An information theoretic approach to statistical dependence: copula information

We discuss the connection between information and copula theories by showing that a copula can be employed to decompose the information content of a multivariate distribution into marginal and dependence components, with the latter quantified by the mutual information. We define the information excess as a measure of deviation from a maximum entropy distribution. The idea of marginal invariant dependence measures is also discussed and used to show that empirical linear correlation underestimates the amplitude of the actual correlation in the case of non-Gaussian marginals. The mutual information is shown to provide an upper bound for the asymptotic empirical log-likelihood of a copula. An analytical expression for the information excess of T-copulas is provided, allowing for simple model identification within this family. We illustrate the framework in a financial data set.Comment: to appear in Europhysics Letter

Faint K Selected Galaxy Correlations and Clustering Evolution

Angular and spatial correlations are measured for K-band--selected galaxies, 248 having redshifts, 54 with z>1, in two patches of combined area 27 arcmin^2. The angular correlation for K<=21.5 mag is (theta/1.4+/-0.19 arcsec e^{+/-0.1})^{-0.8}. From the redshift sample we find that the real-space correlation, calculated with q_0=0.1, of M_K<=-23.5 mag galaxies (k-corrected) is \xi(r) = (r/2.9e^{+/-0.12}1/h Mpc)^{-1.8} at a mean z= 0.34, (r/2.0e^{+/-0.15}1/h Mpc)^{-1.8} at z= 0.62, (r/1.4e^{+/-0.15}1/h Mpc)^{-1.8} at z= 0.97, and (r/1.0e^{+/-0.2}1/h Mpc)^{-1.8} at z= 1.39, the last being a formal upper limit for a blue-biased sample. In general, these are more correlated than optically selected samples in the same redshift ranges. Over the interval 0.32 AB mag, have \xi(r)=(r/2.4e^{+/-0.14}1/h Mpc)^{-1.8} whereas bluer galaxies, which have a mean B of 23.7 mag and mean [OII] equivalent width W_{eq} = 41=\AA, are very weakly correlated, with \xi(r)=(r/0.9e^{+/-0.22}1/h Mpc)^{-1.8}. For our measured growth rate of clustering, this blue population, if non-merging, can grow only into a low-redshift population less luminous than 0.4L_\ast. The cross-correlation of low- and high-luminosity galaxies at z=0.6 appears to have an excess in the correlation amplitude within 100/h kpc. The slow redshift evolution is consistent with these galaxies tracing the mass clustering in low density, Omega= 0.2, relatively unbiased, sigma_8=0.8, universe, but cannot yet exclude other possibilities.Comment: to be published in the Aug 1 ApJ, 20 pages as a uuencoded postscript file Postscript with all figures is available at http://manaslu.astro.utoronto.ca/~carlberg/paper

Landslide Risk: Economic Valuation in the North-Eastern Zone of Medellin City

Natural disasters of a geodynamic nature can cause enormous economic and human losses. The economic costs of a landslide disaster include relocation of communities and physical repair of urban infrastructure. However, when performing a quantitative risk analysis, generally, the indirect economic consequences of such an event are not taken into account. A probabilistic approach methodology that considers several scenarios of hazard and vulnerability to measure the magnitude of the landslide and to quantify the economic costs is proposed. With this approach, it is possible to carry out a quantitative evaluation of the risk by landslides, allowing the calculation of the economic losses before a potential disaster in an objective, standardized and reproducible way, taking into account the uncertainty of the building costs in the study zone. The possibility of comparing different scenarios facilitates the urban planning process, the optimization of interventions to reduce risk to acceptable levels and an assessment of economic losses according to the magnitude of the damage. For the development and explanation of the proposed methodology, a simple case study is presented, located in north-eastern zone of the city of Medellín. This area has particular geomorphological characteristics, and it is also characterized by the presence of several buildings in bad structural conditions. The proposed methodology permits to obtain an estimative of the probable economic losses by earthquake-induced landslides, taking into account the uncertainty of the building costs in the study zone. The obtained estimative shows that the structural intervention of the buildings produces a reduction the order of 21 % in the total landslide risk. © Published under licence by IOP Publishing Ltd

Universality of rain event size distributions

We compare rain event size distributions derived from measurements in climatically different regions, which we find to be well approximated by power laws of similar exponents over broad ranges. Differences can be seen in the large-scale cutoffs of the distributions. Event duration distributions suggest that the scale-free aspects are related to the absence of characteristic scales in the meteorological mesoscale.Comment: 16 pages, 10 figure

