TY - JOUR
T1 - Novel Method for Incorporating Model Uncertainties into Gravitational Wave Parameter Estimates
AU - Moore, Christopher J.
AU - Gair, Jonathan R.
N1 - 6 pages, 3 figures, accepted for publication in Physical Review Letters
PY - 2014/12/19
Y1 - 2014/12/19
N2 - Posterior distributions on parameters computed from experimental data using Bayesian techniques are only as accurate as the models used to construct them. In many applications these models are incomplete, which both reduces the prospects of detection and leads to a systematic error in the parameter estimates. In the analysis of data from gravitational wave detectors, for example, accurate waveform templates can be computed using numerical methods, but the prohibitive cost of these simulations means this can only be done for a small handful of parameters. In this work a novel method to fold model uncertainties into data analysis is proposed; the waveform uncertainty is analytically marginalised over using with a prior distribution constructed by using Gaussian process regression to interpolate the waveform difference from a small training set of accurate templates. The method is well motivated, easy to implement, and no more computationally expensive than standard techniques. The new method is shown to perform extremely well when applied to a toy problem. While we use the application to gravitational wave data analysis to motivate and illustrate the technique, it can be applied in any context where model uncertainties exist.
AB - Posterior distributions on parameters computed from experimental data using Bayesian techniques are only as accurate as the models used to construct them. In many applications these models are incomplete, which both reduces the prospects of detection and leads to a systematic error in the parameter estimates. In the analysis of data from gravitational wave detectors, for example, accurate waveform templates can be computed using numerical methods, but the prohibitive cost of these simulations means this can only be done for a small handful of parameters. In this work a novel method to fold model uncertainties into data analysis is proposed; the waveform uncertainty is analytically marginalised over using with a prior distribution constructed by using Gaussian process regression to interpolate the waveform difference from a small training set of accurate templates. The method is well motivated, easy to implement, and no more computationally expensive than standard techniques. The new method is shown to perform extremely well when applied to a toy problem. While we use the application to gravitational wave data analysis to motivate and illustrate the technique, it can be applied in any context where model uncertainties exist.
KW - gr-qc
U2 - 10.1103/PhysRevLett.113.251101
DO - 10.1103/PhysRevLett.113.251101
M3 - Article
SN - 0031-9007
VL - 113
JO - Physical Review Letters
JF - Physical Review Letters
IS - 25
M1 - 251101
ER -