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二维列联表内禀独立性检验的稳健性评估AI 解读

For testing nested hypotheses from a Bayesian standpoint, a desirable condition is that the prior for the alternative model concentrates mass around the smaller, or null, model. For testing independence in contingency tables, the intrinsic priors satisfy this requirement. Furthermore, the degree of concentration of the priors is controlled by a discrete parameter, t, the training sample size, which plays an important role in the resulting answer. In this article we report on…

贝叶斯变量选择程序的一致性AI 解读

It has long been known that for the comparison of pairwise nested models, a decision based on the Bayes factor produces a consistent model selector (in the frequentist sense). Here we go beyond the usual consistency for nested pairwise models, and show that for a wide class of prior distributions, including intrinsic priors, the corresponding Bayesian procedure for variable selection in normal regression is consistent in the entire class of normal linear models. We find that…

客观贝叶斯变量选择AI 解读

A novel fully automatic Bayesian procedure for variable selection in normal regression models is proposed. The procedure uses the posterior probabilities of the models to drive a stochastic search. The posterior probabilities are computed using intrinsic priors, which can be considered default priors for model selection problems; that is, they are derived from the model structure and are free from tuning parameters. Thus they can be seen as objective priors for variable…

模型选择与假设检验的内在极限程序AI 解读

Improper priors typically arise in default Bayesian estimation problems. In the Bayesian approach to model selection or hypothesis testing, the main tool is the Bayes factor. When improper priors for the parameters appearing in the models are used, the Bayes factor is not well defined. The intrinsic Bayes factor introduced by Berger and Pericchi is an interesting method for overcoming that difficulty. That method is of particular interest as a means for generating proper…