The Measure of a Model

This paper describes measures for evaluating the three determinants of how well a probabilistic classifier performs on a given test set. These determinants are the appropriateness, for the test set, of the results of (1) feature selection, (2) formulation of the parametric form of the model, and (3) parameter estimation. These are part of any model formulation procedure, even if not broken out as separate steps, so the tradeoffs explored in this paper are relevant to a wide variety of methods. The measures are demonstrated in a large experiment, in which they are used to analyze the results of roughly 300 classifiers that perform word-sense disambiguation.Comment: 12 pages, uuencoded compressed postscript fil

Isoscaling as a measure of Symmetry Energy in the Lattice Gas Model

The energetic properties of nuclear clusters inside a low-density, finite-temperature medium are studied with a Lattice Gas Model including isospin dependence and Coulomb forces. Important deviations are observed respect to the Fisher approximation of an ideal gas of non-interacting clusters, but the global energetics can still be approximately expressed in terms of a simple modified energy-density functional. The multi-fragmentation regime appears dominated by combinatorial effects in this model, but the isoscaling of the largest fragment in low energy collisions appears a promising observable for the experimental measurement of the symmetry energy.Comment: 4 pages, 3 figure, submitted to PR

Statistical properties of the localization measure in a finite-dimensional model of the quantum kicked rotator

We study the quantum kicked rotator in the classically fully chaotic regime $K=10$ and for various values of the quantum parameter $k$ using Izrailev's $N$-dimensional model for various $N \le 3000$, which in the limit $N \rightarrow \infty$ tends to the exact quantized kicked rotator. By numerically calculating the eigenfunctions in the basis of the angular momentum we find that the localization length ${\cal L}$ for fixed parameter values has a certain distribution, in fact its inverse is Gaussian distributed, in analogy and in connection with the distribution of finite time Lyapunov exponents of Hamilton systems. However, unlike the case of the finite time Lyapunov exponents, this distribution is found to be independent of $N$, and thus survives the limit $N=\infty$. This is different from the tight-binding model of Anderson localization. The reason is that the finite bandwidth approximation of the underlying Hamilton dynamical system in the Shepelyansky picture (D.L. Shepelyansky, {\em Phys. Rev. Lett.} {\bf 56}, 677 (1986)) does not apply rigorously. This observation explains the strong fluctuations in the scaling laws of the kicked rotator, such as e.g. the entropy localization measure as a function of the scaling parameter $\Lambda={\cal L}/N$, where $\cal L$ is the theoretical value of the localization length in the semiclassical approximation. These results call for a more refined theory of the localization length in the quantum kicked rotator and in similar Floquet systems, where we must predict not only the mean value of the inverse of the localization length $\cal L$ but also its (Gaussian) distribution, in particular the variance. In order to complete our studies we numerically analyze the related behavior of finite time Lyapunov exponents in the standard map and of the 2$\times$2 transfer matrix formalism. This paper is extending our recent work.Comment: 12 pages, 9 figures (accepted for publication in Physical Review E). arXiv admin note: text overlap with arXiv:1301.418

Assessing Financial Model Risk

Model risk has a huge impact on any risk measurement procedure and its quantification is therefore a crucial step. In this paper, we introduce three quantitative measures of model risk when choosing a particular reference model within a given class: the absolute measure of model risk, the relative measure of model risk and the local measure of model risk. Each of the measures has a specific purpose and so allows for flexibility. We illustrate the various notions by studying some relevant examples, so as to emphasize the practicability and tractability of our approach.Comment: 23 pages, 6 figure