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Extreme Value Theory for Binary Expansion Testing 二进制扩展测试的极值理论
Sankhya A Pub Date : 2023-12-06 DOI: 10.1007/s13171-023-00333-7
Siqi Xiang, Wan Zhang, Kai Zhang, J. S. Marron
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引用次数: 0
The Origins of the Stick Breaking Construction 断棍结构的起源
Sankhya A Pub Date : 2023-11-18 DOI: 10.1007/s13171-023-00332-8
Jayaram Sethuraman
{"title":"The Origins of the Stick Breaking Construction","authors":"Jayaram Sethuraman","doi":"10.1007/s13171-023-00332-8","DOIUrl":"https://doi.org/10.1007/s13171-023-00332-8","url":null,"abstract":"","PeriodicalId":21657,"journal":{"name":"Sankhya A","volume":"141 11","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139261457","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 Unified Approach to Hierarchical Random Measures 分层随机测度的统一方法
Sankhya A Pub Date : 2023-11-08 DOI: 10.1007/s13171-023-00330-w
Marta Catalano, Claudio Del Sole, Antonio Lijoi, Igor Prünster
{"title":"A Unified Approach to Hierarchical Random Measures","authors":"Marta Catalano, Claudio Del Sole, Antonio Lijoi, Igor Prünster","doi":"10.1007/s13171-023-00330-w","DOIUrl":"https://doi.org/10.1007/s13171-023-00330-w","url":null,"abstract":"Abstract Hierarchical models enjoy great popularity due to their ability to handle heterogeneous groups of observations by leveraging on their underlying common structure. In a Bayesian nonparametric framework, the hierarchy is introduced at the level of group-specific random measures, and then translated to the observations’ level via suitable transformations. In this work, we propose a new strategy to derive closed-form expressions for the marginal and posterior distributions of each group. Indeed, by directly inserting a suitable set of latent variables into the generative model for the data, we unravel a common core shared by the different hierarchical constructions proposed in the Bayesian nonparametric literature. Specifically, we identify a key identity that underlies these models and highlight its role in the derivation of quantities of interest.","PeriodicalId":21657,"journal":{"name":"Sankhya A","volume":"92 8","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135390377","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
The p-value interpreted as the posterior probability of explaining the data: Applications to multiple testing and to restricted parameter spaces p值被解释为解释数据的后验概率:应用于多次检验和有限参数空间
Sankhya A Pub Date : 2023-11-01 DOI: 10.1007/s13171-023-00328-4
David R. Bickel
{"title":"The p-value interpreted as the posterior probability of explaining the data: Applications to multiple testing and to restricted parameter spaces","authors":"David R. Bickel","doi":"10.1007/s13171-023-00328-4","DOIUrl":"https://doi.org/10.1007/s13171-023-00328-4","url":null,"abstract":"Failures to replicate the results of scientific studies are often attributed to misinterpretations of the p-value. The p-value may be interpreted as an approximate posterior probability, not that the null hypothesis is true but rather that it explains the data as well as the data-generating distribution. That posterior probability modifies the p-value in the following two broad areas of application, leading to new methods of hypothesis testing and effect size estimation. First, when corrected for multiple comparisons, the posterior probability that the null hypothesis adequately explains the data overcomes both the conservative bias of corrected p-values and the anti-conservative bias of commonly used false discovery rate methods. Second, the posterior probability that the null hypothesis adequately explains the data, conditional on a parameter restriction, transforms the p-value in such a way as to overcome difficulties in restricted parameter spaces.","PeriodicalId":21657,"journal":{"name":"Sankhya A","volume":"46 18","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136103379","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: 2
Regression with Variable Dimension Covariates 变维协变量回归
Sankhya A Pub Date : 2023-10-20 DOI: 10.1007/s13171-023-00329-3
Peter Mueller, Fernando Andrés Quintana, Garritt L. Page
{"title":"Regression with Variable Dimension Covariates","authors":"Peter Mueller, Fernando Andrés Quintana, Garritt L. Page","doi":"10.1007/s13171-023-00329-3","DOIUrl":"https://doi.org/10.1007/s13171-023-00329-3","url":null,"abstract":"","PeriodicalId":21657,"journal":{"name":"Sankhya A","volume":"48 3","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135566825","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
Bayesian Ideas in Survey Sampling: The Legacy of Basu 抽样调查中的贝叶斯思想:巴苏的遗产
Sankhya A Pub Date : 2023-10-16 DOI: 10.1007/s13171-023-00327-5
Marco Di Zio, Brunero Liseo, Maria Giovanna Ranalli
