143 research outputs found
Random template placement and prior information
In signal detection problems, one is usually faced with the task of searching
a parameter space for peaks in the likelihood function which indicate the
presence of a signal. Random searches have proven to be very efficient as well
as easy to implement, compared e.g. to searches along regular grids in
parameter space. Knowledge of the parameterised shape of the signal searched
for adds structure to the parameter space, i.e., there are usually regions
requiring to be densely searched while in other regions a coarser search is
sufficient. On the other hand, prior information identifies the regions in
which a search will actually be promising or may likely be in vain. Defining
specific figures of merit allows one to combine both template metric and prior
distribution and devise optimal sampling schemes over the parameter space. We
show an example related to the gravitational wave signal from a binary inspiral
event. Here the template metric and prior information are particularly
contradictory, since signals from low-mass systems tolerate the least mismatch
in parameter space while high-mass systems are far more likely, as they imply a
greater signal-to-noise ratio (SNR) and hence are detectable to greater
distances. The derived sampling strategy is implemented in a Markov chain Monte
Carlo (MCMC) algorithm where it improves convergence.Comment: Proceedings of the 8th Edoardo Amaldi Conference on Gravitational
Waves. 7 pages, 4 figure
Gravitational-Wave Astronomy with Inspiral Signals of Spinning Compact-Object Binaries
Inspiral signals from binary compact objects (black holes and neutron stars)
are primary targets of the ongoing searches by ground-based gravitational-wave
interferometers (LIGO, Virgo, GEO-600 and TAMA-300). We present
parameter-estimation simulations for inspirals of black-hole--neutron-star
binaries using Markov-chain Monte-Carlo methods. For the first time, we have
both estimated the parameters of a binary inspiral source with a spinning
component and determined the accuracy of the parameter estimation, for
simulated observations with ground-based gravitational-wave detectors. We
demonstrate that we can obtain the distance, sky position, and binary
orientation at a higher accuracy than previously suggested in the literature.
For an observation of an inspiral with sufficient spin and two or three
detectors we find an accuracy in the determination of the sky position of
typically a few tens of square degrees.Comment: v2: major conceptual changes, 4 pages, 1 figure, 1 table, submitted
to ApJ
The effects of LIGO detector noise on a 15-dimensional Markov-chain Monte-Carlo analysis of gravitational-wave signals
Gravitational-wave signals from inspirals of binary compact objects (black
holes and neutron stars) are primary targets of the ongoing searches by
ground-based gravitational-wave (GW) interferometers (LIGO, Virgo, and
GEO-600). We present parameter-estimation results from our Markov-chain
Monte-Carlo code SPINspiral on signals from binaries with precessing spins. Two
data sets are created by injecting simulated GW signals into either synthetic
Gaussian noise or into LIGO detector data. We compute the 15-dimensional
probability-density functions (PDFs) for both data sets, as well as for a data
set containing LIGO data with a known, loud artefact ("glitch"). We show that
the analysis of the signal in detector noise yields accuracies similar to those
obtained using simulated Gaussian noise. We also find that while the Markov
chains from the glitch do not converge, the PDFs would look consistent with a
GW signal present in the data. While our parameter-estimation results are
encouraging, further investigations into how to differentiate an actual GW
signal from noise are necessary.Comment: 11 pages, 2 figures, NRDA09 proceeding
Inference on inspiral signals using LISA MLDC data
In this paper we describe a Bayesian inference framework for analysis of data
obtained by LISA. We set up a model for binary inspiral signals as defined for
the Mock LISA Data Challenge 1.2 (MLDC), and implemented a Markov chain Monte
Carlo (MCMC) algorithm to facilitate exploration and integration of the
posterior distribution over the 9-dimensional parameter space. Here we present
intermediate results showing how, using this method, information about the 9
parameters can be extracted from the data.Comment: Accepted for publication in Classical and Quantum Gravity, GWDAW-11
special issu
On the distortion of twin building lattices
We show that twin building lattices are undistorted in their ambient group;
equivalently, the orbit map of the lattice to the product of the associated
twin buildings is a quasi-isometric embedding. As a consequence, we provide an
estimate of the quasi-flat rank of these lattices, which implies that there are
infinitely many quasi-isometry classes of finitely presented simple groups. In
an appendix, we describe how non-distortion of lattices is related to the
integrability of the structural cocycle
Bayesian inference on compact binary inspiral gravitational radiation signals in interferometric data
