49,707 research outputs found
Bayesian coherent analysis of in-spiral gravitational wave signals with a detector network
The present operation of the ground-based network of gravitational-wave laser
interferometers in "enhanced" configuration brings the search for gravitational
waves into a regime where detection is highly plausible. The development of
techniques that allow us to discriminate a signal of astrophysical origin from
instrumental artefacts in the interferometer data and to extract the full range
of information are some of the primary goals of the current work. Here we
report the details of a Bayesian approach to the problem of inference for
gravitational wave observations using a network of instruments, for the
computation of the Bayes factor between two hypotheses and the evaluation of
the marginalised posterior density functions of the unknown model parameters.
The numerical algorithm to tackle the notoriously difficult problem of the
evaluation of large multi-dimensional integrals is based on a technique known
as Nested Sampling, which provides an attractive alternative to more
traditional Markov-chain Monte Carlo (MCMC) methods. We discuss the details of
the implementation of this algorithm and its performance against a Gaussian
model of the background noise, considering the specific case of the signal
produced by the in-spiral of binary systems of black holes and/or neutron
stars, although the method is completely general and can be applied to other
classes of sources. We also demonstrate the utility of this approach by
introducing a new coherence test to distinguish between the presence of a
coherent signal of astrophysical origin in the data of multiple instruments and
the presence of incoherent accidental artefacts, and the effects on the
estimation of the source parameters as a function of the number of instruments
in the network.Comment: 22 page
Noise Enhanced Hypothesis-Testing in the Restricted Bayesian Framework
Cataloged from PDF version of article.Performance of some suboptimal detectors can be enhanced by adding independent noise to their observations. In this paper, the effects of additive noise are investigated according to the restricted Bayes criterion, which provides a generalization of the Bayes and minimax criteria. Based on a generic M-ary composite hypothesis-testing formulation, the optimal probability distribution of additive noise is investigated. Also, sufficient conditions under which the performance of a detector can or cannot be improved via additive noise are derived. In addition, simple hypothesis-testing problems are studied in more detail, and additional improvability conditions that are specific to simple hypotheses are obtained. Furthermore, the optimal probability distribution of the additive noise is shown to include at most mass points in a simple M-ary hypothesis-testing problem under certain conditions. Then, global optimization, analytical and convex relaxation approaches are considered to obtain the optimal noise distribution. Finally, detection examples are presented to investigate the theoretical results
Polarization-based Tests of Gravity with the Stochastic Gravitational-Wave Background
The direct observation of gravitational waves with Advanced LIGO and Advanced
Virgo offers novel opportunities to test general relativity in strong-field,
highly dynamical regimes. One such opportunity is the measurement of
gravitational-wave polarizations. While general relativity predicts only two
tensor gravitational-wave polarizations, general metric theories of gravity
allow for up to four additional vector and scalar modes. The detection of these
alternative polarizations would represent a clear violation of general
relativity. The LIGO-Virgo detection of the binary black hole merger GW170814
has recently offered the first direct constraints on the polarization of
gravitational waves. The current generation of ground-based detectors, however,
is limited in its ability to sensitively determine the polarization content of
transient gravitational-wave signals. Observation of the stochastic
gravitational-wave background, in contrast, offers a means of directly
measuring generic gravitational-wave polarizations. The stochastic background,
arising from the superposition of many individually unresolvable
gravitational-wave signals, may be detectable by Advanced LIGO at
design-sensitivity. In this paper, we present a Bayesian method with which to
detect and characterize the polarization of the stochastic background. We
explore prospects for estimating parameters of the background, and quantify the
limits that Advanced LIGO can place on vector and scalar polarizations in the
absence of a detection. Finally, we investigate how the introduction of new
terrestrial detectors like Advanced Virgo aid in our ability to detect or
constrain alternative polarizations in the stochastic background. We find that,
although the addition of Advanced Virgo does not notably improve detection
prospects, it may dramatically improve our ability to estimate the parameters
of backgrounds of mixed polarization.Comment: 24 pages, 20 figures; Accepted by PRX. This version includes major
changes in response to referee comments and corrects an error in Eq. E
Disentangling causal webs in the brain using functional Magnetic Resonance Imaging: A review of current approaches
In the past two decades, functional Magnetic Resonance Imaging has been used
to relate neuronal network activity to cognitive processing and behaviour.
Recently this approach has been augmented by algorithms that allow us to infer
causal links between component populations of neuronal networks. Multiple
inference procedures have been proposed to approach this research question but
so far, each method has limitations when it comes to establishing whole-brain
connectivity patterns. In this work, we discuss eight ways to infer causality
in fMRI research: Bayesian Nets, Dynamical Causal Modelling, Granger Causality,
Likelihood Ratios, LiNGAM, Patel's Tau, Structural Equation Modelling, and
Transfer Entropy. We finish with formulating some recommendations for the
future directions in this area
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