{"title":"当证据是由相对信念测量时,结合统计证据。","authors":"Michael Evans","doi":"10.3390/e27060654","DOIUrl":null,"url":null,"abstract":"<p><p>The problem of combining statistical evidence concerning an unknown, contained in each of the <i>k</i> Bayesian inference bases, is discussed. This can be considered as being related to the problem of pooling <i>k</i> priors to determine a consensus prior, but the focus here is instead on combining a measure of statistical evidence to obtain a consensus measure of statistical evidence. The linear opinion pool is seen to have the most appropriate properties for this role. In particular, linear pooling preserves a consensus with respect to the evidence, and other rules do not. While linear pooling does not preserve prior independence, it is shown that it still behaves appropriately with respect to the expression of statistical evidence in such a context. For the more general problem of combining statistical evidence, where the priors as well as the sampling models may differ, Jeffrey conditionalization plays a key role.</p>","PeriodicalId":11694,"journal":{"name":"Entropy","volume":"27 6","pages":""},"PeriodicalIF":2.1000,"publicationDate":"2025-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12191512/pdf/","citationCount":"0","resultStr":"{\"title\":\"Combining Statistical Evidence When Evidence Is Measured by Relative Belief.\",\"authors\":\"Michael Evans\",\"doi\":\"10.3390/e27060654\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p><p>The problem of combining statistical evidence concerning an unknown, contained in each of the <i>k</i> Bayesian inference bases, is discussed. This can be considered as being related to the problem of pooling <i>k</i> priors to determine a consensus prior, but the focus here is instead on combining a measure of statistical evidence to obtain a consensus measure of statistical evidence. The linear opinion pool is seen to have the most appropriate properties for this role. In particular, linear pooling preserves a consensus with respect to the evidence, and other rules do not. While linear pooling does not preserve prior independence, it is shown that it still behaves appropriately with respect to the expression of statistical evidence in such a context. For the more general problem of combining statistical evidence, where the priors as well as the sampling models may differ, Jeffrey conditionalization plays a key role.</p>\",\"PeriodicalId\":11694,\"journal\":{\"name\":\"Entropy\",\"volume\":\"27 6\",\"pages\":\"\"},\"PeriodicalIF\":2.1000,\"publicationDate\":\"2025-06-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12191512/pdf/\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Entropy\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://doi.org/10.3390/e27060654\",\"RegionNum\":3,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"PHYSICS, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Entropy","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.3390/e27060654","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, MULTIDISCIPLINARY","Score":null,"Total":0}
Combining Statistical Evidence When Evidence Is Measured by Relative Belief.
The problem of combining statistical evidence concerning an unknown, contained in each of the k Bayesian inference bases, is discussed. This can be considered as being related to the problem of pooling k priors to determine a consensus prior, but the focus here is instead on combining a measure of statistical evidence to obtain a consensus measure of statistical evidence. The linear opinion pool is seen to have the most appropriate properties for this role. In particular, linear pooling preserves a consensus with respect to the evidence, and other rules do not. While linear pooling does not preserve prior independence, it is shown that it still behaves appropriately with respect to the expression of statistical evidence in such a context. For the more general problem of combining statistical evidence, where the priors as well as the sampling models may differ, Jeffrey conditionalization plays a key role.
期刊介绍:
Entropy (ISSN 1099-4300), an international and interdisciplinary journal of entropy and information studies, publishes reviews, regular research papers and short notes. Our aim is to encourage scientists to publish as much as possible their theoretical and experimental details. There is no restriction on the length of the papers. If there are computation and the experiment, the details must be provided so that the results can be reproduced.