Séverine Demeyer

Bayesian framework for proficiency tests using auxiliary information on laboratories

In this paper, we propose a Bayesian framework to analyse proficiency tests results that allows to combine prior information on laboratories and prior knowledge on the consensus value when no measurement uncertainties nor replicates are reported. For these proficiency tests, where the reported data is reduced to its minimum, we advocate that each piece of information related to the measurement process is valuable and can lead to a more reliable estimation of the consensus value and its associated uncertainty. The resulting marginal posterior distribution of the consensus value relies on the management of expert knowledge used to build prior distributions on the consensus value and the laboratory effects. The choices of priors are discussed to promote the method when the required auxiliary information is available. This new approach is applied on a simulated data set and on a real-life environmental proficiency test.

Contributions to Bayesian Structural Equation Modeling

Structural equation models (SEMs) are multivariate latent variable models used to model causality structures in data. A Bayesian estimation and validation of SEMs is proposed and identifiability of parameters is studied. The latter study shows that latent variables should be standardized in the analysis to ensure identifiability. This heuristics is in fact introduced to deal with complex identifiability constraints. To illustrate the point, identifiability constraints are calculated in a marketing application, in which posterior draws of the constraints are derived from the posterior conditional distributions of parameters.