{"title":"Information combination and transformation: a paradox and its resolution","authors":"Hening Huang","doi":"10.1007/s00769-024-01578-x","DOIUrl":null,"url":null,"abstract":"<div><p>In his recent paper (https://doi.org/10.1016/j.measen.2022.100416), Willink showed two contradictory theoretical solutions to the problem of combining and transforming two sets of information about the same quantity. Each set of information is represented by a probability density function (PDF), and the transformation function is nonlinear. We refer to Willink’s contradictory result as “Willink paradox”. Two operations: (a) information combination and (b) information transformation are both mathematically valid according to probability theory. Therefore, the two contradictory solutions are both theoretically correct. In practice such as measurement uncertainty analysis, however, we cannot use both solutions; we must choose one or the other. We propose an entropy metric that can be used to provide a practical solution to the Willink paradox. Three examples are presented to illustrate the Willink paradox and the proposed entropy metric.</p></div>","PeriodicalId":454,"journal":{"name":"Accreditation and Quality Assurance","volume":"29 3","pages":"183 - 187"},"PeriodicalIF":0.8000,"publicationDate":"2024-03-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accreditation and Quality Assurance","FirstCategoryId":"5","ListUrlMain":"https://link.springer.com/article/10.1007/s00769-024-01578-x","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"CHEMISTRY, ANALYTICAL","Score":null,"Total":0}
引用次数: 0
Abstract
In his recent paper (https://doi.org/10.1016/j.measen.2022.100416), Willink showed two contradictory theoretical solutions to the problem of combining and transforming two sets of information about the same quantity. Each set of information is represented by a probability density function (PDF), and the transformation function is nonlinear. We refer to Willink’s contradictory result as “Willink paradox”. Two operations: (a) information combination and (b) information transformation are both mathematically valid according to probability theory. Therefore, the two contradictory solutions are both theoretically correct. In practice such as measurement uncertainty analysis, however, we cannot use both solutions; we must choose one or the other. We propose an entropy metric that can be used to provide a practical solution to the Willink paradox. Three examples are presented to illustrate the Willink paradox and the proposed entropy metric.
期刊介绍：
Accreditation and Quality Assurance has established itself as the leading information and discussion forum for all aspects relevant to quality, transparency and reliability of measurement results in chemical and biological sciences. The journal serves the information needs of researchers, practitioners and decision makers dealing with quality assurance and quality management, including the development and application of metrological principles and concepts such as traceability or measurement uncertainty in the following fields: environment, nutrition, consumer protection, geology, metallurgy, pharmacy, forensics, clinical chemistry and laboratory medicine, and microbiology.
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