Minimum-Width Confidence Bands via Constraint Optimization

Peer reviewe

High-dimensional instrumental variables regression and confidence sets

This article considers inference in linear models with d\_X regressors, some or many of which could be endogenous, and d\_Z instrumental variables (IVs). d\_Z can range from less than d\_X to any order smaller than an exponential in the sample size. For moderate d\_X, identification robust confidence sets are obtained by solving a hierarchy of semidefinite programs. For large d\_X, we propose the STIV estimator. The analysis of its error uses sensitivity characteristics introduced in this paper. Robust confidence sets are derived by solving linear programs. Results on rates of convergence, variable selection, and confidence sets which "adapt" to the sparsity are given. Generalizations include models with endogenous IVs and systems of equations with approximation errors. We also analyse confidence bands for vectors of linear functionals and functions using bias correction. The application is to a demand system with approximation errors, cross-equation restrictions, and thousands of endogenous regressors

Physics with a very long neutrino factory baseline

We discuss the neutrino oscillation physics of a very long neutrino factory baseline over a broad range of lengths (between 6000 km and 9000 km), centered on the ``magic baseline'' ($\sim$ 7500 km) where correlations with the leptonic CP phase are suppressed by matter effects. Since the magic baseline depends only on the density, we study the impact of matter density profile effects and density uncertainties over this range, and the impact of detector locations off the optimal baseline. We find that the optimal constant density describing the physics over this entire baseline range is about 5% higher than the average matter density. This implies that the magic baseline is significantly shorter than previously inferred. However, while a single detector optimization requires fine-tuning of the (very long) baseline length, its combination with a near detector at a shorter baseline is much less sensitive to the far detector location and to uncertainties in the matter density. In addition, we point out different applications of this baseline which go beyond its excellent correlation and degeneracy resolution potential. We demonstrate that such a long baseline assists in the improvement of the $\theta_{13}$ precision and in the resolution of the octant degeneracy. Moreover, we show that the neutrino data from such a baseline could be used to extract the matter density along the profile up to 0.24% at $1 \sigma$ for large $\sin^2 2 \theta_{13}$, providing a useful discriminator between different geophysical models.Comment: 27 pages, 11 figures. Minor changes, references added; version to appear in Phys. Rev.

Joint Bayesian endmember extraction and linear unmixing for hyperspectral imagery

This paper studies a fully Bayesian algorithm for endmember extraction and abundance estimation for hyperspectral imagery. Each pixel of the hyperspectral image is decomposed as a linear combination of pure endmember spectra following the linear mixing model. The estimation of the unknown endmember spectra is conducted in a unified manner by generating the posterior distribution of abundances and endmember parameters under a hierarchical Bayesian model. This model assumes conjugate prior distributions for these parameters, accounts for non-negativity and full-additivity constraints, and exploits the fact that the endmember proportions lie on a lower dimensional simplex. A Gibbs sampler is proposed to overcome the complexity of evaluating the resulting posterior distribution. This sampler generates samples distributed according to the posterior distribution and estimates the unknown parameters using these generated samples. The accuracy of the joint Bayesian estimator is illustrated by simulations conducted on synthetic and real AVIRIS images

Physics and optimization of beta-beams: From low to very high gamma

The physics potential of beta beams is investigated from low to very high gamma values and it is compared to superbeams and neutrino factories. The gamma factor and the baseline are treated as continuous variables in the optimization of the beta beam, while a fixed mass water Cherenkov detector or a totally active scintillator detector is assumed. We include in our discussion also the gamma dependence of the number of ion decays per year. For low gamma, we find that a beta beam could be a very interesting alternative to a superbeam upgrade, especially if it is operated at the second oscillation maximum to reduce correlations and degeneracies. For high gamma, we find that a beta beam could have a potential similar to a neutrino factory. In all cases, the sensitivity of the beta beams to CP violation is very impressive if similar neutrino and anti-neutrino event rates can be achieved.Comment: 34 pages, 16 figures, Fig. 2 modified, discussion improved, refs. added, version to appear in PR