Bayesian estimation in multivariate inter-laboratory studies with unknown covariance matrices

• In the paper we present Bayesian inference procedures for the parameters of multivariate random effects model, which is used as a quantitative tool for performing multivariate key comparisons and multivariate inter-laboratory studies. The developed new approach does not require that the reported covariance matrices of participating laboratories are known and, as such, it can be used when they are estimated from the measurement results. The Bayesian inference procedures are based on samples generated from the derived posterior distribution when the Berger and Bernardo reference prior and the Jeffreys prior are assigned to the model parameter. Three numerical algorithms for the construction of Markov chains are provided and implemented in the CCAUV.V-K1 key comparisons. All three approaches yield similar Bayesian estimators with wider credible intervals when the Berger and Bernardo reference prior is used. Also, the Bayesian estimators for the elements of the inter-laboratory covariance matrix are larger under this prior than for the Jeffreys prior. Finally, the constructed joint credible sets for the components of the overall mean vector indicate the presence of linear dependence between them which cannot be captured when only univariate key comparisons are performed.

Subject headings

TEKNIK OCH TEKNOLOGIER  -- Annan teknik (hsv//swe)

ENGINEERING AND TECHNOLOGY  -- Other Engineering and Technologies (hsv//eng)

NATURVETENSKAP  -- Fysik (hsv//swe)

NATURAL SCIENCES  -- Physical Sciences (hsv//eng)

NATURVETENSKAP  -- Matematik -- Sannolikhetsteori och statistik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Probability Theory and Statistics (hsv//eng)

Keyword

multivariate inter-laboratory studies

key comparisons

multivariate random effects model

objective Bayesian inference

rank plot

(R)over-cap estimates

Publication and Content Type

ref (subject category)

art (subject category)