Rejoinder: Bayesian Checking of the Second Levels of Hierarchical Models
نویسندگان
چکیده
منابع مشابه
Rejoinder: Bayesian Checking of the Second Levels of Hierarchical Models
We would like to thank the discussants for the valuable insights and for commenting on important aspects of model checking that we did not touch in our paper. Our goal was modest (but crucial): to select an appropriate distribution with which to judge the compatibility of the data with a hypothesized (hierarchical) model, when the test statistic is not ancillary and an improper prior is used fo...
متن کاملComment: Bayesian Checking of the Second Levels of Hierarchical Models
Bayarri and Castellanos (BC) have written an interesting paper discussing two forms of posterior model check, one based on cross-validation and one based on replication of new groups in a hierarchical model. We think both these checks are good ideas and can become even more effective when understood in the context of posterior predictive checking. For the purpose of discussion, however, it is m...
متن کاملComment: Bayesian Checking of the Second Levels of Hierarchical Models
This article extends Bayarri and Berger’s (1999) proposal for model evaluation using “partial posterior” p values to the evaluation of second-stage model assumptions in hierarchical models. Applications focus on normal-normal hierarchical models, although the final example involves an application to a beta-binomial model in which the distribution of the test statistic is assumed to be approxima...
متن کاملComment: Bayesian Checking of the Second Levels of Hierarchical Models
We discuss the methods of Evans and Moshonov [Bayesian Analysis 1 (2006) 893–914, Bayesian Statistics and Its Applications (2007) 145–159] concerning checking for prior-data conflict and their relevance to the method proposed in this paper.
متن کاملBayesian Checking of the Second Levels of Hierarchical Models
Hierarchical models are increasingly used in many applications. Along with this increased use comes a desire to investigate whether the model is compatible with the observed data. Bayesian methods are well suited to eliminate the many (nuisance) parameters in these complicated models; in this paper we investigate Bayesian methods for model checking. Since we contemplate model checking as a prel...
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ژورنال
عنوان ژورنال: Statistical Science
سال: 2007
ISSN: 0883-4237
DOI: 10.1214/07-sts235rej