Abstract

We explore the arguments for maximizing the “evidence” as an algorithm for model selection. We show, using a new definition of model complexity which we term “flexibility,” that maximizing the evidence should appeal to both Bayesian and frequentist statisticians. This is due to flexibility’s unique position in the exact decomposition of log-evidence into log-fit minus flexibility. In the Gaussian linear model, flexibility is asymptotically equal to the Bayesian information criterion (BIC) penalty, but we caution against using BIC in place of flexibility for model selection.

中文翻译：

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模型选择中“奥卡姆因素”的确切形式

摘要

我们探讨了最大化“证据”作为模型选择算法的论据。我们使用我们称为“灵活性”的模型复杂性的新定义表明，最大化证据应该吸引贝叶斯和频率统计员。这是由于灵活性在对数证据精确分解为对数拟合减去灵活性方面的独特地位。在高斯线性模型中，灵活性渐近等于贝叶斯信息准则 (BIC) 惩罚，但我们警告不要使用 BIC 代替模型选择的灵活性。