51 research outputs found
The search for spinning black hole binaries in mock LISA data using a genetic algorithm
Coalescing massive Black Hole binaries are the strongest and probably the
most important gravitational wave sources in the LISA band. The spin and
orbital precessions bring complexity in the waveform and make the likelihood
surface richer in structure as compared to the non-spinning case. We introduce
an extended multimodal genetic algorithm which utilizes the properties of the
signal and the detector response function to analyze the data from the third
round of mock LISA data challenge (MLDC 3.2). The performance of this method is
comparable, if not better, to already existing algorithms. We have found all
five sources present in MLDC 3.2 and recovered the coalescence time, chirp
mass, mass ratio and sky location with reasonable accuracy. As for the orbital
angular momentum and two spins of the Black Holes, we have found a large number
of widely separated modes in the parameter space with similar maximum
likelihood values.Comment: 25 pages, 9 figure
BAMBI: blind accelerated multimodal Bayesian inference
In this paper we present an algorithm for rapid Bayesian analysis that
combines the benefits of nested sampling and artificial neural networks. The
blind accelerated multimodal Bayesian inference (BAMBI) algorithm implements
the MultiNest package for nested sampling as well as the training of an
artificial neural network (NN) to learn the likelihood function. In the case of
computationally expensive likelihoods, this allows the substitution of a much
more rapid approximation in order to increase significantly the speed of the
analysis. We begin by demonstrating, with a few toy examples, the ability of a
NN to learn complicated likelihood surfaces. BAMBI's ability to decrease
running time for Bayesian inference is then demonstrated in the context of
estimating cosmological parameters from Wilkinson Microwave Anisotropy Probe
and other observations. We show that valuable speed increases are achieved in
addition to obtaining NNs trained on the likelihood functions for the different
model and data combinations. These NNs can then be used for an even faster
follow-up analysis using the same likelihood and different priors. This is a
fully general algorithm that can be applied, without any pre-processing, to
other problems with computationally expensive likelihood functions.Comment: 12 pages, 8 tables, 17 figures; accepted by MNRAS; v2 to reflect
minor changes in published versio
Use of the MultiNest algorithm for gravitational wave data analysis
We describe an application of the MultiNest algorithm to gravitational wave
data analysis. MultiNest is a multimodal nested sampling algorithm designed to
efficiently evaluate the Bayesian evidence and return posterior probability
densities for likelihood surfaces containing multiple secondary modes. The
algorithm employs a set of live points which are updated by partitioning the
set into multiple overlapping ellipsoids and sampling uniformly from within
them. This set of live points climbs up the likelihood surface through nested
iso-likelihood contours and the evidence and posterior distributions can be
recovered from the point set evolution. The algorithm is model-independent in
the sense that the specific problem being tackled enters only through the
likelihood computation, and does not change how the live point set is updated.
In this paper, we consider the use of the algorithm for gravitational wave data
analysis by searching a simulated LISA data set containing two non-spinning
supermassive black hole binary signals. The algorithm is able to rapidly
identify all the modes of the solution and recover the true parameters of the
sources to high precision.Comment: 18 pages, 4 figures, submitted to Class. Quantum Grav; v2 includes
various changes in light of referee's comment
Bayesian posterior repartitioning for nested sampling
Priors in Bayesian analyses often encode informative domain knowledge that
can be useful in making the inference process more efficient. Occasionally,
however, priors may be unrepresentative of the parameter values for a given
dataset, which can result in inefficient parameter space exploration, or even
incorrect inferences, particularly for nested sampling (NS) algorithms. Simply
broadening the prior in such cases may be inappropriate or impossible in some
applications. Hence our previous solution to this problem, known as posterior
repartitioning (PR), redefines the prior and likelihood while keeping their
product fixed, so that the posterior inferences and evidence estimates remain
unchanged, but the efficiency of the NS process is significantly increased. In
its most practical form, PR raises the prior to some power , which is
introduced as an auxiliary variable that must be determined on a case-by-case
basis, usually by lowering from unity according to some pre-defined
`annealing schedule' until the resulting inferences converge to a consistent
solution. Here we present a very simple yet powerful alternative Bayesian
approach, in which is instead treated as a hyperparameter that is
inferred from the data alongside the original parameters of the problem, and
then marginalised over to obtain the final inference. We show through numerical
examples that this Bayesian PR (BPR) method provides a very robust,
self-adapting and computationally efficient `hands-off' solution to the problem
of unrepresentative priors in Bayesian inference using NS. Moreover, unlike the
original PR method, we show that even for representative priors BPR has a
negligible computational overhead relative to standard nesting sampling, which
suggests that it should be used as the default in all NS analyses
Classifying LISA gravitational wave burst signals using Bayesian evidence
We consider the problem of characterisation of burst sources detected with
the Laser Interferometer Space Antenna (LISA) using the multi-modal nested
sampling algorithm, MultiNest. We use MultiNest as a tool to search for
modelled bursts from cosmic string cusps, and compute the Bayesian evidence
associated with the cosmic string model. As an alternative burst model, we
consider sine-Gaussian burst signals, and show how the evidence ratio can be
used to choose between these two alternatives. We present results from an
application of MultiNest to the last round of the Mock LISA Data Challenge, in
which we were able to successfully detect and characterise all three of the
cosmic string burst sources present in the release data set. We also present
results of independent trials and show that MultiNest can detect cosmic string
signals with signal-to-noise ratio (SNR) as low as ~7 and sine-Gaussian signals
with SNR as low as ~8. In both cases, we show that the threshold at which the
sources become detectable coincides with the SNR at which the evidence ratio
begins to favour the correct model over the alternative.Comment: 21 pages, 11 figures, accepted by CQG; v2 has minor changes for
consistency with accepted versio
Further Sunyaev-Zel'dovich observations of two Planck ERCSC clusters with the Arcminute Microkelvin Imager
We present follow-up observations of two galaxy clusters detected blindly via
the Sunyaev-Zel'dovich (SZ) effect and released in the Planck Early Release
Compact Source Catalogue. We use the Arcminute Microkelvin Imager, a dual-array
14-18 GHz radio interferometer. After radio source subtraction, we find a SZ
decrement of integrated flux density -1.08+/-0.10 mJy toward PLCKESZ
G121.11+57.01, and improve the position measurement of the cluster, finding the
centre to be RA 12 59 36.4, Dec +60 04 46.8, to an accuracy of 20 arcseconds.
The region of PLCKESZ G115.71+17.52 contains strong extended emission, so we
are unable to confirm the presence of this cluster via the SZ effect.Comment: 4 tables, 3 figures, revised after referee's comments and resubmitted
to MNRA
Fitting the Phenomenological MSSM
We perform a global Bayesian fit of the phenomenological minimal
supersymmetric standard model (pMSSM) to current indirect collider and dark
matter data. The pMSSM contains the most relevant 25 weak-scale MSSM
parameters, which are simultaneously fit using `nested sampling' Monte Carlo
techniques in more than 15 years of CPU time. We calculate the Bayesian
evidence for the pMSSM and constrain its parameters and observables in the
context of two widely different, but reasonable, priors to determine which
inferences are robust. We make inferences about sparticle masses, the sign of
the parameter, the amount of fine tuning, dark matter properties and the
prospects for direct dark matter detection without assuming a restrictive
high-scale supersymmetry breaking model. We find the inferred lightest CP-even
Higgs boson mass as an example of an approximately prior independent
observable. This analysis constitutes the first statistically convergent pMSSM
global fit to all current data.Comment: Added references, paragraph on fine-tunin
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