Meyer, Matt Pitkin, Jennifer Toher, Richard Umstätter, Alberto Vecchio, John Veitch, Graham Woan

Date: 26 Jul 2007

Abstract: In this paper we describe a Bayesian inference framework for analysis of data obtained by LISA. We set up a model for binary inspiral signals as defined for the Mock LISA Data Challenge 1.2 (MLDC), and implemented a Markov chain Monte Carlo (MCMC) algorithm to facilitate exploration and integration of the posterior distribution over the 9-dimensional parameter space. Here we present intermediate results showing how, using this method, information about the 9 parameters can be extracted from the data.

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Authors: Reinhard Prix, John T. Whelan

Date: 1 Jul 2007

Abstract: The F-statistic is an optimal detection statistic for continuous gravitational waves, i.e., long-duration (quasi-)monochromatic signals with slowly-varying intrinsic frequency. This method was originally developed in the context of ground-based detectors, but it is equally applicable to LISA where many signals fall into this class of signals. We report on the application of a LIGO/GEO F-statistic code to LISA data-analysis using the long-wavelength limit (LWL), and we present results of our search for white-dwarf binary signals in the first Mock LISA Data Challenge. Somewhat surprisingly, the LWL is found to be sufficient -- even at high frequencies -- for detection of signals and their accurate localization on the sky and in frequency, while a more accurate modelling of the TDI response only seems necessary to correctly estimate the four amplitude parameters.

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Authors: Duncan A. Brown, Jeff Crowder, Curt Cutler, Ilya Mandel, Michele Vallisneri

Date: 19 Apr 2007

Abstract: Gravitational waves from the inspiral and coalescence of supermassive black-hole (SMBH) binaries with masses ~10ˆ6 Msun are likely to be among the strongest sources for the Laser Interferometer Space Antenna (LISA). We describe a three-stage data-analysis pipeline designed to search for and measure the parameters of SMBH binaries in LISA data. The first stage uses a time-frequency track-search method to search for inspiral signals and provide a coarse estimate of the black-hole masses m_1, m_2 and of the coalescence time of the binary t_c. The second stage uses a sequence of matched-filter template banks, seeded by the first stage, to improve the measurement accuracy of the masses and coalescence time. Finally, a Markov Chain Monte Carlo search is used to estimate all nine physical parameters of the binary. Using results from the second stage substantially shortens the Markov Chain burn-in time and allows us to determine the number of SMBH-binary signals in the data before starting parameter estimation. We demonstrate our analysis pipeline using simulated data from the first LISA Mock Data Challenge. We discuss our plan for improving this pipeline and the challenges that will be faced in real LISA data analysis.

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Authors: Alexander Stroeer, John Veitch, Christian Roever, Ed Bloomer, James Clark, Nelson Christensen, Martin Hendry, Chris Messenger, Renate Meyer, Matthew Pitkin, Jennifer Toher, Richard Umstaetter, Alberto Vecchio, Graham Woan

Date: 31 Mar 2007

Abstract: We report on the analysis of selected single source data sets from the first round of the Mock LISA Data Challenges (MLDC) for white dwarf binaries. We implemented an end-to-end pipeline consisting of a grid-based coherent pre-processing unit for signal detection, and an automatic Markov Chain Monte Carlo post-processing unit for signal evaluation. We demonstrate that signal detection with our coherent approach is secure and accurate, and is increased in accuracy and supplemented with additional information on the signal parameters by our Markov Chain Monte Carlo approach. We also demonstrate that the Markov Chain Monte Carlo routine is additionally able to determine accurately the noise level in the frequency window of interest.

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Authors: Jeff Crowder, Neil J. Cornish

Date: 23 Apr 2007

Abstract: We report on the performance of an end-to-end Bayesian analysis pipeline for detecting and characterizing galactic binary signals in simulated LISA data. Our principal analysis tool is the Blocked-Annealed Metropolis Hasting (BAM) algorithm, which has been optimized to search for tens of thousands of overlapping signals across the LISA band. The BAM algorithm employs Bayesian model selection to determine the number of resolvable sources, and provides posterior distribution functions for all the model parameters. The BAM algorithm performed almost flawlessly on all the Round 1 Mock LISA Data Challenge data sets, including those with many highly overlapping sources. The only misses were later traced to a coding error that affected high frequency sources. In addition to the BAM algorithm we also successfully tested a Genetic Algorithm (GA), but only on data sets with isolated signals as the GA has yet to be optimized to handle large numbers of overlapping signals.

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Authors: Neil J. Cornish, Edward K. Porter

Date: 30 Jan 2007

Abstract: The Mock LISA Data Challenge is a worldwide effort to solve the LISA data analysis problem. We present here our results for the Massive Black Hole Binary (BBH) section of Round 1. Our results cover Challenge 1.2.1, where the coalescence of the binary is seen, and Challenge 1.2.2, where the coalescence occurs after the simulated observational period. The data stream is composed of Gaussian instrumental noise plus an unknown BBH waveform. Our search algorithm is based on a variant of the Markov Chain Monte Carlo method that uses Metropolis-Hastings sampling and thermostated frequency annealing. We present results from the training data sets and the blind data sets. We demonstrate that our algorithm is able to rapidly locate the sources, accurately recover the source parameters, and provide error estimates for the recovered parameters.

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Authors: Jeff Crowder, Neil Cornish

Date: 17 Nov 2006

Abstract: Low frequency gravitational wave detectors, such as the Laser Interferometer Space Antenna (LISA), will have to contend with large foregrounds produced by millions of compact galactic binaries in our galaxy. While these galactic signals are interesting in their own right, the unresolved component can obscure other sources. The science yield for the LISA mission can be improved if the brighter and more isolated foreground sources can be identified and regressed from the data. Since the signals overlap with one another we are faced with a ‘cocktail party’ problem of picking out individual conversations in a crowded room. Here we present and implement an end-to-end solution to the galactic foreground problem that is able to resolve tens of thousands of sources from across the LISA band. Our algorithm employs a variant of the Markov Chain Monte Carlo (MCMC) method, which we call the Blocked Annealed Metropolis-Hastings (BAM) algorithm. Following a description of the algorithm and its implementation, we give several examples ranging from searches for a single source to searches for hundreds of overlapping sources. Our examples include data sets from the first round of Mock LISA Data Challenges.

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