A Bayesian Approach to the Detection Problem in Gravitational Wave Astronomy - General Relativity and Quantum CosmologyReport as inadecuate




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Abstract: The analysis of data from gravitational wave detectors can be divided intothree phases: search, characterization, and evaluation. The evaluation of thedetection - determining whether a candidate event is astrophysical in origin orsome artifact created by instrument noise - is a crucial step in the analysis.The on-going analyses of data from ground based detectors employ a frequentistapproach to the detection problem. A detection statistic is chosen, for whichbackground levels and detection efficiencies are estimated from Monte Carlostudies. This approach frames the detection problem in terms of an infinitecollection of trials, with the actual measurement corresponding to somerealization of this hypothetical set. Here we explore an alternative, Bayesianapproach to the detection problem, that considers prior information and theactual data in hand. Our particular focus is on the computational techniquesused to implement the Bayesian analysis. We find that the Parallel TemperedMarkov Chain Monte Carlo PTMCMC algorithm is able to address all three phasesof the anaylsis in a coherent framework. The signals are found by locating theposterior modes, the model parameters are characterized by mapping out thejoint posterior distribution, and finally, the model evidence is computed bythermodynamic integration. As a demonstration, we consider the detectionproblem of selecting between models describing the data as instrument noise, orinstrument noise plus the signal from a single compact galactic binary. Theevidence ratios, or Bayes factors, computed by the PTMCMC algorithm are foundto be in close agreement with those computed using a Reversible Jump MarkovChain Monte Carlo algorithm.



Author: Tyson B. Littenberg, Neil J. Cornish

Source: https://arxiv.org/







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