13,311 research outputs found
Modeling reverberation mapping data II: dynamical modeling of the Lick AGN Monitoring Project 2008 dataset
We present dynamical modeling of the broad line region (BLR) for a sample of
five Seyfert 1 galaxies using reverberation mapping data taken by the Lick AGN
Monitoring Project in 2008. By modeling the AGN continuum light curve and
H line profiles directly we are able to constrain the geometry and
kinematics of the BLR and make a measurement of the black hole mass that does
not depend upon the virial factor, , needed in traditional reverberation
mapping analysis. We find that the geometry of the BLR is generally a thick
disk viewed close to face-on. While the H emission is found to come
preferentially from the far side of the BLR, the mean size of the BLR is
consistent with the lags measured with cross-correlation analysis. The BLR
kinematics are found to be consistent with either inflowing motions or
elliptical orbits, often with some combination of the two. We measure black
hole masses of for Arp
151, for Mrk 1310, for NGC 5548,
for NGC 6814, and for SBS
1116+583A. The factors measured individually for each AGN are found to
correlate with inclination angle, although not with , ,
or FWHM/ of the emission line profile.Comment: 21 pages, 24 figures, 3 tables, Accepted for publication in MNRAS,
corrected masses for NGC 5548 and NGC 6814 in the abstrac
Enjoy the Joy of Copulas: With a Package copula
Copulas have become a popular tool in multivariate modeling successfully applied in many fields. A good open-source implementation of copulas is much needed for more practitioners to enjoy the joy of copulas. This article presents the design, features, and some implementation details of the R package copula. The package provides a carefully designed and easily extensible platform for multivariate modeling with copulas in R. S4 classes for most frequently used elliptical copulas and Archimedean copulas are implemented, with methods for density/distribution evaluation, random number generation, and graphical display. Fitting copula-based models with maximum likelihood method is provided as template examples. With the classes and methods in the package, the package can be easily extended by user-defined copulas and margins to solve problems.
Simplified Pair Copula Constructions --- Limits and Extensions
So called pair copula constructions (PCCs), specifying multivariate
distributions only in terms of bivariate building blocks (pair copulas),
constitute a flexible class of dependence models. To keep them tractable for
inference and model selection, the simplifying assumption that copulas of
conditional distributions do not depend on the values of the variables which
they are conditioned on is popular. In this paper, we show for which classes of
distributions such a simplification is applicable, significantly extending the
discussion of Hob{\ae}k Haff et al. (2010). In particular, we show that the
only Archimedean copula in dimension d \geq 4 which is of the simplified type
is that based on the gamma Laplace transform or its extension, while the
Student-t copula is the only one arising from a scale mixture of Normals.
Further, we illustrate how PCCs can be adapted for situations where conditional
copulas depend on values which are conditioned on
Student-t Processes as Alternatives to Gaussian Processes
We investigate the Student-t process as an alternative to the Gaussian
process as a nonparametric prior over functions. We derive closed form
expressions for the marginal likelihood and predictive distribution of a
Student-t process, by integrating away an inverse Wishart process prior over
the covariance kernel of a Gaussian process model. We show surprising
equivalences between different hierarchical Gaussian process models leading to
Student-t processes, and derive a new sampling scheme for the inverse Wishart
process, which helps elucidate these equivalences. Overall, we show that a
Student-t process can retain the attractive properties of a Gaussian process --
a nonparametric representation, analytic marginal and predictive distributions,
and easy model selection through covariance kernels -- but has enhanced
flexibility, and predictive covariances that, unlike a Gaussian process,
explicitly depend on the values of training observations. We verify empirically
that a Student-t process is especially useful in situations where there are
changes in covariance structure, or in applications like Bayesian optimization,
where accurate predictive covariances are critical for good performance. These
advantages come at no additional computational cost over Gaussian processes.Comment: 13 pages, 6 figures, 1 table. To appear in "The Seventeenth
International Conference on Artificial Intelligence and Statistics (AISTATS),
2014.
Extremal t processes: Elliptical domain of attraction and a spectral representation
The extremal t process was proposed in the literature for modeling spatial
extremes within a copula framework based on the extreme value limit of
elliptical t distributions (Davison, Padoan and Ribatet (2012)). A major
drawback of this max-stable model was the lack of a spectral representation
such that for instance direct simulation was infeasible. The main contribution
of this note is to propose such a spectral construction for the extremal t
process. Interestingly, the extremal Gaussian process introduced by Schlather
(2002) appears as a special case. We further highlight the role of the extremal
t process as the maximum attractor for processes with finite-dimensional
elliptical distributions. All results naturally also hold within the
multivariate domain
The effect of realistic geometries on the susceptibility-weighted MR signal in white matter
Purpose: To investigate the effect of realistic microstructural geometry on
the susceptibility-weighted magnetic resonance (MR) signal in white matter
(WM), with application to demyelination.
Methods: Previous work has modeled susceptibility-weighted signals under the
assumption that axons are cylindrical. In this work, we explore the
implications of this assumption by considering the effect of more realistic
geometries. A three-compartment WM model incorporating relevant properties
based on literature was used to predict the MR signal. Myelinated axons were
modeled with several cross-sectional geometries of increasing realism: nested
circles, warped/elliptical circles and measured axonal geometries from electron
micrographs. Signal simulations from the different microstructural geometries
were compared to measured signals from a Cuprizone mouse model with varying
degrees of demyelination.
Results: Results from simulation suggest that axonal geometry affects the MR
signal. Predictions with realistic models were significantly different compared
to circular models under the same microstructural tissue properties, for
simulations with and without diffusion.
Conclusion: The geometry of axons affects the MR signal significantly.
Literature estimates of myelin susceptibility, which are based on fitting
biophysical models to the MR signal, are likely to be biased by the assumed
geometry, as will any derived microstructural properties.Comment: Accepted March 4 2017, in publication at Magnetic Resonance in
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