14,451 research outputs found
Bayesian modelling of skewness and kurtosis with two-piece scale and shape distributions
We formalise and generalise the definition of the family of univariate double
two--piece distributions, obtained by using a density--based transformation of
unimodal symmetric continuous distributions with a shape parameter. The
resulting distributions contain five interpretable parameters that control the
mode, as well as the scale and shape in each direction. Four-parameter
subfamilies of this class of distributions that capture different types of
asymmetry are discussed. We propose interpretable scale and location-invariant
benchmark priors and derive conditions for the propriety of the corresponding
posterior distribution. The prior structures used allow for meaningful
comparisons through Bayes factors within flexible families of distributions.
These distributions are applied to data from finance, internet traffic and
medicine, comparing them with appropriate competitors
A Simple Approach to Maximum Intractable Likelihood Estimation
Approximate Bayesian Computation (ABC) can be viewed as an analytic
approximation of an intractable likelihood coupled with an elementary
simulation step. Such a view, combined with a suitable instrumental prior
distribution permits maximum-likelihood (or maximum-a-posteriori) inference to
be conducted, approximately, using essentially the same techniques. An
elementary approach to this problem which simply obtains a nonparametric
approximation of the likelihood surface which is then used as a smooth proxy
for the likelihood in a subsequent maximisation step is developed here and the
convergence of this class of algorithms is characterised theoretically. The use
of non-sufficient summary statistics in this context is considered. Applying
the proposed method to four problems demonstrates good performance. The
proposed approach provides an alternative for approximating the maximum
likelihood estimator (MLE) in complex scenarios
Ab initio calculations of the dynamical response of copper
The role of localized -bands in the dynamical response of Cu is
investigated, on the basis of {\em ab initio} pseudopotential calculations. The
density-response function is evaluated in both the random-phase approximation
(RPA) and a time-dependent local-density functional approximation (TDLDA). Our
results indicate that in addition to providing a polarizable background which
lowers the free-electron plasma frequency, d-electrons are responsible, at
higher energies and small momenta, for a double-peak structure in the dynamical
structure factor. These results are in agreement with the experimentally
determined optical response of copper. We also analyze the dependence of
dynamical scattering cross sections on the momentum transfer.Comment: 4 pages, 4 figures, to appear in Phys. Rev.
Short-Time Critical Dynamics of Damage Spreading in the Two-Dimensional Ising Model
The short-time critical dynamics of propagation of damage in the Ising
ferromagnet in two dimensions is studied by means of Monte Carlo simulations.
Starting with equilibrium configurations at and magnetization
, an initial damage is created by flipping a small amount of spins in one
of the two replicas studied. In this way, the initial damage is proportional to
the initial magnetization in one of the configurations upon quenching the
system at , the Onsager critical temperature of the
ferromagnetic-paramagnetic transition. It is found that, at short times, the
damage increases with an exponent , which is much larger
than the exponent characteristic of the initial increase of the
magnetization . Also, an epidemic study was performed. It is found that
the average distance from the origin of the epidemic ()
grows with an exponent , which is the same,
within error bars, as the exponent . However, the survival
probability of the epidemics reaches a plateau so that . On the other
hand, by quenching the system to lower temperatures one observes the critical
spreading of the damage at , where all the measured
observables exhibit power laws with exponents , , and .Comment: 11 pages, 9 figures (included). Phys. Rev. E (2010), in press
Orphan penumbrae: Submerging horizontal fields
We investigate the properties of orphan penumbrae, which are photospheric
filamentary structures observed in active regions near polarity inversion lines
that resemble the penumbra of regular sunspots but are not connected to any
umbra. We use Hinode data from the Solar Optical Telescope to determine the
properties of orphan penumbrae. Spectropolarimetric data are employed to obtain
the vector magnetic field and line-of-sight velocities in the photosphere.
Magnetograms are used to study the overall evolution of these structures, and
G-band and Ca II H filtergrams are to investigate their brightness and apparent
horizontal motions. Orphan penumbrae form between regions of opposite polarity
in places with horizontal magnetic fields. Their magnetic configuration is that
of -shaped flux ropes. In the two cases studied here, the
opposite-polarity regions approach each other with time and the whole structure
submerges as the penumbral filaments disappear. Orphan penumbrae are very
similar to regular penumbrae, including the existence of strong gas flows.
Therefore, they could have a similar origin. The main difference between them
is the absence of a "background" magnetic field in orphan penumbrae. This could
explain most of the observed differences. The fast flows we detect in orphan
penumbrae may be caused by the siphon flow mechanism. Based on the similarities
between orphan and regular penumbrae, we propose that the Evershed flow is also
a manifestation of siphon flows.Comment: 15 pages, 15 figure
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