Use of the MULTINEST algorithm for gravitational wave data analysis

We describe an application of the MultiNest algorithm to gravitational wave data analysis. MultiNest is a multimodal nested sampling algorithm designed to efficiently evaluate the Bayesian evidence and return posterior probability densities for likelihood surfaces containing multiple secondary modes. The algorithm employs a set of live points which are updated by partitioning the set into multiple overlapping ellipsoids and sampling uniformly from within them. This set of live points climbs up the likelihood surface through nested iso-likelihood contours and the evidence and posterior distributions can be recovered from the point set evolution. The algorithm is model-independent in the sense that the specific problem being tackled enters only through the likelihood computation, and does not change how the live point set is updated. In this paper, we consider the use of the algorithm for gravitational wave data analysis by searching a simulated LISA data set containing two non-spinning supermassive black hole binary signals. The algorithm is able to rapidly identify all the modes of the solution and recover the true parameters of the sources to high precision.

[1]  C. Helstrom,et al.  Statistical theory of signal detection , 1968 .

[2]  Owen.  Search templates for gravitational waves from inspiraling binaries: Choice of template spacing. , 1996, Physical review. D, Particles and fields.

[3]  Luc Blanchet,et al.  Gravitational waveforms from inspiralling compact binaries to second-post-Newtonian order , 1996, gr-qc/9602024.

[4]  K. Riedel.  Numerical Bayesian Methods Applied to Signal Processing , 1996 .

[5]  Angular resolution of the LISA gravitational wave detector , 1997, gr-qc/9703068.

[6]  Bernard F. Schutz,et al.  Data analysis of gravitational-wave signals from spinning neutron stars. I. The signal and its detection , 1998 .

[7]  Detecting a stochastic gravitational wave background with the Laser Interferometer Space Antenna , 2001, gr-qc/0106058.

[8]  M. P. Hobson,et al.  Combining cosmological data sets: hyperparameters and Bayesian evidence , 2002 .

[9]  M. Halpern,et al.  First-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Parameter Estimation Methodology , 2003 .

[10]  S. F. Portegies Zwart,et al.  Short-period AM CVn systems as optical, X-ray and gravitational-wave sources , 2004 .

[11]  David J. C. MacKay,et al.  Information Theory, Inference, and Learning Algorithms , 2004, IEEE Transactions on Information Theory.

[12]  Yuhong Yang,et al.  Information Theory, Inference, and Learning Algorithms , 2005 .

[13]  Measuring coalescing massive binary black holes with gravitational waves: The impact of spin-induced precession , 2006 .

[14]  The search for massive black hole binaries with LISA , 2006, gr-qc/0612091.

[15]  Characterizing the galactic gravitational wave background with LISA , 2005, gr-qc/0504071.

[16]  A three-stage search for supermassive black-hole binaries in LISA data , 2007, 0704.2447.

[17]  Report on the second Mock LISA Data Challenge , 2007, 0711.2667.

[18]  B. S. Sathyaprakash,et al.  Report on the first round of the Mock LISA Data Challenges , 2007 .

[19]  Catching supermassive black hole binaries without a net , 2006, gr-qc/0605135.

[20]  A. Liddle,et al.  Information criteria for astrophysical model selection , 2007, astro-ph/0701113.

[21]  F. Feroz,et al.  Multimodal nested sampling: an efficient and robust alternative to Markov Chain Monte Carlo methods for astronomical data analyses , 2007, 0704.3704.

[22]  J. Gair,et al.  The Mock LISA Data Challenges: from Challenge 1B to Challenge 3 , 2008, 0806.2110.

[23]  S. Babak.  Building a stochastic template bank for detecting massive black hole binaries , 2008, 0801.4070.

[24]  F. Feroz,et al.  Bayesian selection of sign μ within mSUGRA in global fits including WMAP5 results , 2008, 0807.4512.

[25]  J. Gair,et al.  A constrained Metropolis–Hastings search for EMRIs in the Mock LISA Data Challenge 1B , 2008, 0804.3322.

[26]  S. Fairhurst,et al.  A hierarchical search for gravitational waves from supermassive black hole binary mergers , 2008, 0804.3274.

[27]  N. Cornish.  Detection strategies for extreme mass ratio inspirals , 2008, 0804.3323.

[28]  A. Vecchio,et al.  Assigning confidence to inspiral gravitational wave candidates with Bayesian model selection , 2008, 0807.4483.

[29]  F. Feroz,et al.  The impact of priors and observables on parameter inferences in the constrained MSSM , 2008, 0809.3792.

[31]  F. Feroz,et al.  Cluster detection in weak lensing surveys , 2008, 0810.0781.

[32]  F. Feroz,et al.  Bayesian modelling of clusters of galaxies from multifrequency‐pointed Sunyaev–Zel'dovich observations , 2008, 0811.1199.

[33]  J. Gair,et al.  Cosmic swarms: a search for supermassive black holes in the LISA data stream with a hybrid evolutionary algorithm , 2009, 0903.3733.

[34]  J. Gair,et al.  An algorithm for the detection of extreme mass ratio inspirals in LISA data , 2009, 0902.4133.

[35]  F. Feroz,et al.  MultiNest: an efficient and robust Bayesian inference tool for cosmology and particle physics , 2008, 0809.3437.

[36]  Characterizing the Gravitational Wave Signature from Cosmic String Cusps , 2008, 0812.1590.

[37]  Neil J. Cornish,et al.  Bayesian approach to the detection problem in gravitational wave astronomy , 2009, 0902.0368.