312,271 research outputs found
The density in the density of states method
It has been suggested that for QCD at finite baryon density the distribution
of the phase angle, i.e. the angle defined as the imaginary part of the
logarithm of the fermion determinant, has a simple Gaussian form. This
distribution provides the density in the density of states approach to the sign
problem. We calculate this phase angle distribution using i) the hadron
resonance gas model; and ii) a combined strong coupling and hopping parameter
expansion in lattice gauge theory. While the former model leads only to a
Gaussian distribution, in the latter expansion we discover terms which cause
the phase angle distribution to deviate, by relative amounts proportional to
powers of the inverse lattice volume, from a simple Gaussian form. We show that
despite the tiny inverse-volume deviation of the phase angle distribution from
a simple Gaussian form, such non-Gaussian terms can have a substantial impact
on observables computed in the density of states/reweighting approach to the
sign problem.Comment: 43 pages, 4 figure
An R Package for a General Class of Inverse Gaussian Distributions
The inverse Gaussian distribution is a positively skewed probability model that has received great attention in the last 20 years. Recently, a family that generalizes this model called inverse Gaussian type distributions has been developed. The new R package named ig has been designed to analyze data from inverse Gaussian type distributions. This package contains basic probabilistic functions, lifetime indicators and a random number generator from this model. Also, parameter estimates and diagnostics analysis can be obtained using likelihood methods by means of this package. In addition, goodness-of-fit methods are implemented in order to detect the suitability of the model to the data. The capabilities and features of the ig package are illustrated using simulated and real data sets. Furthermore, some new results related to the inverse Gaussian type distribution are also obtained. Moreover, a simulation study is conducted for evaluating the estimation method implemented in the ig package.
Moments of the generalized hyperbolic distribution
In this paper we demonstrate a recursive method for obtaining the moments of the generalized hyperbolic distribution. The method is readily programmable for numerical evaluation of moments. For low order moments we also give an alternative derivation of the moments of the generalized hyperbolic distribution. The expressions given for these moments may be used to obtain moments for special cases such as the hyperbolic and normal inverse Gaussian distributions. Moments for limiting cases such as the skew hyperbolic t and variance gamma distributions can be found using the same approach.Generalized hyperbolic distribution; hyperbolic distribution; kurtosis; moments; normal inverse Gaussian distribution; skewed-t distribution; skewness; Student-t distribution.
Expectation Propagation for Poisson Data
The Poisson distribution arises naturally when dealing with data involving
counts, and it has found many applications in inverse problems and imaging. In
this work, we develop an approximate Bayesian inference technique based on
expectation propagation for approximating the posterior distribution formed
from the Poisson likelihood function and a Laplace type prior distribution,
e.g., the anisotropic total variation prior. The approach iteratively yields a
Gaussian approximation, and at each iteration, it updates the Gaussian
approximation to one factor of the posterior distribution by moment matching.
We derive explicit update formulas in terms of one-dimensional integrals, and
also discuss stable and efficient quadrature rules for evaluating these
integrals. The method is showcased on two-dimensional PET images.Comment: 25 pages, to be published at Inverse Problem
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