Variable Selection in the Presence of Factors: A Model Selection Perspective
研究了高斯多元回归模型中，当潜在预测变量包含分类变量（因子）时如何进行变量选择。采用贝叶斯模型选择方法，计算每个模型的後验概率，并解决了因子虚拟变量表示影响竞争模型集的问题，提出了一种无需调参的自动方法。
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 highlight the fact that the set of competing models depends on the dummy variable representation of the factors, an issue already documented by Fernández et al. in a particular example but that has not received any attention since then. We construct methodology that circumvents this problem and that presents very competitive frequentist behavior when compared with recently proposed techniques. Additionally, it is fully automatic, in that it does not require the specification of any tuning parameters.