Presented is a description of a Markov chain Monte Carlo (MCMC) parameter
estimation routine for use with interferometric gravitational radiational data
in searches for binary neutron star inspiral signals. Five parameters
associated with the inspiral can be estimated, and summary statistics are
produced. Advanced MCMC methods were implemented, including importance
resampling and prior distributions based on detection probability, in order to
increase the efficiency of the code. An example is presented from an
application using realistic, albeit fictitious, data.Comment: submitted to Classical and Quantum Gravity. 14 pages, 5 figure
Binary black hole spectroscopy
We study parameter estimation with post-Newtonian (PN) gravitational
waveforms for the quasi-circular, adiabatic inspiral of spinning binary compact
objects. The performance of amplitude-corrected waveforms is compared with that
of the more commonly used restricted waveforms, in Advanced LIGO and EGO. With
restricted waveforms, the properties of the source can only be extracted from
the phasing. For amplitude-corrected waveforms, the spectrum encodes a wealth
of additional information, which leads to dramatic improvements in parameter
estimation. At distances of Mpc, the full PN waveforms allow for
high-accuracy parameter extraction for total mass up to several hundred solar
masses, while with the restricted ones the errors are steep functions of mass,
and accurate parameter estimation is only possible for relatively light stellar
mass binaries. At the low-mass end, the inclusion of amplitude corrections
reduces the error on the time of coalescence by an order of magnitude in
Advanced LIGO and a factor of 5 in EGO compared to the restricted waveforms; at
higher masses these differences are much larger. The individual component
masses, which are very poorly determined with restricted waveforms, become
measurable with high accuracy if amplitude-corrected waveforms are used, with
errors as low as a few percent in Advanced LIGO and a few tenths of a percent
in EGO. The usual spin-orbit parameter is also poorly determined with
restricted waveforms (except for low-mass systems in EGO), but the full
waveforms give errors that are small compared to the largest possible value
consistent with the Kerr bound. This suggests a way of finding out if one or
both of the component objects violate this bound. We also briefly discuss the
effect of amplitude corrections on parameter estimation in Initial LIGO.Comment: 28 pages, many figures. Final version accepted by CQG. More in-depth
treatment of component mass errors and detectability of Kerr bound
violations; improved presentatio
Consistency of the posterior distribution in generalized linear inverse problems
For ill-posed inverse problems, a regularised solution can be interpreted as
a mode of the posterior distribution in a Bayesian framework. This framework
enriches the set the solutions, as other posterior estimates can be used as a
solution to the inverse problem, such as the posterior mean that can be easier
to compute in practice. In this paper we prove consistency of Bayesian
solutions of an ill-posed linear inverse problem in the Ky Fan metric for a
general class of likelihoods and prior distributions in a finite dimensional
setting. This result can be applied to study infinite dimensional problems by
letting the dimension of the unknown parameter grow to infinity which can be
viewed as discretisation on a grid or spectral approximation of an infinite
dimensional problem. Likelihood and the prior distribution are assumed to be in
an exponential form that includes distributions from the exponential family,
and to be differentiable. The observations can be dependent. No assumption of
finite moments of observations, such as expected value or the variance, is
necessary thus allowing for possibly non-regular likelihoods, and allowing for
non-conjugate and improper priors. If the variance exists, it may be
heteroscedastic, namely, it may depend on the unknown function. We observe
quite a surprising phenomenon when applying our result to the spectral
approximation framework where it is possible to achieve the parametric rate of
convergence, i.e the problem becomes self-regularised. We also consider a
particular case of the unknown parameter being on the boundary of the parameter
set, and show that the rate of convergence in this case is faster than for an
interior point parameter.Comment: arXiv admin note: substantial text overlap with arXiv:1110.301
Status of NINJA: the Numerical INJection Analysis project
The 2008 NRDA conference introduced the Numerical INJection Analysis project (NINJA), a new collaborative effort between the numerical relativity community and the data analysis community. NINJA focuses on modeling and searching for gravitational wave signatures from the coalescence of binary system of compact objects. We review the scope of this collaboration and the components of the first NINJA project, where numerical relativity groups shared waveforms and data analysis teams applied various techniques to detect them when embedded in colored Gaussian noise
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