Density estimation for measurement purposes and convergence improvement using MCMC

Abstract

The purpose of this paper is to present a new approach for measurement uncertainty characterization. The Markov Chain Monte Carlo (MCMC) is applied to measurement pdf estimation, which is considered as an inverse problem. The measurement characterization is driven by the pdf estimation in a non-linear Gaussian framework with unknown variance and with limited observed data. Multidimensional integration and support searching, are driven by the Metropolis-Hastings (M-H) autoregressive algorithm which performance is generally better than the M-H random walk. These techniques are applied to a realistic measurement 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.