Journal of Probability and Statistical Science最新文献

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Visualizing Bivariate Statistics Using Ellipses Over a Scatter Plot 在散点图上使用椭圆可视化二元统计
Journal of Probability and Statistical Science Pub Date : 2022-10-03 DOI: 10.37119/jpss2022.v20i1.584
Mamunur Rashid, J. Sarkar, Siddhanta Phuyal
{"title":"Visualizing Bivariate Statistics Using Ellipses Over a Scatter Plot","authors":"Mamunur Rashid, J. Sarkar, Siddhanta Phuyal","doi":"10.37119/jpss2022.v20i1.584","DOIUrl":"https://doi.org/10.37119/jpss2022.v20i1.584","url":null,"abstract":"A scatter plot shows the relationship between two quantitative variables x and y. Sometimes, we can predict one variable as a linear function of the other using the least-squares regression lines of y on x or x on y. These two regression lines together suffice to identify the mean vector, the coefficient of determination, the correlation coefficient, and the ratio of the standard deviations (SD). So, do our proposed summary ellipses. Additionally, the inner ellipse reveals the SDs and the outer ellipse flags potential outliers. \u0000  \u0000 ","PeriodicalId":161562,"journal":{"name":"Journal of Probability and Statistical Science","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129374772","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A new modified Bayesian method for measurement uncertainty analysis and the unification of frequentist and Bayesian inference 一种新的改进贝叶斯方法用于测量不确定度分析及频率与贝叶斯推理的统一
Journal of Probability and Statistical Science Pub Date : 2022-10-03 DOI: 10.37119/jpss2022.v20i1.515
Hening Huang
{"title":"A new modified Bayesian method for measurement uncertainty analysis and the unification of frequentist and Bayesian inference","authors":"Hening Huang","doi":"10.37119/jpss2022.v20i1.515","DOIUrl":"https://doi.org/10.37119/jpss2022.v20i1.515","url":null,"abstract":"This paper proposes a new modification of the traditional Bayesian method for measurement uncertainty analysis.  The new modified Bayesian method is derived from the law of aggregation of information (LAI) and the rule of transformation between the frequentist view and Bayesian view.  It can also be derived from the original Bayes Theorem in continuous form.  We focus on a problem that is often encountered in measurement science: a measurement gives a series of observations.  We consider two cases: (1) there is no genuine prior information about the measurand, so the uncertainty evaluation is purely Type A, and (2) prior information is available and is represented by a normal distribution.  The traditional Bayesian method (also known as the reformulated Bayes Theorem) fails to provide a valid estimate of standard uncertainty in either case.  The new modified Bayesian method provides the same solutions to these two cases as its frequentist counterparts.  The differences between the new modified Bayesian method and the traditional Bayesian method are discussed.  This paper reveals that the traditional Bayesian method is not a self-consistent operation, so it may lead to incorrect inferences in some cases, such as the two cases considered.  In the light of the frequentist-Bayesian transformation rule and the law of aggregation of information (LAI), the frequentist and Bayesian inference are virtually equivalent, so they can be unified, at least in measurement uncertainty analysis.  The unification is of considerable interest because it may resolve the long-standing debate between frequentists and Bayesians.  The unification may also lead to an indisputable, uniform revision of the GUM (Evaluation of measurement data - Guide to the expression of uncertainty in measurement (JCGM 2008)).","PeriodicalId":161562,"journal":{"name":"Journal of Probability and Statistical Science","volume":"44 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121981915","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
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