183,605 research outputs found
Meaningful characterisation of perturbative theoretical uncertainties
We consider the problem of assigning a meaningful degree of belief to
uncertainty estimates of perturbative series. We analyse the assumptions which
are implicit in the conventional estimates made using renormalisation scale
variations. We then formulate a Bayesian model that, given equivalent initial
hypotheses, allows one to characterise a perturbative theoretical uncertainty
in a rigorous way in terms of a credibility interval for the remainder of the
series. We compare its outcome to the conventional uncertainty estimates in the
simple case of the calculation of QCD corrections to the e+e- -> hadrons
process. We find comparable results, but with important conceptual differences.
This work represents a first step in the direction of a more comprehensive and
rigorous handling of theoretical uncertainties in perturbative calculations
used in high energy phenomenology.Comment: 28 pages, 5 figures. Language modified in order to make it more
'bayesian'. No change in results. Version published in JHE
Open-cluster density profiles derived using a kernel estimator
Surface and spatial radial density profiles in open clusters are derived
using a kernel estimator method. Formulae are obtained for the contribution of
every star into the spatial density profile. The evaluation of spatial density
profiles is tested against open-cluster models from N-body experiments with N =
500. Surface density profiles are derived for seven open clusters (NGC 1502,
1960, 2287, 2516, 2682, 6819 and 6939) using Two-Micron All-Sky Survey data and
for different limiting magnitudes. The selection of an optimal kernel
half-width is discussed. It is shown that open-cluster radius estimates hardly
depend on the kernel half-width. Hints of stellar mass segregation and
structural features indicating cluster non-stationarity in the regular force
field are found. A comparison with other investigations shows that the data on
open-cluster sizes are often underestimated. The existence of an extended
corona around the open cluster NGC 6939 was confirmed. A combined function
composed of the King density profile for the cluster core and the uniform
sphere for the cluster corona is shown to be a better approximation of the
surface radial density profile.The King function alone does not reproduce
surface density profiles of sample clusters properly. The number of stars, the
cluster masses and the tidal radii in the Galactic gravitational field for the
sample clusters are estimated. It is shown that NGC 6819 and 6939 are extended
beyond their tidal surfaces.Comment: 17 pages, 15 figure
Comparison of Gravitational Wave Detector Network Sky Localization Approximations
Gravitational waves emitted during compact binary coalescences are a
promising source for gravitational-wave detector networks. The accuracy with
which the location of the source on the sky can be inferred from gravitational
wave data is a limiting factor for several potential scientific goals of
gravitational-wave astronomy, including multi-messenger observations. Various
methods have been used to estimate the ability of a proposed network to
localize sources. Here we compare two techniques for predicting the uncertainty
of sky localization -- timing triangulation and the Fisher information matrix
approximations -- with Bayesian inference on the full, coherent data set. We
find that timing triangulation alone tends to over-estimate the uncertainty in
sky localization by a median factor of for a set of signals from
non-spinning compact object binaries ranging up to a total mass of , and the over-estimation increases with the mass of the system. We
find that average predictions can be brought to better agreement by the
inclusion of phase consistency information in timing-triangulation techniques.
However, even after corrections, these techniques can yield significantly
different results to the full analysis on specific mock signals. Thus, while
the approximate techniques may be useful in providing rapid, large scale
estimates of network localization capability, the fully coherent Bayesian
analysis gives more robust results for individual signals, particularly in the
presence of detector noise.Comment: 11 pages, 7 Figure
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