Prior elicitation in Bayesian quantile regression for longitudinal data

© 2011 Alhamzawi R, et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original auhor and source are credited.This article has been made available through the Brunel Open Access Publishing Fund.In this paper, we introduce Bayesian quantile regression for longitudinal data in terms of informative priors and Gibbs sampling. We develop methods for eliciting prior distribution to incorporate historical data gathered from similar previous studies. The methods can be used either with no prior data or with complete prior data. The advantage of the methods is that the prior distribution is changing automatically when we change the quantile. We propose Gibbs sampling methods which are computationally efficient and easy to implement. The methods are illustrated with both simulation and real data.This article is made available through the Brunel Open Access Publishing Fund

Apocenter glow in eccentric debris disks: implications for Fomalhaut and epsilon Eridani

Debris disks often take the form of eccentric rings with azimuthal asymmetries in surface brightness. Such disks are often described as showing "pericenter glow", an enhancement of the disk brightness in regions nearest the central star. At long wavelengths, however, the disk apocenters should appear brighter than their pericenters: in the long wavelength limit, we find the apocenter/pericenter flux ratio scales as 1+e for disk eccentricity e. We produce new models of this "apocenter glow" to explore its causes and wavelength dependence and study its potential as a probe of dust grain properties. Based on our models, we argue that several far-infrared and (sub)millimeter images of the Fomalhaut and epsilon Eridani debris rings obtained with Herschel, JCMT, SHARC II, ALMA, and ATCA should be reinterpreted as suggestions or examples of apocenter glow. This reinterpretation yields new constraints on the disks' dust grain properties and size distributions.Comment: 20 pages, 7 figures; accepted to Ap

Overcritical state in superconducting round wires sheathed by iron

Magnetic measurements carried out on MgB_2 superconducting round wires have shown that the critical current density J_c(B_a) in wires sheathed by iron can be significantly higher than that in the same bare (unsheathed) wires over a wide applied magnetic field B_a range. The magnetic behavior is, however, strongly dependent on the magnetic history of the sheathed wires, as well as on the wire orientation with respect to the direction of the applied field. The behavior observed can be explained by magnetic interaction between the soft magnetic sheath and superconducting core, which can result in a redistribution of supercurrents in the flux filled superconductor. A phenomenological model explaining the observed behavior is proposed.Comment: 9 pages, 7 figure

A Poisson Regression Examination of the Relationship between Website Traffic and Search Engine Queries

A new area of research involves the use of Google data, which has been normalized and scaled to predict economic activity. This new source of data holds both many advantages as well as disadvantages, which are discussed through the use of daily and weekly data. Daily and weekly data are employed to show the effect of aggregation as it pertains to Google data, which can lead to contradictory findings. In this paper, Poisson regressions are used to explore the relationship between the online traffic to a specific website and the search volumes for certain keyword search queries, along with the rankings of that specific website for those queries. The purpose of this paper is to point out the benefits and the pitfalls of a potential new source of data that lacks transparency in regards to the original level data, which is due to the normalization and scaling procedure utilized by Google.Poisson Regression, Search Engine, Google Insights, Aggregation, Normalization Effects, Scaling Effects

A New Young Diagrammatic Method For Kronecker Products of O(n) and Sp(2m)

A new simple Young diagrammatic method for Kronecker products of O(n) and Sp(2m) is proposed based on representation theory of Brauer algebras. A general procedure for the decomposition of tensor products of representations for O(n) and Sp(2m) is outlined, which is similar to that for U(n) known as the Littlewood rules together with trace contractions from a Brauer algebra and some modification rules given by King.Comment: Latex, 11 pages, no figure

Density Variations over Subparsec Scales in Diffuse Molecular Gas

We present high-resolution observations of interstellar CN, CH, CH^{+}, \ion{Ca}{1}, and \ion{Ca}{2} absorption lines toward the multiple star systems HD206267 and HD217035. Substantial variations in CN absorption are observed among three sight lines of HD206267, which are separated by distances of order 10,000 AU; smaller differences are seen for CH, CH^{+}, and \ion{Ca}{1}. Gas densities for individual velocity components are inferred from a chemical model, independent of assumptions about cloud shape. While the component densities can differ by factors of 5.0 between adjacent sightlines, the densities are always less than 5000 cm^{-3}. Calculations show that the derived density contrasts are not sensitive to the temperature or reaction rates used in the chemical model. A large difference in the CH^{+} profiles (a factor of 2 in column density) is seen in the lower density gas toward HD217035.Comment: 9 pages, 2 figures. Accepted for publication in ApJ