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Register a new userParameter estimation of spinning binary inspirals using Markov-chain Monte Carlo
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Added by
M. V. van der Sluys
Publication date
2008
fields
Physics
and research's language is
English
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We present a Markov-chain Monte-Carlo (MCMC) technique to study the source parameters of gravitational-wave signals from the inspirals of stellar-mass compact binaries detected with ground-based gravitational-wave detectors such as LIGO and Virgo, for the case where spin is present in the more massive compact object in the binary. We discuss aspects of the MCMC algorithm that allow us to sample the parameter space in an efficient way. We show sample runs that illustrate the possibilities of our MCMC code and the difficulties that we encounter.
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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 interferometers (LIGO, Virgo, and GEO-600). We present parameter-estimation simulations for inspirals of black-hole--neutron-star binaries using Markov-chain Monte-Carlo methods. As a specific example of the power of these methods, we consider source localisation in the sky and analyse the degeneracy in it when data from only two detectors are used. We focus on the effect that the black-hole spin has on the localisation estimation. We also report on a comparative Markov-chain Monte-Carlo analysis with two different waveform families, at 1.5 and 3.5 post-Newtonian order.
During the fifth science run of the Laser Interferometer Gravitational-wave Observatory (LIGO), signals modelling the gravitational waves emitted by coalescing non-spinning compact-object binaries were injected into the LIGO data stream. We analysed the data segments into which such injections were made using a Bayesian approach, implemented as a Markov-chain Monte-Carlo technique in our code SPINspiral. This technique enables us to determine the physical parameters of such a binary inspiral, including masses and spin, following a possible detection trigger. For the first time, we publish the results of a realistic parameter-estimation analysis of waveforms embedded in real detector noise. We used both spinning and non-spinning waveform templates for the data analysis and demonstrate that the intrinsic source parameters can be estimated with an accuracy of better than 1-3% in the chirp mass and 0.02-0.05 (8-20%) in the symmetric mass ratio if non-spinning waveforms are used. We also find a bias between the injected and recovered parameters, and attribute it to the difference in the post-Newtonian orders of the waveforms used for injection and analysis.
We introduce a fast Markov Chain Monte Carlo (MCMC) exploration of the astrophysical parameter space using a modified version of the publicly available code CIGALE (Code Investigating GALaxy emission). The original CIGALE builds a grid of theoretical Spectral Energy Distribution (SED) models and fits to photometric fluxes from Ultraviolet (UV) to Infrared (IR) to put contraints on parameters related to both formation and evolution of galaxies. Such a grid-based method can lead to a long and challenging parameter extraction since the computation time increases exponentially with the number of parameters considered and results can be dependent on the density of sampling points, which must be chosen in advance for each parameter. Markov Chain Monte Carlo methods, on the other hand, scale approximately linearly with the number of parameters, allowing a faster and more accurate exploration of the parameter space by using a smaller number of efficiently chosen samples. We test our MCMC version of the code CIGALE (called CIGALEMC) with simulated data. After checking the ability of the code to retrieve the input parameters used to build the mock sample, we fit theoretical SEDs to real data from the well known and studied SINGS sample. We discuss constraints on the parameters and show the advantages of our MCMC sampling method in terms of accuracy of the results and optimization of CPU time.
The coalescence of binary neutron stars are one of the main sources of gravitational waves for ground-based gravitational wave detectors. As Bayesian inference for binary neutron stars is computationally expensive, more efficient and faster converging algorithms are always needed. In this work, we conduct a feasibility study using a Hamiltonian Monte Carlo algorithm (HMC). The HMC is a sampling algorithm that takes advantage of gradient information from the geometry of the parameter space to efficiently sample from the posterior distribution, allowing the algorithm to avoid the random-walk behaviour commonly associated with stochastic samplers. As well as tuning the algorithms free parameters specifically for gravitational wave astronomy, we introduce a method for approximating the gradients of the log-likelihood that reduces the runtime for a $10^6$ trajectory run from ten weeks, using numerical derivatives along the Hamiltonian trajectories, to one day, in the case of non-spinning neutron stars. Testing our algorithm against a set of neutron star binaries using a detector network composed of Advanced LIGO and Advanced Virgo at optimal design, we demonstrate that not only is our algorithm more efficient than a standard sampler, but a $10^6$ trajectory HMC produces an effective sample size on the order of $10^4 - 10^5$ statistically independent samples.
Bayesian analysis of LISA data sets based on Markov chain Monte Carlo methods has been shown to be a challenging problem, in part due to the complicated structure of the likelihood function consisting of several isolated local maxima that dramatically reduces the efficiency of the sampling techniques. Here we introduce a new fully Markovian algorithm, a Delayed Rejection Metropolis-Hastings Markov chain Monte Carlo method, to efficiently explore these kind of structures and we demonstrate its performance on selected LISA data sets containing a known number of stellar-mass binary signals embedded in Gaussian stationary noise.
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