Markov chain Monte Carlo posterior density approximation for a groove-dimensioning purpose

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.

[1]  N. Ravishanker,et al.  Bayesian Analysis of ARMA Processes: Complete Sampling Based Inference Under Full Likelihoods , 1996 .

[2]  Gilles Fleury,et al.  Model selection via worst-case criterion for nonlinear bounded-error estimation , 1999, IMTC/99. Proceedings of the 16th IEEE Instrumentation and Measurement Technology Conference (Cat. No.99CH36309).

[3]  Pierre-Olivier Amblard,et al.  MCMC methods for discrete source separation , 2001 .

[4]  Julian Besag,et al.  Markov Chain Monte Carlo for Statistical Inference , 2002 .

[5]  B. Presnell,et al.  Intentionally biased bootstrap methods , 1999 .

[6]  Andrej Pázman.  Probability distribution of the multivariate nonlinear least squares estimates , 1984, Kybernetika.

[7]  Christian P. Robert,et al.  Monte Carlo Statistical Methods , 2005, Springer Texts in Statistics.

[8]  A. Gelfand,et al.  On Markov Chain Monte Carlo Acceleration , 1994 .

[9]  Ronald L. Wasserstein,et al.  Monte Carlo: Concepts, Algorithms, and Applications , 1997 .

[10]  Gilles Fleury,et al.  Model selection based on robustness criterion with measurement application , 1999, Optics & Photonics.

[11]  B. Carlin,et al.  Bayesian Model Choice Via Markov Chain Monte Carlo Methods , 1995 .

[12]  J. Shao.  Bootstrap Model Selection , 1996 .

[13]  Adrian F. M. Smith,et al.  Bayesian computation via the gibbs sampler and related markov chain monte carlo methods (with discus , 1993 .

[14]  J. Møller.  Perfect simulation of conditionally specified models , 1999 .

[15]  Radford M. Neal.  Slice Sampling , 2003, The Annals of Statistics.

[16]  J. Oksman,et al.  A Parametric Estimation Approach for Groove Dimensioning Using Remote Field Eddy Current Inspection , 1999 .

[17]  Petar M. Djuric,et al.  Perfect sampling: a review and applications to signal processing , 2002, IEEE Trans. Signal Process..

[18]  S. Chib,et al.  Understanding the Metropolis-Hastings Algorithm , 1995 .

[19]  David Bruce Wilson,et al.  Exact sampling with coupled Markov chains and applications to statistical mechanics , 1996, Random Struct. Algorithms.

[20]  Gilles Fleury,et al.  Bootstrap methods applied to indirect measurement , 2001 .

[21]  M. J. Box.  Bias in Nonlinear Estimation , 1971 .

[22]  G. Fleury,et al.  Non-intrusive time-of-flight flowmeter—parametric estimation and optimisation , 1995 .