65,454 research outputs found
Higher Accuracy for Bayesian and Frequentist Inference: Large Sample Theory for Small Sample Likelihood
Recent likelihood theory produces -values that have remarkable accuracy
and wide applicability. The calculations use familiar tools such as maximum
likelihood values (MLEs), observed information and parameter rescaling. The
usual evaluation of such -values is by simulations, and such simulations do
verify that the global distribution of the -values is uniform(0, 1), to high
accuracy in repeated sampling. The derivation of the -values, however,
asserts a stronger statement, that they have a uniform(0, 1) distribution
conditionally, given identified precision information provided by the data. We
take a simple regression example that involves exact precision information and
use large sample techniques to extract highly accurate information as to the
statistical position of the data point with respect to the parameter:
specifically, we examine various -values and Bayesian posterior survivor
-values for validity. With observed data we numerically evaluate the various
-values and -values, and we also record the related general formulas. We
then assess the numerical values for accuracy using Markov chain Monte Carlo
(McMC) methods. We also propose some third-order likelihood-based procedures
for obtaining means and variances of Bayesian posterior distributions, again
followed by McMC assessment. Finally we propose some adaptive McMC methods to
improve the simulation acceptance rates. All these methods are based on
asymptotic analysis that derives from the effect of additional data. And the
methods use simple calculations based on familiar maximizing values and related
informations. The example illustrates the general formulas and the ease of
calculations, while the McMC assessments demonstrate the numerical validity of
the -values as percentage position of a data point. The example, however, is
very simple and transparent, and thus gives little indication that in a wide
generality of models the formulas do accurately separate information for almost
any parameter of interest, and then do give accurate -value determinations
from that information. As illustration an enigmatic problem in the literature
is discussed and simulations are recorded; various examples in the literature
are cited.Comment: Published in at http://dx.doi.org/10.1214/07-STS240 the Statistical
Science (http://www.imstat.org/sts/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Inference and Optimization of Real Edges on Sparse Graphs - A Statistical Physics Perspective
Inference and optimization of real-value edge variables in sparse graphs are
studied using the Bethe approximation and replica method of statistical
physics. Equilibrium states of general energy functions involving a large set
of real edge-variables that interact at the network nodes are obtained in
various cases. When applied to the representative problem of network resource
allocation, efficient distributed algorithms are also devised. Scaling
properties with respect to the network connectivity and the resource
availability are found, and links to probabilistic Bayesian approximation
methods are established. Different cost measures are considered and algorithmic
solutions in the various cases are devised and examined numerically. Simulation
results are in full agreement with the theory.Comment: 21 pages, 10 figures, major changes: Sections IV to VII updated,
Figs. 1 to 3 replace
Interaction Between Ion Beams and Plasmas
Interaction between low energy cesium ion beam and thermal cesium plasm
Pion Interferometry for a Granular Source of Quark-Gluon Plasma Droplets
We examine the two-pion interferometry for a granular source of quark-gluon
plasma droplets. The evolution of the droplets is described by relativistic
hydrodynamics with an equation of state suggested by lattice gauge results.
Pions are assumed to be emitted thermally from the droplets at the freeze-out
configuration characterized by a freeze-out temperature . We find that the
HBT radius decreases if the initial size of the droplets decreases.
On the other hand, depends on the droplet spatial distribution and
is relatively independent of the droplet size. It increases with an increase in
the width of the spatial distribution and the collective-expansion velocity of
the droplets. As a result, the value of can lie close to
for a granular quark-gluon plasma source. The granular model of the emitting
source may provide an explanation to the RHIC HBT puzzle and may lead to a new
insight into the dynamics of the quark-gluon plasma phase transition.Comment: 5 pages, 4 figure
Signals in Single-Event Pion Interferometry for Granular Sources of Quark-Gluon Plasma Droplets
We investigate two-pion Bose-Einstein correlations of quark-gluon plasma
droplet sources in single-event measurements. We find that the distribution of
the fluctuation between correlation functions of the single- and mixed-events
provide useful signals to detect the granular structure of the source.Comment: 6 pages, 6 figures, in LaTe
Does HBT Measure the Freeze-out Source Distribution?
It is generally assumed that as a result of multiple scattering, the source
distribution measured in HBT interferometry corresponds to a chaotic source at
freeze-out. This assumption is subject to question as effects of multiple
scattering in HBT measurements must be investigated within a quantum-mechanical
framework. Applying the Glauber multiple scattering theory at high energies and
the optical model at lower energies, we find that multiple scattering leads to
an effective HBT density distribution that depends on the initial chaotic
source distribution with an absorption.Comment: 4 pages, talk presented at QM2004 Conference, January 11-17, 2004,
Oakland, California, USA, to be published in the Proceeding
Pion Interferometry for Hydrodynamical Expanding Source with a Finite Baryon Density
We calculate the two-pion correlation function for an expanding hadron source
with a finite baryon density. The space-time evolution of the source is
described by relativistic hydrodynamics and the Hanbury-Brown-Twiss (HBT)
radius is extracted after effects of collective expansion and multiple
scattering on the HBT interferometry have been taken into account, using
quantum probability amplitudes in a path-integral formalism. We find that this
radius is substantially smaller than the HBT radius extracted from the
freeze-out configuration.Comment: 4 pages, 2 figure
Visualising vitreous through modified trans-scleral illumination by maximising the Tyndall effect
Background: A new technique for visualisation of the vitreous base is described. It uses a standard lightpipe for scleral indentation and transillumination. Visualisation of the vitreous using low light levels can be achieved by enhancing the Tyndall effect. Discussion: Perfluorocarbon liquid (PFCL) is used to confine the aqueous environment to the anterior vitreous cavity and triamcinolone is added to increase light scatter. The technique clearly differentiates vitreous from PFCL and infusion fluid, and facilitates trimming of the vitreous base, draining of subretinal fluid and air/fluid exchange.published_or_final_versio
Melt-growth dynamics in CdTe crystals
We use a new, quantum-mechanics-based bond-order potential (BOP) to reveal
melt-growth dynamics and fine-scale defect formation mechanisms in CdTe
crystals. Previous molecular dynamics simulations of semiconductors have shown
qualitatively incorrect behavior due to the lack of an interatomic potential
capable of predicting both crystalline growth and property trends of many
transitional structures encountered during the melt crystal
transformation. Here we demonstrate successful molecular dynamics simulations
of melt-growth in CdTe using a BOP that significantly improves over other
potentials on property trends of different phases. Our simulations result in a
detailed understanding of defect formation during the melt-growth process.
Equally important, we show that the new BOP enables defect formation mechanisms
to be studied at a scale level comparable to empirical molecular dynamics
simulation methods with a fidelity level approaching quantum-mechanical method
- …