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含分类变量的变量选择：模型选择视角AI 解读

In the context of a Gaussian multiple regression model, we address the problem of variable selection when in the list of potential predictors there are factors, that is, categorical variables. We adopt a model selection perspective, that is, we approach the problem by constructing a class of models, each corresponding to a particular selection of active variables. The methodology is Bayesian and proceeds by computing the posterior probability of each of these models. We…

用于贝叶斯变量选择的 g 先验混合AI 解读

Zellner's g prior remains a popular conventional prior for use in Bayesian variable selection, despite several undesirable consistency issues. In this article we study mixtures of g priors as an alternative to default g priors that resolve many of the problems with the original formulation while maintaining the computational tractability that has made the g prior so popular. We present theoretical properties of the mixture g priors and provide real and simulated examples to…

高斯过程的默认先验AI 解读

Motivated by the statistical evaluation of complex computer models, we deal with the issue of objective prior specification for the parameters of Gaussian processes. In particular, we derive the Jeffreys-rule, independence Jeffreys and reference priors for this situation, and prove that the resulting posterior distributions are proper under a quite general set of conditions. A proper flat prior strategy, based on maximum likelihood estimates, is also considered, and all…