arXiv subjects

F. Gamboa

Publications and source records attributed to F. Gamboa.

3 recordsLinked to original sources

arXiv2019

Sensitivity Analysis and Generalized Chaos Expansions. Lower Bounds for Sobol indices

The so-called polynomial chaos expansion is widely used in computer experiments. For example, it is a powerful tool to estimate Sobol' sensitivity indices. In this paper, we consider generalized chaos expansions built on general tensor Hilbert basis. In this frame, we revisit the computation of the Sobol' indices and give general lower bounds for these indices. The case of the eigenfunctions system associated with a Poincar{\'e} differential operator leads to lower bounds involving the derivatives of the analyzed function and provides an efficient tool for variable screening. These lower bounds are put in action both on toy and real life models demonstrating their accuracy.

math.ST↗

arXiv2018

Sensitivity indices for output on a Riemannian manifold

In the context of computer code experiments, sensitivity analysis of a complicated input-output system is often performed by ranking the so-called Sobol indices. One reason of the popularity of Sobol's approach relies on the simplicity of the statistical estimation of these indices using the so-called Pick and Freeze method. In this work we propose and study sensitivity indices for the case where the output lies on a Riemannian manifold. These indices are based on a Cram\'er von Mises like criterion that takes into account the geometry of the output support. We propose a Pick-Freeze like estimator of these indices based on an $U$--statistic. The asymptotic properties of these estimators are studied. Further, we provide and discuss some interesting numerical examples.

math.ST↗

arXiv2013

In situ comparison of the critical current density in $Y Ba_2 Cu_3 O_{7-δ}$ thin films measured by the screening technique under two criteria

In this investigation we report the determination of the critical current density $J_c$ flowing in a $\mathrm{Y}\mathrm{Ba}_2\mathrm{Cu}_3\mathrm{O}_{7-δ}$ superconducting thin film. Estimation of $J_c$ was carried out by an inductive technique, the so-called screening technique, in which both the imaginary part of the fundamental harmonic of susceptibility $χ''_1$ and third harmonic voltage $V_3$ criteria were considered for the determination of the full penetration field. In order to verify the reliability of this technique under two criteria, we investigated the homogeneity of $J_c$ via transport measurements conducted on four microbridges patterned in the same film. Based on the transport method we found that both techniques yield similar results in the determination of $J_c$ for temperatures close to critical temperature $T_c$. However, at temperatures relatively far from $T_c$, the $V_3$ criterion showed a better agreement with the transport data. Furthermore, using both criteria, we propose a methodology to estimate in situ the coil factor associated with the $V_3$ criterion, avoiding in this way the need of implementing an additional technique.

cond-mat.supr-con↗