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 $d$-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 $T= \infty$ and magnetization $M=0$, 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 $M_0$ in one of the configurations upon quenching the system at $T_C$, the Onsager critical temperature of the ferromagnetic-paramagnetic transition. It is found that, at short times, the damage increases with an exponent $\theta_D=1.915(3)$, which is much larger than the exponent $\theta=0.197$ characteristic of the initial increase of the magnetization $M(t)$. Also, an epidemic study was performed. It is found that the average distance from the origin of the epidemic ($\langle R^2(t)\rangle$) grows with an exponent $z^* \approx \eta \approx 1.9$, which is the same, within error bars, as the exponent $\theta_D$. However, the survival probability of the epidemics reaches a plateau so that $\delta=0$. On the other hand, by quenching the system to lower temperatures one observes the critical spreading of the damage at $T_{D}\simeq 0.51 T_C$, where all the measured observables exhibit power laws with exponents $\theta_D = 1.026(3)$, $\delta = 0.133(1)$, and $z^*=1.74(3)$.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 $\Omega$-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