1,056 research outputs found
On Multivariate Records from Random Vectors with Independent Components
Let be independent copies of a
random vector with values in and with a
continuous distribution function. The random vector is a
complete record, if each of its components is a record. As we require
to have independent components, crucial results for univariate
records clearly carry over. But there are substantial differences as well:
While there are infinitely many records in case , there occur only
finitely many in the series if . Consequently, there is a terminal
complete record with probability one. We compute the distribution of the random
total number of complete records and investigate the distribution of the
terminal record. For complete records, the sequence of waiting times forms a
Markov chain, but differently from the univariate case, now the state infinity
is an absorbing element of the state space
Some Results on Joint Record Events
Let be independent and identically distributed random
variables on the real line with a joint continuous distribution function .
The stochastic behavior of the sequence of subsequent records is well known.
Alternatively to that, we investigate the stochastic behavior of arbitrary
, under the condition that they are records, without knowing their
orders in the sequence of records. The results are completely different. In
particular it turns out that the distribution of , being a record, is not
affected by the additional knowledge that is a record as well. On the
contrary, the distribution of , being a record, is affected by the
additional knowledge that is a record as well. If has a density, then
the gain of this additional information, measured by the corresponding
Kullback-Leibler distance, is , independent of . We derive the limiting
joint distribution of two records, which is not a bivariate extreme value
distribution. We extend this result to the case of three records. In a special
case we also derive the limiting joint distribution of increments among
records
Accuracy of core mass estimates in simulated observations of dust emission
We study the reliability of mass estimates obtained for molecular cloud cores
using sub-millimetre and infrared dust emission. We use magnetohydrodynamic
simulations and radiative transfer to produce synthetic observations with
spatial resolution and noise levels typical of Herschel surveys. We estimate
dust colour temperatures using different pairs of intensities, calculate column
densities and compare the estimated masses with the true values. We compare
these results to the case when all five Herschel wavelengths are available. We
investigate the effects of spatial variations of dust properties and the
influence of embedded heating sources. Wrong assumptions of dust opacity and
its spectral index beta can cause significant systematic errors in mass
estimates. These are mainly multiplicative and leave the slope of the mass
spectrum intact, unless cores with very high optical depth are included.
Temperature variations bias colour temperature estimates and, in quiescent
cores with optical depths higher than for normal stable cores, masses can be
underestimated by up to one order of magnitude. When heated by internal
radiation sources the observations recover the true mass spectra. The shape,
although not the position, of the mass spectrum is reliable against
observational errors and biases introduced in the analysis. This changes only
if the cores have optical depths much higher than expected for basic
hydrostatic equilibrium conditions. Observations underestimate the value of
beta whenever there are temperature variations along the line of sight. A bias
can also be observed when the true beta varies with wavelength. Internal
heating sources produce an inverse correlation between colour temperature and
beta that may be difficult to separate from any intrinsic beta(T) relation of
the dust grains. This suggests caution when interpreting the observed mass
spectra and the spectral indices.Comment: Revised version, 17 pages, 17 figures, submitted to A&
Statistical Modeling of Spatial Extremes
The areal modeling of the extremes of a natural process such as rainfall or
temperature is important in environmental statistics; for example,
understanding extreme areal rainfall is crucial in flood protection. This
article reviews recent progress in the statistical modeling of spatial
extremes, starting with sketches of the necessary elements of extreme value
statistics and geostatistics. The main types of statistical models thus far
proposed, based on latent variables, on copulas and on spatial max-stable
processes, are described and then are compared by application to a data set on
rainfall in Switzerland. Whereas latent variable modeling allows a better fit
to marginal distributions, it fits the joint distributions of extremes poorly,
so appropriately-chosen copula or max-stable models seem essential for
successful spatial modeling of extremes.Comment: Published in at http://dx.doi.org/10.1214/11-STS376 the Statistical
Science (http://www.imstat.org/sts/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Rejoinder to "Statistical Modeling of Spatial Extremes"
Rejoinder to "Statistical Modeling of Spatial Extremes" by A. C. Davison, S.
A. Padoan and M. Ribatet [arXiv:1208.3378].Comment: Published in at http://dx.doi.org/10.1214/12-STS376REJ the
Statistical Science (http://www.imstat.org/sts/) by the Institute of
Mathematical Statistics (http://www.imstat.org
A Corona Australis cloud filament seen in NIR scattered light I. Comparison with extinction of background stars
With current near-infrared (NIR) instruments the near-infrared light
scattered from interstellar clouds can be mapped over large areas. The surface
brightness carries information on the line-of-sight dust column density.
