60,104 research outputs found
Maximum Likelihood Estimation and Uniform Inference with Sporadic Identification Failure
This paper analyzes the properties of a class of estimators, tests, and confidence sets (CS's) when the parameters are not identified in parts of the parameter space. Specifically, we consider estimator criterion functions that are sample averages and are smooth functions of a parameter theta. This includes log likelihood, quasi-log likelihood, and least squares criterion functions. We determine the asymptotic distributions of estimators under lack of identification and under weak, semi-strong, and strong identification. We determine the asymptotic size (in a uniform sense) of standard t and quasi-likelihood ratio (QLR) tests and CS's. We provide methods of constructing QLR tests and CS's that are robust to the strength of identification. The results are applied to two examples: a nonlinear binary choice model and the smooth transition threshold autoregressive (STAR) model.Asymptotic size, Binary choice, Confidence set, Estimator, Identification, Likelihood, Nonlinear models, Test, Smooth transition threshold autoregression, Weak identification
Average-Atom Model for X-ray Scattering from Warm Dense Matter
A scheme for analyzing Thomson scattering of x-rays by warm dense matter,
based on the average-atom model, is developed. Emphasis is given to x-ray
scattering by bound electrons. Contributions to the scattered x-ray spectrum
from elastic scattering by electrons moving with the ions and from inelastic
scattering by free and bound electrons are evaluated using parameters (chemical
potential, average ionic charge, free electron density, bound and continuum
wave functions, and occupation numbers) taken from the average-atom model. The
resulting scheme provides a relatively simple diagnostic for use in connection
with x-ray scattering measurements. Applications are given to dense hydrogen,
beryllium, aluminum, titanium, and tin plasmas. At high momentum transfer,
contributions from inelastic scattering by bound electrons are dominant
features of the scattered x-ray spectrum for aluminum, titanium, and tin.Comment: 22 pages, 10 figures Presentation at Workshop IV: Computational
Challenges in Warm Dense Matter at IPAM (UCLA) May 21 - 25, 201
Using the X-FEL to understand X-ray Thomson scattering for partially ionized plasmas
For the last decade numerous researchers have been trying to develop
experimental techniques to use X-ray Thomson scattering as a method to measure
the temperature, electron density, and ionization state of high energy density
plasmas such as those used in inertial confinement fusion. With the advent of
the X-ray free electron laser (X-FEL) at the SLAC Linac Coherent Light Source
(LCLS) we now have such a source available in the keV regime. One challenge
with X-ray Thomson scattering experiments is understanding how to model the
scattering for partially ionized plasmas. Most Thomson scattering codes used to
model experimental data greatly simplify or neglect the contributions of the
bound electrons to the scattered intensity. In this work we take the existing
models of Thomson scattering that include elastic ion-ion scattering and the
electron-electron plasmon scattering and add the contribution of the bound
electrons in the partially ionized plasmas. Except for hydrogen plasmas almost
every plasma that is studied today has bound electrons and it is important to
understand their contribution to the Thomson scattering, especially as new
X-ray sources such as the X-FEL will allow us to study much higher Z plasmas.
Currently most experiments have looked at hydrogen or beryllium. We will first
look at the bound electron contributions to beryllium by analysing existing
experimental data. We then consider several higher Z materials such as Cr and
predict the existence of additional peaks in the scattering spectrum that
requires new computational tools to understand. For a Sn plasma we show that
the bound contributions changes the shape of the scattered spectrum in a way
that would change the plasma temperature and density inferred by the
experiment.Comment: 13th International Conference on X-ray Lasers Paris, France June 10,
2012 through June 15, 201
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