23,912 research outputs found
Scaling of Model Approximation Errors and Expected Entropy Distances
We compute the expected value of the Kullback-Leibler divergence to various
fundamental statistical models with respect to canonical priors on the
probability simplex. We obtain closed formulas for the expected model
approximation errors, depending on the dimension of the models and the
cardinalities of their sample spaces. For the uniform prior, the expected
divergence from any model containing the uniform distribution is bounded by a
constant , and for the models that we consider, this bound is
approached if the state space is very large and the models' dimension does not
grow too fast. For Dirichlet priors the expected divergence is bounded in a
similar way, if the concentration parameters take reasonable values. These
results serve as reference values for more complicated statistical models.Comment: 13 pages, 3 figures, WUPES'1
A New Robust Regression Method Based on Minimization of Geodesic Distances on a Probabilistic Manifold: Application to Power Laws
In regression analysis for deriving scaling laws that occur in various
scientific disciplines, usually standard regression methods have been applied,
of which ordinary least squares (OLS) is the most popular. In many situations,
the assumptions underlying OLS are not fulfilled, and several other approaches
have been proposed. However, most techniques address only part of the
shortcomings of OLS. We here discuss a new and more general regression method,
which we call geodesic least squares regression (GLS). The method is based on
minimization of the Rao geodesic distance on a probabilistic manifold. For the
case of a power law, we demonstrate the robustness of the method on synthetic
data in the presence of significant uncertainty on both the data and the
regression model. We then show good performance of the method in an application
to a scaling law in magnetic confinement fusion.Comment: Published in Entropy. This is an extended version of our paper at the
34th International Workshop on Bayesian Inference and Maximum Entropy Methods
in Science and Engineering (MaxEnt 2014), 21-26 September 2014, Amboise,
Franc
Numerical study of hot strongly interacting matter
I review recent progress in study of strongly interacting matter at high
temperatures using Monte-Carlo simulations in lattice QCD.Comment: Talk presented at Conference on Computational Physics, Oct. 30 - Nov.
3, 2011, Gatlinburg TN, LaTeX uses jpconf11.clo, jpconf.cl
Entropy and Long range correlations in literary English
Recently long range correlations were detected in nucleotide sequences and in
human writings by several authors. We undertake here a systematic investigation
of two books, Moby Dick by H. Melville and Grimm's tales, with respect to the
existence of long range correlations. The analysis is based on the calculation
of entropy like quantities as the mutual information for pairs of letters and
the entropy, the mean uncertainty, per letter. We further estimate the number
of different subwords of a given length . Filtering out the contributions
due to the effects of the finite length of the texts, we find correlations
ranging to a few hundred letters. Scaling laws for the mutual information
(decay with a power law), for the entropy per letter (decay with the inverse
square root of ) and for the word numbers (stretched exponential growth with
and with a power law of the text length) were found.Comment: 8 page
The specific entropy of elliptical galaxies: an explanation for profile-shape distance indicators?
Dynamical systems in equilibrium have a stationary entropy; we suggest that
elliptical galaxies, as stellar systems in a stage of quasi-equilibrium, may
have a unique specific entropy. This uniqueness, a priori unknown, should be
reflected in correlations between the parameters describing the mass (light)
distribution in galaxies. Following recent photometrical work (Caon et al.
