Bayesian Checking of the Second Levels of Hierarchical Models
نویسنده
چکیده
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 preliminary, exploratory analysis, we concentrate on objective Bayesian methods in which careful specification of an informative prior distribution is avoided. Numerous examples are given and different proposals are investigated and critically compared.
منابع مشابه
Comment: 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 کاملComment on “Bayesian Checking of the Second Levels of Hierarchical Models” by Bayarri and Castellanos
We discuss the methods of Evans and Moshonov (2006, 2007) concerning checking for prior-data conflict and their relevance to the method proposed in this paper.
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Housing price data is correlated to their location in different neighborhoods and their correlation is type of spatial (location). The price of housing is varius in different months, so they also have a time correlation. Spatio-temporal models are used to analyze this type of the data. An important purpose of reviewing this type of the data is to fit a suitable model for the spatial-temporal an...
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 Level of Hierarchical Models: Cross-Validated Posterior Predictive Checks Using Discrepancy Measures
We compliment Bayarri and Castellanos (BC) on producing an interesting and insightful paper on model checking applied to the second level of hierarchical models. Distributions of test statistics (functions of the observed data not involving parameters) for judging appropriateness of hierarchical models typically involve nuisance (i.e., unknown) parameters. BC (2007) focus on ways to remove the ...
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