{"title":"零和/或一增广β矩形回归模型的贝叶斯推理","authors":"Ana R. S. Silva, C. Azevedo, J. Bazán, J. Nobre","doi":"10.1214/21-bjps505","DOIUrl":null,"url":null,"abstract":"Abstract. In this paper we developed a full set of Bayesian inference tools, for zero-and/or-one augmented beta rectangular regression models to analyze limited-augmented data, under a new parameterization. This parameterization: facilitates the development of both regression models and inferential tools as well as make simplifies the respective computational implementations. The proposed Bayesian tools were parameter estimation, model fit assessment, model comparison (information criteria), residual analysis and case influence diagnostics, developed through MCMC algorithms. In addition, we adapted available methods of posterior predictive checking, using appropriate discrepancy measures. We conducted several simulation studies, considering some situations of practical interest, aiming to evaluate: prior sensitivity choice, parameter recovery of the proposed model and estimation method, the impact of transforming the observed zeros and ones, along with the use of non-augmented models, and the behavior of the proposed model fit assessment and model comparison tools. A psychometric real data set was analyzed to illustrate the performance of the developed tools, illustrating the advantages of the developed analysis framework.","PeriodicalId":51242,"journal":{"name":"Brazilian Journal of Probability and Statistics","volume":" ","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2021-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Bayesian inference for zero-and/or-one augmented beta rectangular regression models\",\"authors\":\"Ana R. S. Silva, C. Azevedo, J. Bazán, J. Nobre\",\"doi\":\"10.1214/21-bjps505\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract. In this paper we developed a full set of Bayesian inference tools, for zero-and/or-one augmented beta rectangular regression models to analyze limited-augmented data, under a new parameterization. This parameterization: facilitates the development of both regression models and inferential tools as well as make simplifies the respective computational implementations. The proposed Bayesian tools were parameter estimation, model fit assessment, model comparison (information criteria), residual analysis and case influence diagnostics, developed through MCMC algorithms. In addition, we adapted available methods of posterior predictive checking, using appropriate discrepancy measures. We conducted several simulation studies, considering some situations of practical interest, aiming to evaluate: prior sensitivity choice, parameter recovery of the proposed model and estimation method, the impact of transforming the observed zeros and ones, along with the use of non-augmented models, and the behavior of the proposed model fit assessment and model comparison tools. A psychometric real data set was analyzed to illustrate the performance of the developed tools, illustrating the advantages of the developed analysis framework.\",\"PeriodicalId\":51242,\"journal\":{\"name\":\"Brazilian Journal of Probability and Statistics\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2021-11-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Brazilian Journal of Probability and Statistics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1214/21-bjps505\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"STATISTICS & PROBABILITY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Brazilian Journal of Probability and Statistics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1214/21-bjps505","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
Bayesian inference for zero-and/or-one augmented beta rectangular regression models
Abstract. In this paper we developed a full set of Bayesian inference tools, for zero-and/or-one augmented beta rectangular regression models to analyze limited-augmented data, under a new parameterization. This parameterization: facilitates the development of both regression models and inferential tools as well as make simplifies the respective computational implementations. The proposed Bayesian tools were parameter estimation, model fit assessment, model comparison (information criteria), residual analysis and case influence diagnostics, developed through MCMC algorithms. In addition, we adapted available methods of posterior predictive checking, using appropriate discrepancy measures. We conducted several simulation studies, considering some situations of practical interest, aiming to evaluate: prior sensitivity choice, parameter recovery of the proposed model and estimation method, the impact of transforming the observed zeros and ones, along with the use of non-augmented models, and the behavior of the proposed model fit assessment and model comparison tools. A psychometric real data set was analyzed to illustrate the performance of the developed tools, illustrating the advantages of the developed analysis framework.
期刊介绍:
The Brazilian Journal of Probability and Statistics aims to publish high quality research papers in applied probability, applied statistics, computational statistics, mathematical statistics, probability theory and stochastic processes.
More specifically, the following types of contributions will be considered:
(i) Original articles dealing with methodological developments, comparison of competing techniques or their computational aspects.
(ii) Original articles developing theoretical results.
(iii) Articles that contain novel applications of existing methodologies to practical problems. For these papers the focus is in the importance and originality of the applied problem, as well as, applications of the best available methodologies to solve it.
(iv) Survey articles containing a thorough coverage of topics of broad interest to probability and statistics. The journal will occasionally publish book reviews, invited papers and essays on the teaching of statistics.