Chiral Corrections to Lattice Calculations of Charge Radii

Logarithmic divergences in pion and proton charge radii associated with chiral loops are investigated to assess systematic uncertainties in current lattice determinations of charge radii. The chiral corrections offer a possible solution to the long standing problem of why present lattice calculations yield proton and pion radii which are similar in size.Comment: PostScript file only. Ten pages. Figures included. U. of MD Preprint #92-19

Decay constants of heavy pseudoscalar mesons from QCD sum rules

We revisit the sum-rule extraction of the decay constants of the D, Ds, B, and Bs mesons from the two-point correlator of heavy-light pseudoscalar currents. We use the operator product expansion for this correlator expressed in terms of the MSbar heavy-quark mass, for which the perturbative expansion exhibits a reasonable convergence. Our main emphasis is laid on the control over the uncertainties in the decay constants, related both to the input QCD parameters and to the limited accuracy of the method of sum-rules. This becomes possible due to the application of our procedure of extracting hadron observables that involves as novel feature dual thresholds depending on the Borel parameter. For charmed mesons, we find the decay constants f_D=206.2\pm 7.3(OPE)\pm 5.1(syst) MeV and f_Ds=245.3\pm 15.7(OPE)\pm 4.5(syst) MeV. For beauty mesons, the decay constants turn out to be extremely sensitive to the precise value of mb(mb). By requiring our sum-rule estimate to match the average of the lattice results for f_B, a very accurate value mb(mb)=4.245\pm 0.025 GeV is extracted, leading to f_B=193.4\pm 12.3(OPE)\pm 4.3(syst) MeV and f_Bs=232.5\pm 18.6(OPE)\pm 2.4(syst) MeV.Comment: 12 page

A Path Algorithm for Constrained Estimation

Many least squares problems involve affine equality and inequality constraints. Although there are variety of methods for solving such problems, most statisticians find constrained estimation challenging. The current paper proposes a new path following algorithm for quadratic programming based on exact penalization. Similar penalties arise in $l_1$ regularization in model selection. Classical penalty methods solve a sequence of unconstrained problems that put greater and greater stress on meeting the constraints. In the limit as the penalty constant tends to $\infty$, one recovers the constrained solution. In the exact penalty method, squared penalties are replaced by absolute value penalties, and the solution is recovered for a finite value of the penalty constant. The exact path following method starts at the unconstrained solution and follows the solution path as the penalty constant increases. In the process, the solution path hits, slides along, and exits from the various constraints. Path following in lasso penalized regression, in contrast, starts with a large value of the penalty constant and works its way downward. In both settings, inspection of the entire solution path is revealing. Just as with the lasso and generalized lasso, it is possible to plot the effective degrees of freedom along the solution path. For a strictly convex quadratic program, the exact penalty algorithm can be framed entirely in terms of the sweep operator of regression analysis. A few well chosen examples illustrate the mechanics and potential of path following.Comment: 26 pages, 5 figure

Validation of nonlinear PCA

Linear principal component analysis (PCA) can be extended to a nonlinear PCA by using artificial neural networks. But the benefit of curved components requires a careful control of the model complexity. Moreover, standard techniques for model selection, including cross-validation and more generally the use of an independent test set, fail when applied to nonlinear PCA because of its inherent unsupervised characteristics. This paper presents a new approach for validating the complexity of nonlinear PCA models by using the error in missing data estimation as a criterion for model selection. It is motivated by the idea that only the model of optimal complexity is able to predict missing values with the highest accuracy. While standard test set validation usually favours over-fitted nonlinear PCA models, the proposed model validation approach correctly selects the optimal model complexity.Comment: 12 pages, 5 figure

Decuplet Baryon Structure from Lattice QCD

The electromagnetic properties of the SU(3)-flavor baryon decuplet are examined within a lattice simulation of quenched QCD. Electric charge radii, magnetic moments, and magnetic radii are extracted from the E0 and M1 form factors. Preliminary results for the E2 and M3 moments are presented giving the first model independent insight to the shape of the quark distribution in the baryon ground state. As in our octet baryon analysis, the lattice results give evidence of spin-dependent forces and mass effects in the electromagnetic properties. The quark charge distribution radii indicate these effects act in opposing directions. Some baryon dependence of the effective quark magnetic moments is seen. However, this dependence in decuplet baryons is more subtle than that for octet baryons. Of particular interest are the lattice predictions for the magnetic moments of $\Omega^-$ and $\Delta^{++}$ for which new recent experimental measurements are available. The lattice prediction of the $\Delta^{++}/p$ ratio appears larger than the experimental ratio, while the lattice prediction for the $\Omega^-/p$ magnetic moment ratio is in good agreement with the experimental ratio.Comment: RevTeX manuscript, 34 pages plus 21 figures (available upon request