Classifying LISA gravitational wave burst signals using Bayesian evidence

Abstract. Nested sampling is a technique for efficiently computing the probability of a data set under a particular hypothesis, also called the Bayesian Evidence or Marginal Likelihood, and for evaluating the posterior. MultiNest is a multi-modal nested sampling algorithm which has been designed to efficiently explore and characterize posterior probability surfaces containing multiple secondary solutions. We have applied the MultiNest algorithm to a number of problems in gravitational wave data analysis. In this article, we describe the algorithm and present results for several applications of the algorithm to analysis of mock LISA data. We summarise recently published results for a test case in which we searched for two non-spinning black hole binary merger signals in simulated LISA data. We also describe results obtained with MultiNest in the most recent round of the Mock LISA Data Challenge (MLDC), in which the algorithm was used to search for and characterise both spinning supermassive black hole binary inspirals and bursts from cosmic string cusps. In all these applications, the algorithm found the correct number of signals and efficiently recovered the posterior probability distribution. Moreover, in most cases the waveform corresponding to the best a-posteriori parameters had an overlap in excess of 99% with the true signal.

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“…These features were also seen and discussed in [20]. Further details of our methods and results can be found in a separate paper [21]. …”

Section: Challenge 34: Cosmic String Burstsmentioning

confidence: 77%

Nested sampling as a tool for LISA data analysis

Gair

Feroz

Babak

et al. 2010

J. Phys.: Conf. Ser.

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“…It seems that mirages were not noticed by the other research groups who participated in the MLDC 3 searches for string-cusp bursts [19,20]. We conjecture that the reason is as follows.…”

Section: Effects Of Degeneracies On Searchesmentioning

confidence: 87%

“…Two other reports on LISA string-burst searches, also developed and tested in the context of MLDC 3, have appeared recently [19,20]. Our work differs p from those in several ways: First, we use the F -statistic and FFT to improve search efficiency.…”

Section: Introductionmentioning

confidence: 99%

Searches for cosmic-string gravitational-wave bursts in Mock LISA Data

Cohen

Cutler

Vallisneri

2010

Class. Quantum Grav.

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Abstract. A network of observable, macroscopic cosmic (super-)strings may well have formed in the early Universe. If so, the cusps that generically develop on cosmic-string loops emit bursts of gravitational radiation that could be detectable by gravitational-wave interferometers, such as the ground-based LIGO/Virgo detectors and the planned, space-based LISA detector. Here we report on two versions of a LISA-oriented string-burst search pipeline that we have developed and tested within the context of the Mock LISA Data Challenges. The two versions rely on the publicly available MultiNest and PyMC software packages, respectively. To reduce the effective dimensionality of the search space, our implementations use the F -statistic to analytically maximize over the signal's amplitude and polarization, A and ψ, and use the FFT to search quickly over burst arrival times t C . The standard F -statistic is essentially a frequentist statistic that maximizes the likelihood; we also demonstrate an approximate, Bayesian version of the F -statistic that incorporates realistic priors on A and ψ. We calculate how accurately LISA can expect to measure the physical parameters of stringburst sources, and compare to results based on the Fisher-matrix approximation. To understand LISA's angular resolution for string-burst sources, we draw maps of the waveform fitting factor [maximized over (A, ψ, t C )] as a function of sky position; these maps dramatically illustrate why (for LISA) inferring the correct sky location of the emitting string loop will often be practically impossible. In addition, we identify and elucidate several symmetries that are imbedded in this search problem, and we derive the distribution of cut-off frequencies fmax for observable bursts.

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“…This separation also allows for the calculation of the ‘local’ evidence associated with each mode. M ulti N est has been shown to be of substantial use in astrophysics and particle physics (see Feroz et al 2008a, 2009b,c, 2010; Feroz, Marshall & Hobson 2008b; Trotta et al 2008; Gair et al 2010), typically showing great improvement in efficiency over traditional MCMC techniques.…”

Section: Bayesian Inference and Multinestmentioning

confidence: 99%

BAMBI: blind accelerated multimodal Bayesian inference

Graff¹,

Feroz²,

Hobson³

et al. 2012

Monthly Notices of the Royal Astronomical Society

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In this paper we present an algorithm for rapid Bayesian analysis that combines the benefits of nested sampling and artificial neural networks. The blind accelerated multimodal Bayesian inference (BAMBI) algorithm implements the MultiNest package for nested sampling as well as the training of an artificial neural network (NN) to learn the likelihood function. In the case of computationally expensive likelihoods, this allows the substitution of a much more rapid approximation in order to increase significantly the speed of the analysis. We begin by demonstrating, with a few toy examples, the ability of a NN to learn complicated likelihood surfaces. BAMBI's ability to decrease running time for Bayesian inference is then demonstrated in the context of estimating cosmological parameters from Wilkinson Microwave Anisotropy Probe and other observations. We show that valuable speed increases are achieved in addition to obtaining NNs trained on the likelihood functions for the different model and data combinations. These NNs can then be used for an even faster follow-up analysis using the same likelihood and different priors. This is a fully general algorithm that can be applied, without any pre-processing, to other problems with computationally expensive likelihood functions.Comment: 12 pages, 8 tables, 17 figures; accepted by MNRAS; v2 to reflect minor changes in published versio

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Classifying LISA gravitational wave burst signals using Bayesian evidence

Cited by 14 publications

References 26 publications

Nested sampling as a tool for LISA data analysis

Nested sampling as a tool for LISA data analysis

Searches for cosmic-string gravitational-wave bursts in Mock LISA Data

BAMBI: blind accelerated multimodal Bayesian inference

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