Markov Chain Monte Carlo Posterior Density Approximation for a Groove-Dimensioning Purpose

José Ismael de La Rosa Vargas (1) , Gilles Fleury (2) , Sonia Esther Osuna (3) , Marie-Eve Davoust (2)

1 UAZ - Universidad Autonoma de Zacatecas [Autonomous University of Zacatecas]
2 SUPELEC-Campus Gif
3 IPN - Instituto Politecnico Nacional [Mexico]

The purpose of this paper is to present a new approach for measurand uncertainty characterization. The Markov chain Monte Carlo (MCMC) is applied to measurand probability density function (pdf) estimation, which is considered as an inverse problem. The measurement characterization is driven by the pdf estimation in a nonlinear Gaussian framework with unknown variance and with limited observed data. These techniques are applied to a realistic measurand problem of groove dimensioning using remote field eddy current (RFEC) inspection. The application of resampling methods such as bootstrap and the perfect sampling for convergence diagnostics purposes gives large improvements in the accuracy of the MCMC estimates.

Keywords: weighted bootstrap; Gibbs sampling; indirect measurement; Markov chain Monte Carlo (MCMC); Metropolis–Hastings (M–H); nonlinear regression; perfect sampling; weighted bootstrap.

Domains: Mathematics [math]; Probability [math.PR]; Engineering Sciences [physics]; Signal and Image processing; Computer Science [cs]; Signal and Image Processing

José Ismael de La Rosa Vargas, Gilles Fleury, Sonia Esther Osuna, Marie-Eve Davoust. Markov Chain Monte Carlo Posterior Density Approximation for a Groove-Dimensioning Purpose. IEEE Transactions on Instrumentation and Measurement, 2006, Vol. 55 (N°1), pp. 112-122. ⟨10.1109/TIM.2005.861495⟩. ⟨hal-00260575⟩