{"title":"Bayesian Ideas in Survey Sampling: The Legacy of Basu","authors":"Marco Di Zio, Brunero Liseo, Maria Giovanna Ranalli","doi":"10.1007/s13171-023-00327-5","DOIUrl":"https://doi.org/10.1007/s13171-023-00327-5","url":null,"abstract":"Abstract Survey sampling and, more generally, Official Statistics are experiencing an important renovation time. On one hand, there is the need to exploit the huge information potentiality that the digital revolution made available in terms of data. On the other hand, this process occurred simultaneously with a progressive deterioration of the quality of classical sample surveys, due to a decreasing willingness to participate and an increasing rate of missing responses. The switch from survey-based inference to a hybrid system involving register-based information has made more stringent the debate and the possible resolution of the design-based versus model-based approaches controversy. In this new framework, the use of statistical models seems unavoidable and it is today a relevant part of the official statistician toolkit. Models are important in several different contexts, from Small area estimation to non sampling error adjustment, but they are also crucial for correcting bias due to over and undercoverage of administrative data, in order to prevent potential selection bias, and to deal with different definitions and/or errors in the measurement process of the administrative sources. The progressive shift from a design-based to a model-based approach in terms of super-population is a matter of fact in the practice of the National Statistical Institutes. However, the introduction of Bayesian ideas in official statistics still encounters difficulties and resistance. In this work, we attempt a non-systematic review of the Bayesian development in this area and try to highlight the extra benefit that a Bayesian approach might provide. Our general conclusion is that, while the general picture is today clear and most of the basic topics of survey sampling can be easily rephrased and tackled from a Bayesian perspective, much work is still necessary for the availability of a ready-to-use platform of Bayesian survey sampling in the presence of complex sampling design, non-ignorable missing data patterns, and large datasets.","PeriodicalId":21657,"journal":{"name":"Sankhya A","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136113540","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
Nonparametric Recursive Method for Generalized Kernel Estimators for Dependent Functional Data 相关泛函数据广义核估计的非参数递推方法
Sankhya A Pub Date : 2023-09-19 DOI: 10.1007/s13171-023-00325-7
Yousri Slaoui
{"title":"Nonparametric Recursive Method for Generalized Kernel Estimators for Dependent Functional Data","authors":"Yousri Slaoui","doi":"10.1007/s13171-023-00325-7","DOIUrl":"https://doi.org/10.1007/s13171-023-00325-7","url":null,"abstract":"","PeriodicalId":21657,"journal":{"name":"Sankhya A","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135014026","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
The Case of the Jeffreys-Lindley-paradox as a Bayes-frequentist Compromise: A Perspective Based on the Rao-Lovric-Theorem jeffreys - lindley悖论作为bayes - frequentiist妥协的案例:基于rao - lovrici定理的视角
Sankhya A Pub Date : 2023-09-11 DOI: 10.1007/s13171-023-00321-x
Riko Kelter
{"title":"The Case of the Jeffreys-Lindley-paradox as a Bayes-frequentist Compromise: A Perspective Based on the Rao-Lovric-Theorem","authors":"Riko Kelter","doi":"10.1007/s13171-023-00321-x","DOIUrl":"https://doi.org/10.1007/s13171-023-00321-x","url":null,"abstract":"Abstract Testing a precise hypothesis can lead to substantially different results in the frequentist and Bayesian approach, a situation which is highlighted by the Jeffreys-Lindley paradox. While there exist various explanations why the paradox occurs, this article extends prior work by placing the less well-studied point-null-zero-probability paradox at the center of the analysis. The relationship between the two paradoxes is analyzed based on accepting or rejecting the existence of precise hypotheses. The perspective provided in this paper aims at demonstrating how the Bayesian and frequentist solutions can be reconciled when paying attention to the assumption of the point-null-zero-probability paradox. As a result, the Jeffreys-Lindley-paradox can be reinterpreted as a Bayes-frequentist compromise. The resolution shows that divergences between Bayesian and frequentist modes of inference stem from (a) accepting the existence of a precise hypothesis or not, (b) the assignment of positive measure to a null set and (c) the use of unstandardized p-values or p-values standardized to tail-area probabilities.","PeriodicalId":21657,"journal":{"name":"Sankhya A","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135981682","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
On Bounded Completeness and The $$L_1$$-Denseness of Likelihood Ratios 论似然比的有界完备性和$$L_1$$ -密度
Sankhya A Pub Date : 2023-09-09 DOI: 10.1007/s13171-023-00324-8
Marc Hallin, Bas J. M. Werker, Bo Zhou
{"title":"On Bounded Completeness and The $$L_1$$-Denseness of Likelihood Ratios","authors":"Marc Hallin, Bas J. M. Werker, Bo Zhou","doi":"10.1007/s13171-023-00324-8","DOIUrl":"https://doi.org/10.1007/s13171-023-00324-8","url":null,"abstract":"","PeriodicalId":21657,"journal":{"name":"Sankhya A","volume":"31 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136193074","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 Stochastic Fubini-Type Theorem 新的随机富比尼类型定理
Sankhya A Pub Date : 2021-02-01 DOI: 10.1007/s13171-019-00195-y
M. Baumann
{"title":"A New Stochastic Fubini-Type Theorem","authors":"M. Baumann","doi":"10.1007/s13171-019-00195-y","DOIUrl":"https://doi.org/10.1007/s13171-019-00195-y","url":null,"abstract":"","PeriodicalId":21657,"journal":{"name":"Sankhya A","volume":" 3","pages":"408-420"},"PeriodicalIF":0.0,"publicationDate":"2021-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141221530","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
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