446 research outputs found
A Bayesian approach to the study of white dwarf binaries in LISA data: The application of a reversible jump Markov chain Monte Carlo method
The Laser Interferometer Space Antenna (LISA) defines new demands on data
analysis efforts in its all-sky gravitational wave survey, recording
simultaneously thousands of galactic compact object binary foreground sources
and tens to hundreds of background sources like binary black hole mergers and
extreme mass ratio inspirals. We approach this problem with an adaptive and
fully automatic Reversible Jump Markov Chain Monte Carlo sampler, able to
sample from the joint posterior density function (as established by Bayes
theorem) for a given mixture of signals "out of the box'', handling the total
number of signals as an additional unknown parameter beside the unknown
parameters of each individual source and the noise floor. We show in examples
from the LISA Mock Data Challenge implementing the full response of LISA in its
TDI description that this sampler is able to extract monochromatic Double White
Dwarf signals out of colored instrumental noise and additional foreground and
background noise successfully in a global fitting approach. We introduce 2
examples with fixed number of signals (MCMC sampling), and 1 example with
unknown number of signals (RJ-MCMC), the latter further promoting the idea
behind an experimental adaptation of the model indicator proposal densities in
the main sampling stage. We note that the experienced runtimes and degeneracies
in parameter extraction limit the shown examples to the extraction of a low but
realistic number of signals.Comment: 18 pages, 9 figures, 3 tables, accepted for publication in PRD,
revised versio
Optimizing gravitational-wave searches for a population of coalescing binaries: Intrinsic parameters
We revisit the problem of searching for gravitational waves from inspiralling
compact binaries in Gaussian coloured noise. For binaries with quasicircular
orbits and non-precessing component spins, considering dominant mode emission
only, if the intrinsic parameters of the binary are known then the optimal
statistic for a single detector is the well-known two-phase matched filter.
However, the matched filter signal-to-noise ratio is /not/ in general an
optimal statistic for an astrophysical population of signals, since their
distribution over the intrinsic parameters will almost certainly not mirror
that of noise events, which is determined by the (Fisher) information metric.
Instead, the optimal statistic for a given astrophysical distribution will be
the Bayes factor, which we approximate using the output of a standard template
matched filter search. We then quantify the possible improvement in number of
signals detected for various populations of non-spinning binaries: for a
distribution of signals uniformly distributed in volume and with component
masses distributed uniformly over the range ,
at fixed expected SNR, we find more
signals at a false alarm threshold of Hz in a single detector. The
method may easily be generalized to binaries with non-precessing spins.Comment: Version accepted by Phys. Rev.
How would GW150914 look with future GW detector networks?
The first detected gravitational wave signal, GW150914, was produced by the
coalescence of a stellar-mass binary black hole. Along with the subsequent
detection of GW151226, GW170104 and the candidate event LVT151012, this gives
us evidence for a population of black hole binaries with component masses in
the tens of solar masses. As detector sensitivity improves, this type of source
is expected to make a large contribution to the overall number of detections,
but has received little attention compared to binary neutron star systems in
studies of projected network performance. We simulate the observation of a
system like GW150914 with different proposed network configurations, and study
the precision of parameter estimates, particularly source location, orientation
and masses. We find that the improvements to low frequency sensitivity that are
expected with continued commissioning will improve the precision of chirp mass
estimates by an order of magnitude, whereas the improvements in sky location
and orientation are driven by the expanded network configuration. This
demonstrates that both sensitivity and number of detectors will be important
factors in the scientific potential of second generation detector networks.Comment: 18 pages, 5 figures, 2 table
Markov chain Monte Carlo searches for Galactic binaries in Mock LISA Data Challenge 1B data sets
We are developing a Bayesian approach based on Markov chain Monte Carlo
techniques to search for and extract information about white dwarf binary
systems with the Laser Interferometer Space Antenna (LISA). Here we present
results obtained by applying an initial implementation of this method to some
of the data sets released in Round 1B of the Mock LISA Data Challenges. For
Challenges 1B.1.1a and 1b the signals were recovered with parameters lying
within the 95.5% posterior probability interval and the correlation between the
true and recovered waveform is in excess of 99%. Results were not submitted for
Challenge 1B.1.1c due to some convergence problems of the algorithms, despite
this, the signal was detected in a search over a 2 mHz band.Comment: 11 pages, 5 figures, 12th GWDAW (Gravitational Wave Data Analysis
Workshop). Accepted for publication in CQ
Accelerating gravitational wave parameter estimation with multi-band template interpolation
Parameter estimation on gravitational wave signals from compact binary
coalescence (CBC) requires the evaluation of computationally intensive waveform
models, typically the bottleneck in the analysis. This cost will increase
further as low frequency sensitivity in later second and third generation
detectors motivates the use of longer waveforms.
