546 research outputs found
Bayesian evidence for two companions orbiting HIP 5158
We present results of a Bayesian analysis of radial velocity (RV) data for
the star HIP 5158, confirming the presence of two companions and also
constraining their orbital parameters. Assuming Keplerian orbits, the
two-companion model is found to be e^{48} times more probable than the
one-planet model, although the orbital parameters of the second companion are
only weakly constrained. The derived orbital periods are 345.6 +/- 2.0 d and
9017.8 +/- 3180.7 d respectively, and the corresponding eccentricities are 0.54
+/- 0.04 and 0.14 +/- 0.10. The limits on planetary mass (m \sin i) and
semimajor axis are (1.44 +/- 0.14 M_{J}, 0.89 +/- 0.01 AU) and (15.04 +/- 10.55
M_{J}, 7.70 +/- 1.88 AU) respectively. Owing to large uncertainty on the mass
of the second companion, we are unable to determine whether it is a planet or a
brown dwarf. The remaining `noise' (stellar jitter) unaccounted for by the
model is 2.28 +/- 0.31 m/s. We also analysed a three-companion model, but found
it to be e^{8} times less probable than the two-companion model.Comment: 5 pages, 4 figures, 3 tables. Added a couple of figures showing the
residuals after one and two companion fits. Accepted for publication in MNRAS
Letter
Exploring Multi-Modal Distributions with Nested Sampling
In performing a Bayesian analysis, two difficult problems often emerge.
First, in estimating the parameters of some model for the data, the resulting
posterior distribution may be multi-modal or exhibit pronounced (curving)
degeneracies. Secondly, in selecting between a set of competing models,
calculation of the Bayesian evidence for each model is computationally
expensive using existing methods such as thermodynamic integration. Nested
Sampling is a Monte Carlo method targeted at the efficient calculation of the
evidence, but also produces posterior inferences as a by-product and therefore
provides means to carry out parameter estimation as well as model selection.
The main challenge in implementing Nested Sampling is to sample from a
constrained probability distribution. One possible solution to this problem is
provided by the Galilean Monte Carlo (GMC) algorithm. We show results of
applying Nested Sampling with GMC to some problems which have proven very
difficult for standard Markov Chain Monte Carlo (MCMC) and down-hill methods,
due to the presence of large number of local minima and/or pronounced (curving)
degeneracies between the parameters. We also discuss the use of Nested Sampling
with GMC in Bayesian object detection problems, which are inherently
multi-modal and require the evaluation of Bayesian evidence for distinguishing
between true and spurious detections.Comment: Refereed conference proceeding, presented at 32nd International
Workshop on Bayesian Inference and Maximum Entropy Methods in Science and
Engineerin
Testing the mutual consistency of different supernovae surveys
It is now common practice to constrain cosmological parameters using
supernovae (SNe) catalogues constructed from several different surveys. Before
performing such a joint analysis, however, one should check that parameter
constraints derived from the individual SNe surveys that make up the catalogue
are mutually consistent. We describe a statistically-robust mutual consistency
test, which we calibrate using simulations, and apply it to each pairwise
combination of the surveys making up, respectively, the UNION2 catalogue and
the very recent JLA compilation by Betoule et al. We find no inconsistencies in
the latter case, but conclusive evidence for inconsistency between some survey
pairs in the UNION2 catalogue.Comment: 8 pages, 9 figures, submitted to MNRA
Weak lensing by triaxial galaxy clusters
Weak gravitational lensing studies of galaxy clusters often assume a
spherical cluster model to simplify the analysis, but some recent studies have
suggested this simplifying assumption may result in large biases in estimated
cluster masses and concentration values, since clusters are expected to exhibit
triaxiality. Several such analyses have, however, quoted expressions for the
spatial derivatives of the lensing potential in triaxial models, which are open
to misinterpretation. In this paper, we give a clear description of weak
lensing by triaxial NFW galaxy clusters and also present an efficient and
robust method to model these clusters and obtain parameter estimates. By
considering four highly triaxial NFW galaxy clusters, we re-examine the impact
of simplifying spherical assumptions and found that while the concentration
estimates are largely unbiased except in one of our traixial NFW simulated
clusters, for which the concentration is only slightly biased, the masses are
significantly biased, by up to 40%, for all the clusters we analysed. Moreover,
we find that such assumptions can lead to the erroneous conclusion that some
substructure is present in the galaxy clusters or, even worse, that multiple
galaxy clusters are present in the field. Our cluster fitting method also
allows one to answer the question of whether a given cluster exhibits
triaxiality or a simple spherical model is good enough.Comment: 8 pages, 3 figures, 2 tables, minor changes in response to referee's
comments, accepted for publication in MNRA
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
The impact of priors and observables on parameter inferences in the Constrained MSSM
We use a newly released version of the SuperBayeS code to analyze the impact
of the choice of priors and the influence of various constraints on the
statistical conclusions for the preferred values of the parameters of the
Constrained MSSM. We assess the effect in a Bayesian framework and compare it
with an alternative likelihood-based measure of a profile likelihood. We employ
a new scanning algorithm (MultiNest) which increases the computational
efficiency by a factor ~200 with respect to previously used techniques. We
demonstrate that the currently available data are not yet sufficiently
constraining to allow one to determine the preferred values of CMSSM parameters
in a way that is completely independent of the choice of priors and statistical
measures. While b->s gamma generally favors large m_0, this is in some contrast
with the preference for low values of m_0 and m_1/2 that is almost entirely a
consequence of a combination of prior effects and a single constraint coming
from the anomalous magnetic moment of the muon, which remains somewhat
controversial. Using an information-theoretical measure, we find that the
cosmological dark matter abundance determination provides at least 80% of the
total constraining power of all available observables. Despite the remaining
uncertainties, prospects for direct detection in the CMSSM remain excellent,
with the spin-independent neutralino-proton cross section almost guaranteed
above sigma_SI ~ 10^{-10} pb, independently of the choice of priors or
statistics. Likewise, gluino and lightest Higgs discovery at the LHC remain
highly encouraging. While in this work we have used the CMSSM as particle
physics model, our formalism and scanning technique can be readily applied to a
wider class of models with several free parameters.Comment: Minor changes, extended discussion of profile likelihood. Matches
JHEP accepted version. SuperBayeS code with MultiNest algorithm available at
http://www.superbayes.or
A Coverage Study of the CMSSM Based on ATLAS Sensitivity Using Fast Neural Networks Techniques
We assess the coverage properties of confidence and credible intervals on the
CMSSM parameter space inferred from a Bayesian posterior and the profile
likelihood based on an ATLAS sensitivity study. In order to make those
calculations feasible, we introduce a new method based on neural networks to
approximate the mapping between CMSSM parameters and weak-scale particle
masses. Our method reduces the computational effort needed to sample the CMSSM
parameter space by a factor of ~ 10^4 with respect to conventional techniques.
We find that both the Bayesian posterior and the profile likelihood intervals
can significantly over-cover and identify the origin of this effect to physical
boundaries in the parameter space. Finally, we point out that the effects
intrinsic to the statistical procedure are conflated with simplifications to
the likelihood functions from the experiments themselves.Comment: Further checks about accuracy of neural network approximation, fixed
typos, added refs. Main results unchanged. Matches version accepted by JHE
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