321 research outputs found
On combining information from multiple gravitational wave sources
In the coming years, advanced gravitational wave detectors will observe
signals from a large number of compact binary coalescences. The majority of
these signals will be relatively weak, making the precision measurement of
subtle effects, such as deviations from general relativity, challenging in the
individual events. However, many weak observations can be combined into precise
inferences, if information from the individual signals is combined in an
appropriate way. In this study we revisit common methods for combining multiple
gravitational wave observations to test general relativity, namely (i)
multiplying the individual likelihoods of beyond-general-relativity parameters
and (ii) multiplying the Bayes Factor in favor of general relativity from each
event. We discuss both methods and show that they make stringent assumptions
about the modified theory of gravity they test. In particular, the former
assumes that all events share the same beyond-general-relativity parameter,
while the latter assumes that the theory of gravity has a new unrelated
parameter for each detection. We show that each method can fail to detect
deviations from general relativity when the modified theory being tested
violates these assumptions. We argue that these two methods are the extreme
limits of a more generic framework of hierarchical inference on hyperparameters
that characterize the underlying distribution of single-event parameters. We
illustrate our conclusions first using a simple model of Gaussian likelihoods,
and also by applying parameter estimation techniques to a simulated dataset of
gravitational waveforms in a model where the graviton is massive. We argue that
combining information from multiple sources requires explicit assumptions that
make the results inherently model-dependent.Comment: 9 pages, 3 figure
Reanalysis of LIGO black-hole coalescences with alternative prior assumptions
We present a critical reanalysis of the black-hole binary coalescences
detected during LIGO's first observing run under different Bayesian prior
assumptions. We summarize the main findings of Vitale et al. (2017) and show
additional marginalized posterior distributions for some of the binaries'
intrinsic parameters.Comment: Proceedings of IAU Symposium 338: Gravitational Wave Astrophysics
(Baton Rouge, LA, October 2017
Impact of Bayesian prior on the characterization of binary black hole coalescences
In a regime where data are only mildly informative, prior choices can play a
significant role in Bayesian statistical inference, potentially affecting the
inferred physics. We show this is indeed the case for some of the parameters
inferred from current gravitational-wave measurements of binary black hole
coalescences. We reanalyze the first detections performed by the twin LIGO
interferometers using alternative (and astrophysically motivated) prior
assumptions. We find different prior distributions can introduce deviations in
the resulting posteriors that impact the physical interpretation of these
systems. For instance, (i) limits on the credible interval on the
effective black hole spin are subject to variations of if a prior with black hole spins mostly aligned to the binary's angular
momentum is considered instead of the standard choice of isotropic spin
directions, and (ii) under priors motivated by the initial stellar mass
function, we infer tighter constraints on the black hole masses, and in
particular, we find no support for any of the inferred masses within the
putative mass gap .Comment: 6 Pages, 2 Figures; see also 1712.06635 Data release at
https://github.com/vitale82/GWprior
Gravitational-wave astrophysics with effective-spin measurements: asymmetries and selection biases
Gravitational waves emitted by coalescing compact objects carry information
about the spin of the individual bodies. However, with present detectors only
the mass-weighted combination of the components of the spin along the orbital
angular momentum can be measured accurately. This quantity, the effective spin
, is conserved up to at least the second post-Newtonian
order. The measured distribution of values from a
population of detected binaries, and in particular whether this distribution is
symmetric about zero, encodes valuable information about the underlying
compact-binary formation channels. In this paper we focus on two important
complications of using the effective spin to study astrophysical population
properties: (i) an astrophysical distribution for values
which is symmetric does not necessarily lead to a symmetric distribution for
the detected effective spin values, leading to a \emph{selection bias}; and
(ii) the posterior distribution of for individual events
is \emph{asymmetric} and it cannot usually be treated as a Gaussian. We find
that the posterior distributions for systematically show
fatter tails toward larger positive values, unless the total mass is large or
the mass ratio is smaller than . Finally we show that
uncertainties in the measurement of are systematically
larger when the true value is negative than when it is positive. All these
factors can bias astrophysical inference about the population when we have more
than events and should be taken into account when using
gravitational-wave measurements to characterize astrophysical populations.Comment: An online generator for synthetic posteriors
can be found at: http://superstring.mit.edu/welcome.html Comments are welcom
On combining information from multiple gravitational wave sources
In the coming years, advanced gravitational wave detectors will observe signals from a large number of compact binary coalescences. The majority of these signals will be relatively weak, making the precision measurement of subtle effects, such as deviations from general relativity, challenging in the individual events. However, many weak observations can be combined into precise inferences, if information from the individual signals is combined in an appropriate way. In this study we revisit common methods for combining multiple gravitational wave observations to test general relativity, namely (i) multiplying the individual likelihoods of beyond-general-relativity parameters and (ii) multiplying the Bayes factor in favor of general relativity from each event. We discuss both methods and show that they make stringent assumptions about the modified theory of gravity they test. In particular, the former assumes that all events share the same beyond-general-relativity parameter, while the latter assumes that the theory of gravity has a new unrelated parameter for each detection. We show that each method can fail to detect deviations from general relativity when the modified theory being tested violates these assumptions. We argue that these two methods are the extreme limits of a more generic framework of hierarchical inference on hyperparameters that characterize the underlying distribution of single-event parameters. We illustrate our conclusions first using a simple model of Gaussian likelihoods and also by applying parameter estimation techniques to a simulated dataset of gravitational waveforms in a model where the graviton is massive. We argue that combining information from multiple sources requires explicit assumptions that make the results inherently model dependent
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