A tutorial and a user-friendly program for evaluating risks of false decisions in conformity assessment of a multicomponent material or object due to measurement uncertainty, based on a Bayesian approach, are presented. The developed program consists of two separate MS-Excel spreadsheets. It allows calculation of the consumer's and producer's risks concerning each component of the material whose concentration was tested (‘particular risks’) as well as concerning the material as a whole (‘total risks’). According to the Bayesian framework, probability density functions of the actual/‘true’ component concentrations (prior pdfs) and likelihood functions (likelihoods) of the corresponding test results are used to model the knowledge about the material or object. Both cases of independent and correlated variables (the actual concentrations and the test results) are treated in the present work. Spreadsheets provide an estimate of the joint posterior pdf for the actual component concentrations as the normalized product of the multivariate prior pdf and the likelihood, starting from normal or log-normal prior pdfs and normal likelihoods, using Markov chain Monte Carlo (MCMC) simulations by the Metropolis-Hastings algorithm. The principles of Bayesian inference and MCMC are described for users with basic knowledge in statistics, necessary for correct formulation of a task and interpretation of the calculation results. The spreadsheet program was validated by comparison of the obtained results with analytical results calculated in the R programming environment. The developed program allows estimation of risks greater than 0.003% with standard deviations of such estimates spreading from 0.001% to 1.5%, depending on the risk value. Such estimation characteristics are satisfactory, taking into account known variability in measurement uncertainty associated with the test results of multicomponent materials.

Tutorial and spreadsheets for Bayesian evaluation of risks of false decisions on conformity of a multicomponent material or object due to measurement uncertainty / da Silva, Ricardo J. N. B.; Pennecchi, Francesca R.; Hibbert, D. Brynn; Kuselman, Ilya. - In: CHEMOMETRICS AND INTELLIGENT LABORATORY SYSTEMS. - ISSN 0169-7439. - 182:(2018), pp. 109-116. [10.1016/j.chemolab.2018.09.004]

Tutorial and spreadsheets for Bayesian evaluation of risks of false decisions on conformity of a multicomponent material or object due to measurement uncertainty

Pennecchi, Francesca R.;
2018

Abstract

A tutorial and a user-friendly program for evaluating risks of false decisions in conformity assessment of a multicomponent material or object due to measurement uncertainty, based on a Bayesian approach, are presented. The developed program consists of two separate MS-Excel spreadsheets. It allows calculation of the consumer's and producer's risks concerning each component of the material whose concentration was tested (‘particular risks’) as well as concerning the material as a whole (‘total risks’). According to the Bayesian framework, probability density functions of the actual/‘true’ component concentrations (prior pdfs) and likelihood functions (likelihoods) of the corresponding test results are used to model the knowledge about the material or object. Both cases of independent and correlated variables (the actual concentrations and the test results) are treated in the present work. Spreadsheets provide an estimate of the joint posterior pdf for the actual component concentrations as the normalized product of the multivariate prior pdf and the likelihood, starting from normal or log-normal prior pdfs and normal likelihoods, using Markov chain Monte Carlo (MCMC) simulations by the Metropolis-Hastings algorithm. The principles of Bayesian inference and MCMC are described for users with basic knowledge in statistics, necessary for correct formulation of a task and interpretation of the calculation results. The spreadsheet program was validated by comparison of the obtained results with analytical results calculated in the R programming environment. The developed program allows estimation of risks greater than 0.003% with standard deviations of such estimates spreading from 0.001% to 1.5%, depending on the risk value. Such estimation characteristics are satisfactory, taking into account known variability in measurement uncertainty associated with the test results of multicomponent materials.
File in questo prodotto:
File Dimensione Formato  
Kuselman_2018_Chemometrics_182.pdf

non disponibili

Descrizione: Articolo principale
Tipologia: Versione editoriale
Licenza: Non Pubblico - Accesso privato/ristretto
Dimensione 962.05 kB
Formato Adobe PDF
962.05 kB Adobe PDF   Visualizza/Apri   Richiedi una copia
Accepted_Kuselman_2018_Chemometrics_182.pdf

embargo fino al 16/09/2020

Descrizione: Articolo principale
Tipologia: Documento in Post-print
Licenza: Creative Commons
Dimensione 2.76 MB
Formato Adobe PDF
2.76 MB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11696/59857
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 15
  • ???jsp.display-item.citation.isi??? 15
social impact