基于贝叶斯准则的变量选择,The Journal of the Royal Statistical ...

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基于标准选择的贝叶斯方法包括基于边际似然的最高后验模型 (HPM) 和偏差信息标准 (DIC)。DIC 在实践中很受欢迎，因为它通常可以相对容易地从基于采样的方法中估计出来，而且 DIC 在各种贝叶斯软件中都很容易获得。我们发现基于 DIC 的选择的灵敏度可能很高，在 90-100% 的范围内。然而，DIC 的正确选择可以在 0-2% 的范围内。随着样本量的增加，这些表现始终如一。我们确定边际似然和 DIC 渐近地不喜欢欠拟合模型，这解释了这两个标准的高敏感性。然而，在 g 的 线性模型中，DIC 的错误选择概率仍然低于正常数 -priors 而边际似然的误选概率在某些条件下收敛到 0。我们的结果的一个结果是，不仅 DIC 不能渐近区分数据生成模型和过度拟合模型，而且事实上，它也不能渐近区分两个过度拟合模型。我们在多个模拟研究和非小细胞肺癌患者癌症恶病质的生物标志物选择问题中说明了这些结果。我们进一步研究了广义线性模型中 HPM 和 DIC 的性能，因为从业者经常选择使用在此类非共轭设置中的软件中容易获得的 DIC。 Bayesian approaches for criterion based selection include the marginal likelihood based highest posterior model (HPM) and the deviance information criterion (DIC). The DIC is popular in practice as it can often be estimated from sampling-based methods with relative ease and DIC is readily available in various Bayesian software. We find that sensitivity of DIC-based selection can be high, in the range of 90–100%. However, correct selection by DIC can be in the range of 0–2%. These performances persist consistently with increase in sample size. We establish that both marginal likelihood and DIC asymptotically disfavour under-fitted models, explaining the high sensitivities of both criteria. However, mis-selection probability of DIC remains bounded below by a positive constant in linear models with g -priors whereas mis-selection probability by marginal likelihood converges to 0 under certain conditions. A consequence of our results is that not only the DIC cannot asymptotically differentiate between the data-generating and an over-fitted model, but, in fact, it cannot asymptotically differentiate between two over-fitted models as well. We illustrate these results in multiple simulation studies and in a biomarker selection problem on cancer cachexia of non-small cell lung cancer patients. We further study the performances of HPM and DIC in generalized linear model as practitioners often choose to use DIC that is readily available in software in such non-conjugate settings.