Pub Date : 2023-09-21DOI: 10.1007/s11749-023-00888-5
Samuel Pawel, Frederik Aust, Leonhard Held, Eric-Jan Wagenmakers
Abstract The ongoing replication crisis in science has increased interest in the methodology of replication studies. We propose a novel Bayesian analysis approach using power priors: The likelihood of the original study’s data is raised to the power of $$alpha $$ α , and then used as the prior distribution in the analysis of the replication data. Posterior distribution and Bayes factor hypothesis tests related to the power parameter $$alpha $$ α quantify the degree of compatibility between the original and replication study. Inferences for other parameters, such as effect sizes, dynamically borrow information from the original study. The degree of borrowing depends on the conflict between the two studies. The practical value of the approach is illustrated on data from three replication studies, and the connection to hierarchical modeling approaches explored. We generalize the known connection between normal power priors and normal hierarchical models for fixed parameters and show that normal power prior inferences with a beta prior on the power parameter $$alpha $$ α align with normal hierarchical model inferences using a generalized beta prior on the relative heterogeneity variance $$I^2$$ I2 . The connection illustrates that power prior modeling is unnatural from the perspective of hierarchical modeling since it corresponds to specifying priors on a relative rather than an absolute heterogeneity scale.
科学中持续的重复性危机增加了人们对重复性研究方法的兴趣。我们提出了一种新的贝叶斯分析方法，使用幂先验:将原始研究数据的似然提高到$$alpha $$ α的幂，然后用作复制数据分析中的先验分布。与功率参数$$alpha $$ α相关的后验分布和贝叶斯因子假设检验量化了原始研究和复制研究之间的相容程度。对其他参数的推断，如效应大小，动态地从原始研究中借用信息。借鉴的程度取决于两种研究之间的冲突。该方法的实用价值是通过三个复制研究的数据来说明的，并探讨了与分层建模方法的联系。我们对固定参数的正常功率先验和正常层次模型之间的已知联系进行了推广，并表明在功率参数$$alpha $$ α上具有beta先验的正常功率先验推断与在相对异质性方差$$I^2$$ I 2上使用广义beta先验的正常层次模型推断一致。这种联系说明，从分层建模的角度来看，权力先验建模是不自然的，因为它对应于在相对而不是绝对异质性尺度上指定先验。
{"title":"Power priors for replication studies","authors":"Samuel Pawel, Frederik Aust, Leonhard Held, Eric-Jan Wagenmakers","doi":"10.1007/s11749-023-00888-5","DOIUrl":"https://doi.org/10.1007/s11749-023-00888-5","url":null,"abstract":"Abstract The ongoing replication crisis in science has increased interest in the methodology of replication studies. We propose a novel Bayesian analysis approach using power priors: The likelihood of the original study’s data is raised to the power of $$alpha $$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>α</mml:mi> </mml:math> , and then used as the prior distribution in the analysis of the replication data. Posterior distribution and Bayes factor hypothesis tests related to the power parameter $$alpha $$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>α</mml:mi> </mml:math> quantify the degree of compatibility between the original and replication study. Inferences for other parameters, such as effect sizes, dynamically borrow information from the original study. The degree of borrowing depends on the conflict between the two studies. The practical value of the approach is illustrated on data from three replication studies, and the connection to hierarchical modeling approaches explored. We generalize the known connection between normal power priors and normal hierarchical models for fixed parameters and show that normal power prior inferences with a beta prior on the power parameter $$alpha $$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>α</mml:mi> </mml:math> align with normal hierarchical model inferences using a generalized beta prior on the relative heterogeneity variance $$I^2$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msup> <mml:mi>I</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:math> . The connection illustrates that power prior modeling is unnatural from the perspective of hierarchical modeling since it corresponds to specifying priors on a relative rather than an absolute heterogeneity scale.","PeriodicalId":101465,"journal":{"name":"test","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136135886","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}
Abstract This paper is motivated by the growing interest in estimating gender wage differences in official statistics. The wage of an employee is hypothetically a reflection of her or his characteristics, such as education level or work experience. It is possible that men and women with the same characteristics earn different wages. Our goal is to estimate the differences between wages at different quantiles, using sample survey data within a superpopulation framework. To do this, we use a parametric approach based on conditional distributions of the wages in function of some auxiliary information, as well as a counterfactual distribution. We show in our simulation studies that the use of auxiliary information well correlated with the wages reduces the variance of the counterfactual quantile estimates compared to those of the competitors. Since, in general, wage distributions are heavy-tailed, the interest is to model wages by using heavy-tailed distributions like the GB2 distribution. We illustrate the approach using this distribution and the wages for men and women using simulated and real data from the Swiss Federal Statistical Office.
