{"title":"处理放射性同位素年代测定中 \"负年龄 \"和 \"负原子数 \"难题的统计方法","authors":"W.-K. Hu , W. Jiang , Z.-T. Lu","doi":"10.1016/j.quageo.2024.101521","DOIUrl":null,"url":null,"abstract":"<div><p>In radioisotope dating, statistical fluctuations of atom counts or decay counts can sometimes lead to unphysical results, such as negative counts after subtracting the background or negative apparent ages near the boundaries of the dating range. How to treat these boundary cases with a unified approach and give proper estimates on age limits and confidence intervals is an important issue in radioisotope dating. In this work, we combine the Feldman-Cousins likelihood-ratio ordering method for interval estimation, a Frequentist approach to make consistent transitions from the choice of one-sided limits to two-sided confidence intervals, and a Bayesian method to treat the background uncertainties. This data treatment method naturally eliminates the unphysical results. We use <sup>81</sup>Kr dating and Atom Trap Trace Analysis as an example to illustrate the advantages. This method can be generalized to other radioisotopes and ultra-sensitive analysis techniques.</p></div>","PeriodicalId":54516,"journal":{"name":"Quaternary Geochronology","volume":"81 ","pages":"Article 101521"},"PeriodicalIF":1.7000,"publicationDate":"2024-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A statistical method for treating the “negative-age” and “negative-atom-number” conundrums in radioisotope dating\",\"authors\":\"W.-K. Hu , W. Jiang , Z.-T. Lu\",\"doi\":\"10.1016/j.quageo.2024.101521\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In radioisotope dating, statistical fluctuations of atom counts or decay counts can sometimes lead to unphysical results, such as negative counts after subtracting the background or negative apparent ages near the boundaries of the dating range. How to treat these boundary cases with a unified approach and give proper estimates on age limits and confidence intervals is an important issue in radioisotope dating. In this work, we combine the Feldman-Cousins likelihood-ratio ordering method for interval estimation, a Frequentist approach to make consistent transitions from the choice of one-sided limits to two-sided confidence intervals, and a Bayesian method to treat the background uncertainties. This data treatment method naturally eliminates the unphysical results. We use <sup>81</sup>Kr dating and Atom Trap Trace Analysis as an example to illustrate the advantages. This method can be generalized to other radioisotopes and ultra-sensitive analysis techniques.</p></div>\",\"PeriodicalId\":54516,\"journal\":{\"name\":\"Quaternary Geochronology\",\"volume\":\"81 \",\"pages\":\"Article 101521\"},\"PeriodicalIF\":1.7000,\"publicationDate\":\"2024-04-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Quaternary Geochronology\",\"FirstCategoryId\":\"89\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S1871101424000256\",\"RegionNum\":2,\"RegionCategory\":\"地球科学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"GEOGRAPHY, PHYSICAL\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Quaternary Geochronology","FirstCategoryId":"89","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1871101424000256","RegionNum":2,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"GEOGRAPHY, PHYSICAL","Score":null,"Total":0}
A statistical method for treating the “negative-age” and “negative-atom-number” conundrums in radioisotope dating
In radioisotope dating, statistical fluctuations of atom counts or decay counts can sometimes lead to unphysical results, such as negative counts after subtracting the background or negative apparent ages near the boundaries of the dating range. How to treat these boundary cases with a unified approach and give proper estimates on age limits and confidence intervals is an important issue in radioisotope dating. In this work, we combine the Feldman-Cousins likelihood-ratio ordering method for interval estimation, a Frequentist approach to make consistent transitions from the choice of one-sided limits to two-sided confidence intervals, and a Bayesian method to treat the background uncertainties. This data treatment method naturally eliminates the unphysical results. We use 81Kr dating and Atom Trap Trace Analysis as an example to illustrate the advantages. This method can be generalized to other radioisotopes and ultra-sensitive analysis techniques.
期刊介绍:
Quaternary Geochronology is an international journal devoted to the publication of the highest-quality, peer-reviewed articles on all aspects of dating methods applicable to the Quaternary Period - the last 2.6 million years of Earth history. Reliable ages are fundamental to place changes in climates, landscapes, flora and fauna - including the evolution and ecological impact of humans - in their correct temporal sequence, and to understand the tempo and mode of geological and biological processes.