1993; Graham & Colless 1997; Prugniel & Simien 1997), we use the Sersic law to
describe the light profile of elliptical galaxies and an analytical
approximation to its three dimensional deprojection. The specific entropy is
calculated supposing that the galaxy behaves as a spherical, isotropic,
one-component system in hydrostatic equilibrium, obeying the ideal gas state
equations. We predict a relation between the 3 parameters of the Sersic,
defining a surface in the parameter space, an `Entropic Plane', by analogy with
the well-known Fundamental Plane. We have analysed elliptical galaxies in Coma
and ABCG 85 clusters and a group of galaxies (associated with NGC 4839). We
show that the galaxies in clusters follow closely a relation predicted by the
constant specific entropy hypothesis with a one-sigma dispersion of 9.5% around
the mean value of the specific entropy. Assuming that the specific entropy is
also the same for galaxies of different clusters, we are able to derive
relative distances between the studied clusters. If the errors are only due to
the determination of the specific entropy (about 10%), then the error in the
relative distance determination should be less than 20% for rich clusters. We
suggest that the unique specific entropy may provide a physical explanation for
the distance indicators based on the Sersic profile put forward by Young &
Currie (1994, 1995) and discussed by Binggeli & Jerjen (1998).Comment: Submitted to MNRAS (05/05/99), 15 pages, 10 figure
Correlation functions of the energy-momentum tensor in SU(2) gauge theory at finite temperature
We calculate correlation functions of the energy-momentum tensor in the
vicinity of the deconfinement phase transition of (3+1)-dimensional SU(2) gauge
theory and discuss their critical behavior in the vicinity of the second order
deconfinement transition. We show that correlation functions of the trace of
the energy momentum tensor diverge uniformly at the critical point in
proportion to the specific heat singularity. Correlation functions of the
pressure, on the other hand, stay finite at the critical point. We discuss the
consequences of these findings for the analysis of transport coefficients, in
particular the bulk viscosity, in the vicinity of a second order phase
transition point.Comment: 24 pages, 6 figure
Robust scaling in fusion science: case study for the L-H power threshold
In regression analysis for deriving scaling laws in the context of fusion studies, standard regression methods are usually applied, of which ordinary least squares (OLS) is the most popular. However, concerns have been raised with respect to several assumptions underlying OLS in its application to fusion data. More sophisticated statistical techniques are available, but they are not widely used in the fusion community and, moreover, the predictions by scaling laws may vary significantly depending on the particular regression technique. Therefore we have developed a new regression method, which we call geodesic least squares regression (GLS), that is robust in the presence of significant uncertainty on both the data and the regression model. The method is based on probabilistic modeling of all variables involved in the scaling expression, using adequate probability distributions and a natural similarity measure between them (geodesic distance). In this work we revisit the scaling law for the power threshold for the L-to-H transition in tokamaks, using data from the multi-machine ITPA databases. Depending on model assumptions, OLS can yield different predictions of the power threshold for ITER. In contrast, GLS regression delivers consistent results. Consequently, given the ubiquity and importance of scaling laws and parametric dependence studies in fusion research, GLS regression is proposed as a robust and easily implemented alternative to classic regression techniques
Consistency tests in cosmology using relative entropy
With the high-precision data from current and upcoming experiments, it
becomes increasingly important to perform consistency tests of the standard
cosmological model. In this work, we focus on consistency measures between
different data sets and methods that allow us to assess the goodness of fit of
different models. We address both of these questions using the relative entropy
or Kullback-Leibler (KL) divergence [Kullback et al., 1951]. First, we revisit
the relative entropy as a consistency measure between data sets and further
investigate some of its key properties, such as asymmetry and path dependence.
We then introduce a novel model rejection framework, which is based on the
relative entropy and the posterior predictive distribution. We validate the
method on several toy models and apply it to Type Ia supernovae data from the
JLA and CMB constraints from Planck 2015, testing the consistency of the data
with six different cosmological models.Comment: 31 pages, 10 figures, 4 tables, updated following referee's comments,
matches version accepted by JCA
Macromolecular theory of solvation and structure in mixtures of colloids and polymers
The structural and thermodynamic properties of mixtures of colloidal spheres
and non-adsorbing polymer chains are studied within a novel general
two-component macromolecular liquid state approach applicable for all size
asymmetry ratios. The dilute limits, when one of the components is at infinite
dilution but the other concentrated, are presented and compared to field theory
and models which replace polymer coils with spheres. Whereas the derived
analytical results compare well, qualitatively and quantitatively, with
mean-field scaling laws where available, important differences from ``effective
sphere'' approaches are found for large polymer sizes or semi-dilute
concentrations.Comment: 23 pages, 10 figure
- …