{"title":"Gender wage difference estimation at quantile levels using sample survey data","authors":"Mihaela-Cătălina Anastasiade-Guinand, Alina Matei, Yves Tillé","doi":"10.1007/s11749-023-00885-8","DOIUrl":"https://doi.org/10.1007/s11749-023-00885-8","url":null,"abstract":"Abstract This paper is motivated by the growing interest in estimating gender wage differences in official statistics. The wage of an employee is hypothetically a reflection of her or his characteristics, such as education level or work experience. It is possible that men and women with the same characteristics earn different wages. Our goal is to estimate the differences between wages at different quantiles, using sample survey data within a superpopulation framework. To do this, we use a parametric approach based on conditional distributions of the wages in function of some auxiliary information, as well as a counterfactual distribution. We show in our simulation studies that the use of auxiliary information well correlated with the wages reduces the variance of the counterfactual quantile estimates compared to those of the competitors. Since, in general, wage distributions are heavy-tailed, the interest is to model wages by using heavy-tailed distributions like the GB2 distribution. We illustrate the approach using this distribution and the wages for men and women using simulated and real data from the Swiss Federal Statistical Office.","PeriodicalId":101465,"journal":{"name":"test","volume":"34 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":"135014871","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}
Pub Date : 2023-09-15DOI: 10.1007/s11749-023-00887-6
Mingao Yuan
{"title":"On the Randić index and its variants of network data","authors":"Mingao Yuan","doi":"10.1007/s11749-023-00887-6","DOIUrl":"https://doi.org/10.1007/s11749-023-00887-6","url":null,"abstract":"","PeriodicalId":101465,"journal":{"name":"test","volume":"237 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135352740","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}
Pub Date : 2023-09-14DOI: 10.1007/s11749-023-00886-7
Marie Perrot-Dockès, Gilles Blanchard, Pierre Neuvial, Etienne Roquain
{"title":"Selective inference for false discovery proportion in a hidden Markov model","authors":"Marie Perrot-Dockès, Gilles Blanchard, Pierre Neuvial, Etienne Roquain","doi":"10.1007/s11749-023-00886-7","DOIUrl":"https://doi.org/10.1007/s11749-023-00886-7","url":null,"abstract":"","PeriodicalId":101465,"journal":{"name":"test","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134911663","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}
Pub Date : 2023-09-13DOI: 10.1007/s11749-023-00884-9
Rahul Ghosal, Arnab Maity
{"title":"Variable selection in function-on-scalar single-index model via the alternating direction method of multipliers","authors":"Rahul Ghosal, Arnab Maity","doi":"10.1007/s11749-023-00884-9","DOIUrl":"https://doi.org/10.1007/s11749-023-00884-9","url":null,"abstract":"","PeriodicalId":101465,"journal":{"name":"test","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135785111","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}
Pub Date : 2023-09-12DOI: 10.1007/s11749-023-00878-7
Małgorzata Łazȩcka, Bartosz Kołodziejek, Jan Mielniczuk
Abstract We study properties of two resampling scenarios: Conditional Randomisation and Conditional Permutation schemes, which are relevant for testing conditional independence of discrete random variables X and Y given a random variable Z . Namely, we investigate asymptotic behaviour of estimates of a vector of probabilities in such settings, establish their asymptotic normality and ordering between asymptotic covariance matrices. The results are used to derive asymptotic distributions of the empirical Conditional Mutual Information in those set-ups. Somewhat unexpectedly, the distributions coincide for the two scenarios, despite differences in the asymptotic distributions of the estimates of probabilities. We also prove validity of permutation p -values for the Conditional Permutation scheme. The above results justify consideration of conditional independence tests based on resampled p -values and on the asymptotic chi-square distribution with an adjusted number of degrees of freedom. We show in numerical experiments that when the ratio of the sample size to the number of possible values of the triple exceeds 0.5, the test based on the asymptotic distribution with the adjustment made on a limited number of permutations is a viable alternative to the exact test for both the Conditional Permutation and the Conditional Randomisation scenarios. Moreover, there is no significant difference between the performance of exact tests for Conditional Permutation and Randomisation schemes, the latter requiring knowledge of conditional distribution of X given Z , and the same conclusion is true for both adaptive tests.
