770 research outputs found
Classification of chirp signals using hierarchical bayesian learning and MCMC methods
This paper addresses the problem of classifying chirp signals using hierarchical Bayesian learning together with Markov chain Monte Carlo (MCMC) methods. Bayesian learning consists of estimating the distribution of the observed data conditional on each class from a set of training samples. Unfortunately, this estimation requires to evaluate intractable multidimensional integrals. This paper studies an original implementation of hierarchical Bayesian learning that estimates the class conditional probability densities using MCMC methods. The performance of this implementation is first studied via an academic example for which the class conditional densities are known. The problem of classifying chirp signals is then addressed by using a similar hierarchical Bayesian learning implementation based on a Metropolis-within-Gibbs algorithm
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
Basic Parameter Estimation of Binary Neutron Star Systems by the Advanced LIGO/Virgo Network
Within the next five years, it is expected that the Advanced LIGO/Virgo
network will have reached a sensitivity sufficient to enable the routine
detection of gravitational waves. Beyond the initial detection, the scientific
promise of these instruments relies on the effectiveness of our physical
parameter estimation capabilities. The majority of this effort has been towards
the detection and characterization of gravitational waves from compact binary
coalescence, e.g. the coalescence of binary neutron stars. While several
previous studies have investigated the accuracy of parameter estimation with
advanced detectors, the majority have relied on approximation techniques such
as the Fisher Matrix. Here we report the statistical uncertainties that will be
achievable for optimal detection candidates (SNR = 20) using the full parameter
estimation machinery developed by the LIGO/Virgo Collaboration via Markov-Chain
Monte Carlo methods. We find the recovery of the individual masses to be
fractionally within 9% (15%) at the 68% (95%) credible intervals for equal-mass
systems, and within 1.9% (3.7%) for unequal-mass systems. We also find that the
Advanced LIGO/Virgo network will constrain the locations of binary neutron star
mergers to a median uncertainty of 5.1 deg^2 (13.5 deg^2) on the sky. This
region is improved to 2.3 deg^2 (6 deg^2) with the addition of the proposed
LIGO India detector to the network. We also report the average uncertainties on
the luminosity distances and orbital inclinations of ideal detection candidates
that can be achieved by different network configurations.Comment: Second version: 15 pages, 9 figures, accepted in Ap
Coherent Bayesian analysis of inspiral signals
We present in this paper a Bayesian parameter estimation method for the
analysis of interferometric gravitational wave observations of an inspiral of
binary compact objects using data recorded simultaneously by a network of
several interferometers at different sites. We consider neutron star or black
hole inspirals that are modeled to 3.5 post-Newtonian (PN) order in phase and
2.5 PN in amplitude. Inference is facilitated using Markov chain Monte Carlo
methods that are adapted in order to efficiently explore the particular
parameter space. Examples are shown to illustrate how and what information
about the different parameters can be derived from the data. This study uses
simulated signals and data with noise characteristics that are assumed to be
defined by the LIGO and Virgo detectors operating at their design
sensitivities. Nine parameters are estimated, including those associated with
the binary system, plus its location on the sky. We explain how this technique
will be part of a detection pipeline for binary systems of compact objects with
masses up to 20 \sunmass, including cases where the ratio of the individual
masses can be extreme.Comment: Accepted for publication in Classical and Quantum Gravity, Special
issue for GWDAW-1
Noise residuals for GW150914 using maximum likelihood and numerical relativity templates
We reexamine the results presented in a recent work by Nielsen et al. [1], in
which the properties of the noise residuals in the 40\,ms chirp domain of
GW150914 were investigated. This paper confirmed the presence of strong (i.e.,
about 0.80) correlations between residual noise in the Hanford and Livingston
detectors in the chirp domain as previously seen by us [2] when using a
numerical relativity template given in [3]. It was also shown in [1] that a
so-called maximum likelihood template can reduce these statistically
significant cross-correlations. Here, we demonstrate that the reduction of
correlation and statistical significance is due to (i) the use of a peculiar
template which is qualitatively different from the properties of GW150914
originally published by LIGO, (ii) a suspicious MCMC chain, (iii) uncertainties
in the matching of the maximum likelihood (ML) template to the data in the
Fourier domain, and (iv) a biased estimation of the significance that gives
counter-intuitive results. We show that rematching the maximum likelihood
template to the data in the 0.2\,s domain containing the GW150914 signal
restores these correlations at the level of of those found in [1]. With
necessary corrections, the probability given in [1] will decrease by more than
one order of magnitude. Since the ML template is itself problematic, results
associated with this template are illustrative rather than final.Comment: Minor correction
Coherent Bayesian inference on compact binary inspirals using a network of interferometric gravitational wave detectors
Presented in this paper is a Markov chain Monte Carlo (MCMC) routine for
conducting coherent parameter estimation for interferometric gravitational wave
observations of an inspiral of binary compact objects using data from multiple
detectors. The MCMC technique uses data from several interferometers and infers
all nine of the parameters (ignoring spin) associated with the binary system,
including the distance to the source, the masses, and the location on the sky.
The Metropolis-algorithm utilises advanced MCMC techniques, such as importance
resampling and parallel tempering. The data is compared with time-domain
inspiral templates that are 2.5 post-Newtonian (PN) in phase and 2.0 PN in
amplitude. Our routine could be implemented as part of an inspiral detection
pipeline for a world wide network of detectors. Examples are given for
simulated signals and data as seen by the LIGO and Virgo detectors operating at
their design sensitivity.Comment: 10 pages, 4 figure
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
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