Density estimation for measurement purposes and convergence improvement using mcmc

Abstract

Absfmcf-Thepurposeof thispaper b topresent (I new approach for measurement uncertain@ chnmcteriiotion. The Markov Chain Monte Cor10 (MCMC) is applied to m e o t pdf estimation, which is considered as on inverseproblem. The meosuremenl ehsrmlerirntion is driven by the pdf estimation in (I non-linear Gaussian fromrwork wilh unknown varionee and with limited obserwd daln Multidimensionnl integrrrtion a.nd support seorehing, are driven by fhc Mdropolis-H.sfings (M-H) autoregressive 01-gorilhm which perfonnonce isgenerdly bener fhan the M-H random wlk These techniques nre applied to (I redistic meclsurementproblcnt of groow dimrnsioning using Remote Field Eddy Current (RFEC) inspection The applicntion of resampling methods such as boofstrop and the perfect snmp h g for convergence diagnosticspurposes, gives large improwments in fhc accuracy of Ihc M C M C rrtimnfer.

A Statistical Inference Comparison for Measurement Estimation Using Stochastic Simulation Techniques

“…In recent years, this way to tackling problems points toward the use of Bayesian methods or even ideas about data fusion. When modelling deals with complex problems but there is a maximum of information, and the problem is studied in a Bayesian framework, then the Monte Carlo procedures known as Monte Carlo Markov Chains (MCMC) [33], provide a set of tools to obtain practical solutions of the proposed models [9], [10].…”

“…The measurement modelling has been considered in various works [2]- [10]. The principal contribution of this work is presented in sections III, IV, and V where a comparison of the different schemes for estimation and uncertainty characterization is shown.…”

“…The Remote Field Eddy Current (RFEC) inspection technique 1 is used for dimensioning grooves that may occur in ferromagnetic conductive pipes (this is a practical measurand estimation problem, however, in this study only simulated data is used). This task involves the depth d and the length l estimation of corrosion grooves from measurements of a picked-up coil signal phase y i at different positions x i closest to the defect (measurand estimation problem presented in [4], [5] and [10]). The dimensions of the groove to be estimated are linked to the parametric model (eq.…”

“…The approaches detailed in [10] are used, these are the Gibbs simulation procedure and the hybrid Gibbs Metropolis-Hastings procedure. If the assumed hypotheses about the errors are valid, the performance comparison could be made in a similar framework of the bootstrap proposed methods but in this case using auxiliary tools such as MCMC, and also equivalent framework with respect to PMC and MCLHS (see section § III).…”

“…In the sampling procedure is substituted the likelihood function L(y|θ), previously used according to the Gibbs sampling, by a new function that has been proposed by Pázman [30]. This last likelihood function takes into account the nonlinearities of parameters and also the nonlinearities mapped to the measurands d et l. The proposed matrix ∆ has the assignment ∆ = λK(θ), with an heuristic value for λ = 3.2 and K(θ) obtained according to the Cholesky decomposition of F (θ) −1 which is the inverse of the Fisher information matrix [10]. The number of realized simulations of the Gibbs M-H scheme was 6000 for a single chain (G-M-H 1 ) (the first 1000 were discarded and the remaining 5000 were used to construct the statistical populations).…”