{"title":"Analysis of conditional randomisation and permutation schemes with application to conditional independence testing","authors":"Małgorzata Łazȩcka, Bartosz Kołodziejek, Jan Mielniczuk","doi":"10.1007/s11749-023-00878-7","DOIUrl":"https://doi.org/10.1007/s11749-023-00878-7","url":null,"abstract":"Abstract We study properties of two resampling scenarios: Conditional Randomisation and Conditional Permutation schemes, which are relevant for testing conditional independence of discrete random variables X and Y given a random variable Z . Namely, we investigate asymptotic behaviour of estimates of a vector of probabilities in such settings, establish their asymptotic normality and ordering between asymptotic covariance matrices. The results are used to derive asymptotic distributions of the empirical Conditional Mutual Information in those set-ups. Somewhat unexpectedly, the distributions coincide for the two scenarios, despite differences in the asymptotic distributions of the estimates of probabilities. We also prove validity of permutation p -values for the Conditional Permutation scheme. The above results justify consideration of conditional independence tests based on resampled p -values and on the asymptotic chi-square distribution with an adjusted number of degrees of freedom. We show in numerical experiments that when the ratio of the sample size to the number of possible values of the triple exceeds 0.5, the test based on the asymptotic distribution with the adjustment made on a limited number of permutations is a viable alternative to the exact test for both the Conditional Permutation and the Conditional Randomisation scenarios. Moreover, there is no significant difference between the performance of exact tests for Conditional Permutation and Randomisation schemes, the latter requiring knowledge of conditional distribution of X given Z , and the same conclusion is true for both adaptive tests.","PeriodicalId":101465,"journal":{"name":"test","volume":"40 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135826240","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}
Pub Date : 2023-08-29DOI: 10.1007/s11749-023-00880-z
Ye Tian, Yang Feng
{"title":"Comments on: Statistical Inference and Large-scale Multiple Testing for High-dimensional Regression Models","authors":"Ye Tian, Yang Feng","doi":"10.1007/s11749-023-00880-z","DOIUrl":"https://doi.org/10.1007/s11749-023-00880-z","url":null,"abstract":"","PeriodicalId":101465,"journal":{"name":"test","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136248421","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}
Pub Date : 2023-05-05DOI: 10.1007/s11749-023-00863-0
Laura Freijeiro-González, Manuel Febrero-Bande, Wenceslao González-Manteiga
{"title":"Correction: Novel specification tests for synchronous additive concurrent model formulation based on martingale difference divergence","authors":"Laura Freijeiro-González, Manuel Febrero-Bande, Wenceslao González-Manteiga","doi":"10.1007/s11749-023-00863-0","DOIUrl":"https://doi.org/10.1007/s11749-023-00863-0","url":null,"abstract":"","PeriodicalId":101465,"journal":{"name":"test","volume":"102 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136229979","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}
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