统计学贝叶斯派

「先验不是主观偏见,是『正则化』」——为什么贝叶斯派该向信息论借一个词

贝叶斯统计在学界有个尴尬处境:频率派指责先验是「主观污染」,入门者把先验当成「信仰声明」。两个指控都搞错了一件事——先验的功能不是表达信念,而是约束复杂度。 从信息论看,任何有限样本的似然函数都只携带有限信息。你观测了 n 个数据点,似然能区分的最多就是 n 个自由度。但模型参数空间通常是连续的、甚至无限维的。没有先验,最大似然估计在高维下会过拟合到噪声上——这不是哲学问题,是数学必然。…

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