658 research outputs found
Variational Inference for Generalized Linear Mixed Models Using Partially Noncentered Parametrizations
The effects of different parametrizations on the convergence of Bayesian
computational algorithms for hierarchical models are well explored. Techniques
such as centering, noncentering and partial noncentering can be used to
accelerate convergence in MCMC and EM algorithms but are still not well studied
for variational Bayes (VB) methods. As a fast deterministic approach to
posterior approximation, VB is attracting increasing interest due to its
suitability for large high-dimensional data. Use of different parametrizations
for VB has not only computational but also statistical implications, as
different parametrizations are associated with different factorized posterior
approximations. We examine the use of partially noncentered parametrizations in
VB for generalized linear mixed models (GLMMs). Our paper makes four
contributions. First, we show how to implement an algorithm called nonconjugate
variational message passing for GLMMs. Second, we show that the partially
noncentered parametrization can adapt to the quantity of information in the
data and determine a parametrization close to optimal. Third, we show that
partial noncentering can accelerate convergence and produce more accurate
posterior approximations than centering or noncentering. Finally, we
demonstrate how the variational lower bound, produced as part of the
computation, can be useful for model selection.Comment: Published in at http://dx.doi.org/10.1214/13-STS418 the Statistical
Science (http://www.imstat.org/sts/) by the Institute of Mathematical
Statistics (http://www.imstat.org
A frictional Cosserat model for the flow of granular materials through a vertical channel
A rigid-plastic Cosserat model has been used to study dense, fully developed
flow of granular materials through a vertical channel. Frictional models based
on the classical continuum do not predict the occurrence of shear layers, at
variance with experimental observations. This feature has been attributed to
the absence of a material length scale in their constitutive equations. The
present model incorporates such a material length scale by treating the
granular material as a Cosserat continuum. Thus localised couple stresses exist
and the stress tensor is asymmetric. The velocity profiles predicted by the
model are in close agreement with available experimental data. The predicted
dependence of the shear layer thickness on the width of the channel is in
reasonable agreement with data. In the limit of the ratio of the particle
diameter to the half-width of the channel being small, the model predicts that
the shear layer thickness scaled by the particle diameter grows.Comment: 17 pages, 12 PostScript figures, uses AmsLaTeX, psfrag and natbib.
Accepted for publication in Acta Mechanic
Readiness: Is Your Child Ready for Kindergarten?
A handbook has been designed to aid parents or care givers in guiding their preschooler towards a successful formal education. The handbook will allow parents or care givers to be more involved in their child\u27s first five years of learning. It will also enable the preschooler to have a better chance for success in his or her education. The handbook consists of suggested activities developed by the author with the parent or caregiver in mind. These activities are designed for the parent or caregiver to incorporate within their everyday routine. These activities are organized in order of age levels and learning areas. The learning areas are social, emotional, academic and physical readiness. These activities are designed to further increase the parent or caregiver\u27s involvement in the readiness of their preschooler. Current literature and research involving the topic of Kindergarten Readiness were explored
A frictional Cosserat model for the slow shearing of granular materials
A rigid-plastic Cosserat model for slow frictional flow of granular materials, proposed by us in an earlier paper, has been used to analyse plane and cylindrical Couette flow. In this model, the hydrodynamic fields of a classical continuum are supplemented by the couple stress and the intrinsic angular velocity fields. The balance of angular momentum, which is satisfied implicitly in a classical continuum, must be enforced in a Cosserat continuum. As a result, the stress tensor could be asymmetric, and the angular velocity of a material point may differ from half the local vorticity. An important consequence of treating the granular medium as a Cosserat continuum is that it incorporates a material length scale in the model, which is absent in frictional models based on a classical continuum. Further, the Cosserat model allows determination of the velocity fields uniquely in viscometric flows, in contrast to classical frictional models. Experiments on viscometric flows of dense, slowly deforming granular materials indicate that shear is confined to a narrow region, usually a few grain diameters thick, while the remaining material is largely undeformed. This feature is captured by the present model, and the velocity profile predicted for cylindrical Couette flow is in good agreement with reported data. When the walls of the Couette cell are smoother than the granular material, the model predicts that the shear layer thickness is independent of the Couette gap H when the latter is large compared to the grain diameter dp. When the walls are of the same roughness as the granular material, the model predicts that the shear layer thickness varies as (H/dp)1/3 (in the limit H/dp [dbl greater-than sign] 1) for plane shear under gravity and cylindrical Couette flow
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