<abstract xmlns="http://www.w3.org/1999/xhtml"><p> Let a quantity of interest, Y, be modeled in terms of a quantity X and a set of other quantities Z. Suppose that for Z there is type B information, by which we mean that it leads directly to a joint state-of-knowledge probability density function (PDF) for that set, without reference to likelihoods. Suppose also that for X there is type A information, which signifies that a likelihood is available. The posterior for X is then obtained by updating its prior with said likelihood by means of Bayes’ rule, where the prior encodes whatever type B information there may be available for X. If there is no such information, an appropriate non-informative prior should be used. Once the PDFs for X and Z have been constructed, they can be propagated through the measurement model to obtain the PDF for Y, either analytically or numerically. But suppose that, at the same time, there is also information of type A, type B or both types together for the quantity Y. By processing such information in the manner described above we obtain another PDF for Y. Which one is right? Should both PDFs be merged somehow? Is there another way of applying Bayes’ rule such that a single PDF for Y is obtained that encodes all existing information? In this paper we examine what we believe should be the proper ways of dealing with such a (not uncommon) situation.</p></abstract>

Let a quantity of interest, Y, be modeled in terms of a quantity X and a set of other quantities Z. Suppose that for Z there is type B information, by which we mean that it leads directly to a joint state-of-knowledge probability density function (PDF) for that set, without reference to likelihoods. Suppose also that for X there is type A information, which signifies that a likelihood is available. The posterior for X is then obtained by updating its prior with said likelihood by means of Bayes’ rule, where the prior encodes whatever type B information there may be available for X. If there is no such information, an appropriate non-informative prior should be used. Once the PDFs for X and Z have been constructed, they can be propagated through the measurement model to obtain the PDF for Y, either analytically or numerically. But suppose that, at the same time, there is also information of type A, type B or both types together for the quantity Y. By processing such information in the manner described above we obtain another PDF for Y. Which one is right? Should both PDFs be merged somehow? Is there another way of applying Bayes’ rule such that a single PDF for Y is obtained that encodes all existing information? In this paper we examine what we believe should be the proper ways of dealing with such a (not uncommon) situation.

Bayesian Analysis of a Simple Measurement Model Distinguishing between Types of Information

Department of Mechanical and Metallurgical Engineering, Pontificia Universidad Católica de Chile, Vicuña Mackenna 4860, Santiago, Chile

Metrolytik, Kernstockstr. 4, 8600 Bruck an der Mur, Austria

Measurement Science Review

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Let a quantity of interest, Y, be modeled in terms of a quantity X and a set of other quantities Z. Suppose that for Z there is type B information, by which we...

Bayesian Analysis of a Simple Measurement Model Distinguishing between Types of Information

Publié en ligne: 30 déc. 2015

Pages: 274 - 283

Reçu: 28 juil. 2015

Accepté: 02 déc. 2015

DOI: https://doi.org/10.1515/msr-2015-0038

Mots clés
Measurement uncertainty, probability density function, Bayesian statistics, information types, data processing

© by Ignacio Lira

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Bayesian Analysis of a Simple Measurement Model Distinguishing between Types of Information

Publié en ligne: 30 déc. 2015

Pages: 274 - 283

Reçu: 28 juil. 2015

Accepté: 02 déc. 2015

DOI: https://doi.org/10.1515/msr-2015-0038

Mots clésMeasurement uncertainty, probability density function, Bayesian statistics, information types, data processing

© by Ignacio Lira

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Mots clés
Measurement uncertainty, probability density function, Bayesian statistics, information types, data processing