Therefore, scattered light could provide an important tool to study mass
distribution in quiescent interstellar clouds at a high, even sub-arcsecond
resolution. We wish to confirm the assumption that light scattering dominates
the surface brightness in all NIR bands. Furthermore, we want to show that
scattered light can be used for an accurate estimation of dust column densities
in clouds with Av in the range 1-15mag. We have obtained NIR images of a
quiescent filament in the Corona Australis molecular cloud. The observations
provide maps of diffuse surface brightness in J, H, and Ks bands. Using the
assumption that signal is caused by scattered light we convert surface
brightness data into a map of dust column density. The same observations
provide colour excesses for a large number of background stars. These data are
used to derive an extinction map of the cloud. The two, largely independent
tracers of the cloud structure are compared. Results. In regions below Av=15m
both diffuse surface brightness and background stars lead to similar column
density estimates. The existing differences can be explained as a result of
normal observational errors and bias in the sampling of extinctions provided by
the background stars. There is no indication that thermal dust emission would
have a significant contribution even in the Ks band. The results show that,
below Av=15mag, scattered light does provide a reliable way to map cloud
structure. Compared with the use of background stars it can also in practice
provide a significantly higher spatial resolution.Comment: 14 pages, 15 figures, accepted to A&A, the version includes small
changes in the text and an added appendi
The Density Variance Mach Number Relation in the Taurus Molecular Cloud
Supersonic turbulence in molecular clouds is a key agent in generating
density enhancements that may subsequently go on to form stars. The stronger
the turbulence - the higher the Mach number - the more extreme the density
fluctuations are expected to be. Numerical models predict an increase in
density variance with rms Mach number of the form: sigma^{2}_{rho/rho_{0}} =
b^{2}M^{2}, where b is a numerically-estimated parameter, and this prediction
forms the basis of a large number of analytic models of star formation. We
provide an estimate of the parameter b from 13CO J=1-0 spectral line imaging
observations and extinction mapping of the Taurus molecular cloud, using a
recently developed technique that needs information contained solely in the
projected column density field to calculate sigma^{2}_{rho/rho_{0}}. We find b
~ 0.48, which is consistent with typical numerical estimates, and is
characteristic of turbulent driving that includes a mixture of solenoidal and
compressive modes. More conservatively, we constrain b to lie in the range
0.3-0.8, depending on the influence of sub-resolution structure and the role of
diffuse atomic material in the column density budget. We also report a break in
the Taurus column density power spectrum at a scale of ~1pc, and find that the
break is associated with anisotropy in the power spectrum. The break is
observed in both 13CO and dust extinction power spectra, which, remarkably, are
effectively identical despite detailed spatial differences between the 13CO and
dust extinction maps. [ abridged ]Comment: 8 pages, 9 figures. Accepted for publication in A&
Simulating Supersonic Turbulence in Magnetized Molecular Clouds
We present results of large-scale three-dimensional simulations of weakly
magnetized supersonic turbulence at grid resolutions up to 1024^3 cells. Our
numerical experiments are carried out with the Piecewise Parabolic Method on a
Local Stencil and assume an isothermal equation of state. The turbulence is
driven by a large-scale isotropic solenoidal force in a periodic computational
domain and fully develops in a few flow crossing times. We then evolve the flow
for a number of flow crossing times and analyze various statistical properties
of the saturated turbulent state. We show that the energy transfer rate in the
inertial range of scales is surprisingly close to a constant, indicating that
Kolmogorov's phenomenology for incompressible turbulence can be extended to
magnetized supersonic flows. We also discuss numerical dissipation effects and
convergence of different turbulence diagnostics as grid resolution refines from
256^3 to 1024^3 cells.Comment: 10 pages, 3 figures, to appear in the proceedings of the DOE/SciDAC
2009 conferenc
A method for reconstructing the PDF of a 3D turbulent density field from 2D observations
We introduce a method for calculating the probability density function (PDF)
of a turbulent density field in three dimensions using only information
contained in the projected two-dimensional column density field. We test the
method by applying it to numerical simulations of hydrodynamic and
magnetohydrodynamic turbulence in molecular clouds. To a good approximation,
the PDF of log(normalised column density) is a compressed, shifted version of
the PDF of log(normalised density). The degree of compression can be determined
observationally from the column density power spectrum, under the assumption of
statistical isotropy of the turbulence.Comment: 5 pages, 2 figures, accepted for publication in MNRAS Letter
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