1. bookVolume 15 (2015): Issue 6 (December 2015)
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License
Format
Journal
eISSN
1335-8871
First Published
07 Mar 2008
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6 times per year
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English
access type Open Access

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

Published Online: 30 Dec 2015
Volume & Issue: Volume 15 (2015) - Issue 6 (December 2015)
Page range: 274 - 283
Received: 28 Jul 2015
Accepted: 02 Dec 2015
Journal Details
License
Format
Journal
eISSN
1335-8871
First Published
07 Mar 2008
Publication timeframe
6 times per year
Languages
English
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.

Keywords

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