A Statistical Inference Comparison for Measurement Estimation Using Stochastic Simulation Techniques

The purpose of this paper is to present a comparison of different techniques for making statistical inference about a measurement system model. This comparison involves results when two main assumptions are made: 1) the unknowable behavior of the probability density function (pdf) p (e) of errors since the real measurement systems are always exposed to continuous perturbations of an unknown nature and 2) the assumption that, after some experimentation, one can obtain sufficient information that can be incorporated into the modeling as prior information. The first assumption leads us to propose the use of two approaches, which permit building hybrid algorithms; such approaches are the nonparametric bootstrap and the kernel methods. The second assumption makes possible the exploration of a Bayesian framework solution and Monte Carlo Markov chain auxiliary that is used to access the
a

posteriori
pdf of the measurement. For both assumptions over p (e) and the model, different classical criteria can be used; one also uses an extension of a recent criterion of entropy minimization. The entropy criterion is constructed on the basis of a symmetrized kernel estimate p
n
,
h
(
e
) of p(e). Finally, a comparison between results obtained with the different schemes proposed by De la Rosa is presented.