We describe a method for accelerating parameter estimation by exploiting the
chirping behaviour of the signals to sample the waveform sparsely for portions
where the full frequency resolution is not required. We demonstrate that the
method can reproduce the original results with a waveform mismatch of , but with a waveform generation cost up to times
lower for computationally costly frequency-domain waveforms starting from below
8 Hz
Measuring intermediate mass black hole binaries with advanced gravitational wave detectors
We perform a systematic study to explore the accuracy with which the
parameters of intermediate-mass black-hole binary systems can be measured from
their gravitational wave (GW) signatures using second-generation GW detectors.
We make use of the most recent reduced-order models containing inspiral, merger
and ringdown signals of aligned-spin effective-one-body waveforms (SEOBNR) to
significantly speed up the calculations. We explore the phenomenology of the
measurement accuracies for binaries with total masses between 50 and 500
and mass ratios between 0.1 and 1. We find that (i) at total masses
below ~200 , where the signal-to-noise-ratio is dominated by the
inspiral portion of the signal, the chirp mass parameter can be accurately
measured; (ii) at higher masses, the information content is dominated by the
ringdown, and total mass is measured more accurately; (iii) the mass of the
lower-mass companion is poorly estimated, especially at high total mass and
more extreme mass ratios; (iv) spin cannot be accurately measured for our
injection set with non-spinning components. Most importantly, we find that for
binaries with non-spinning components at all values of the mass ratio in the
considered range and at network signal-to-noise ratio of 15, analyzed with
spin-aligned templates, the presence of an intermediate-mass black hole with
mass >100 can be confirmed with 95% confidence in any binary that
includes a component with a mass of 130 or greater.Comment: 6 pages, 8 figures; published versio
Observational Black Hole Spectroscopy: A time-domain multimode analysis of GW150914
The detection of the least damped quasi-normal mode from the remnant of the
gravitational wave event GW150914 realised the long sought possibility to
observationally study the properties of quasi-stationary black hole spacetimes
through gravitational waves. Past literature has extensively explored this
possibility and the emerging field has been named "black hole spectroscopy". In
this study, we present results regarding the ringdown spectrum of GW150914,
obtained by application of Bayesian inference to identify and characterise the
ringdown modes. We employ a pure time-domain analysis method which infers from
the data the time of transition between the non-linear and quasi-linear regime
of the post-merger emission in concert with all other parameters characterising
the source. We find that the data provides no evidence for the presence of more
than one quasi-normal mode. However, from the central frequency and damping
time posteriors alone, no unambiguous identification of a single mode is
possible. More in-depth analysis adopting a ringdown model based on results in
perturbation theory over the Kerr metric, confirms that the data do not provide
enough evidence to discriminate among an and the subset of modes.
Our work provides the first comprehensive agnostic framework to observationally
investigate astrophysical black holes' ringdown spectra.Comment: 9 pages, 8 figure
Fixed Investment in the American Business Cycle, 1919-83
Contributions are made by this paper in three areas, methodological, data creation, and empirical. The methodological section finds that, while structural model building exercises may be useful in suggesting lists of variables that may play an explanatory role in investment equations, they generally achieve identification of structural parameters only by imposing arbitrary and unbelievable simplifying assumptions and exclusion restrictions.The paper advocates a hybrid methodology combining guidance from traditional structural models on the choice and form of explanatory variables to be included, with estimation in a reduced-form format that introduces all explanatory variables and the lagged dependent variable with the same number of unconstrained lag coefficients. The second contribution is the use of a new set of quarterly data for major expenditure categories of GNP extending back to 1919. The data file also contains quarterly data back to 1919 for other variables, including the capital stock, interest rates, the cost of capital including tax incentive effects, a proxy for Tobin's "Q", and the real money supply.The empirical results support the view that there are two basic impulses in the business cycle, real and financial.The real impulse appears in our statistical evidence as an autonomous innovation to investment in structures. We interpret these structures innovations as due in turn to changes in the rate of population growth, episodes of speculation and overbuilding, and Schumpeterian waves of innovation.The financial impulse works through the effect on investment of changes in the money supply, as well as the real interest rate (in the case of postwar investment in durable equipment).There is a strong role for the money supply as a determinant of investment behavior, relative to such other factors as the user cost of capital or Tobin's "Q". The role of the money supply is interpreted as primarily reflecting the banking contraction of 1929-33 and the episodes of credit crunches and disintermediation in the postwar years. Another feature of the empirical work is the attention paid to aggregation. Coefficient estimates are more stable when four types of investment expenditures are aggregated along the structures-equipment dimension than along the household-business dimension. Historical decompositions highlight the role of autonomous innovations in structures investment and in the money supply, and an inspection of residuals suggests that the main autonomous downward shift in spending in 1929-30 was in fixed investment, not nondurable consumption.
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