26 research outputs found
Discriminating between a Stochastic Gravitational Wave Background and Instrument Noise
The detection of a stochastic background of gravitational waves could
significantly impact our understanding of the physical processes that shaped
the early Universe. The challenge lies in separating the cosmological signal
from other stochastic processes such as instrument noise and astrophysical
foregrounds. One approach is to build two or more detectors and cross correlate
their output, thereby enhancing the common gravitational wave signal relative
to the uncorrelated instrument noise. When only one detector is available, as
will likely be the case with the Laser Interferometer Space Antenna (LISA),
alternative analysis techniques must be developed. Here we show that models of
the noise and signal transfer functions can be used to tease apart the
gravitational and instrument noise contributions. We discuss the role of
gravitational wave insensitive "null channels" formed from particular
combinations of the time delay interferometry, and derive a new combination
that maintains this insensitivity for unequal arm length detectors. We show
that, in the absence of astrophysical foregrounds, LISA could detect signals
with energy densities as low as with just
one month of data. We describe an end-to-end Bayesian analysis pipeline that is
able to search for, characterize and assign confidence levels for the detection
of a stochastic gravitational wave background, and demonstrate the
effectiveness of this approach using simulated data from the third round of
Mock LISA Data Challenges.Comment: 10 Pages, 10 Figure
Computational methods for Bayesian model choice
In this note, we shortly survey some recent approaches on the approximation
of the Bayes factor used in Bayesian hypothesis testing and in Bayesian model
choice. In particular, we reassess importance sampling, harmonic mean sampling,
and nested sampling from a unified perspective.Comment: 12 pages, 4 figures, submitted to the proceedings of MaxEnt 2009,
July 05-10, 2009, to be published by the American Institute of Physic
A Bayesian Approach to the Detection Problem in Gravitational Wave Astronomy
The analysis of data from gravitational wave detectors can be divided into
three phases: search, characterization, and evaluation. The evaluation of the
detection - determining whether a candidate event is astrophysical in origin or
some artifact created by instrument noise - is a crucial step in the analysis.
The on-going analyses of data from ground based detectors employ a frequentist
approach to the detection problem. A detection statistic is chosen, for which
background levels and detection efficiencies are estimated from Monte Carlo
studies. This approach frames the detection problem in terms of an infinite
collection of trials, with the actual measurement corresponding to some
realization of this hypothetical set. Here we explore an alternative, Bayesian
approach to the detection problem, that considers prior information and the
actual data in hand. Our particular focus is on the computational techniques
used to implement the Bayesian analysis. We find that the Parallel Tempered
Markov Chain Monte Carlo (PTMCMC) algorithm is able to address all three phases
of the anaylsis in a coherent framework. The signals are found by locating the
posterior modes, the model parameters are characterized by mapping out the
joint posterior distribution, and finally, the model evidence is computed by
thermodynamic integration. As a demonstration, we consider the detection
problem of selecting between models describing the data as instrument noise, or
instrument noise plus the signal from a single compact galactic binary. The
evidence ratios, or Bayes factors, computed by the PTMCMC algorithm are found
to be in close agreement with those computed using a Reversible Jump Markov
Chain Monte Carlo algorithm.Comment: 19 pages, 12 figures, revised to address referee's comment
Characterizing the Gravitational Wave Signature from Cosmic String Cusps
Cosmic strings are predicted to form kinks and cusps that travel along the
string at close to the speed of light. These disturbances are radiated away as
highly beamed gravitational waves that produce a burst like pulse as the cone
of emission sweeps past an observer. Gravitational wave detectors such as the
Laser Interferometer Space Antenna (LISA) and the Laser Interferometer
Gravitational wave Observatory (LIGO) will be capable of detecting these bursts
for a wide class of string models. Such a detection would illuminate the fields
of string theory, cosmology, and relativity. Here we develop template based
Markov Chain Monte Carlo (MCMC) techniques that can efficiently detect and
characterize the signals from cosmic string cusps. We estimate how well the
signal parameters can be recovered by the advanced LIGO-Virgo network and the
LISA detector using a combination of MCMC and Fisher matrix techniques. We also
consider joint detections by the ground and space based instruments. We show
that a parallel tempered MCMC approach can detect and characterize the signals
from cosmic string cusps, and we demonstrate the utility of this approach on
simulated data from the third round of Mock LISA Data Challenges (MLDCs).Comment: 10 pages, 10 figure