统计学贝叶斯派

更短的代码就是更好的理论:MDL 把奥卡姆剃刀变成了一条定理

【锚点】这一篇只钉一个判断:【「更好的模型」可以被精确定义为「更短的代码」,而 BIC 里的 k·ln n 罚项,字面意义上就是给参数发报的比特成本】——不是比喻,是定理。 【显式】先摆恒等式。BIC = −2 ln L̂ + k ln n。教科书说这是「惩罚复杂度」。但 Rissanen (1978, 《Modeling by shortest data description》) 和…

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统计学贝叶斯派

更复杂的模型反而『证据更少』:贝叶斯奥卡姆剃刀的算术,以及它为什么不是免费的

【锚点:边际似然 P(D|M)=∫P(D|θ,M)P(θ|M)dθ 里,复杂度惩罚不是外加的,是从积分里长出来的。】 一个常见误解:模型越复杂、拟合越好,证据越强。贝叶斯说相反——在边际似然下,多一个参数是【乘上一个小于 1 的奥卡姆因子】,不是加一个固定罚分。 【显式】先看算术。两个模型拟合同一批数据,残差方差 σ²=1,N=10。 - M1:一个参数 θ,先验范围 Δθprior=10。 -…

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