# 贝叶斯统计

## 贝叶斯公式

${\displaystyle P(A\mid B)={\frac {P(B\mid A)P(A)}{P(B)}}}$

${\displaystyle P(B)=P(B\mid A_{1})P(A_{1})+P(B\mid A_{2})P(A_{2})+\dots +P(B\mid A_{n})P(A_{n})=\sum _{i}P(B\mid A_{i})P(A_{i})}$

${\displaystyle B}$概率分布一般是连续的，这往往造成${\displaystyle P(B)}$的计算涉及到复杂的积分。不过，使用或马尔可夫链蒙特卡洛等方法可在不涉及计算${\displaystyle P(B)}$的情况下求得所需的最大后验概率，在这种情况下可以只考虑先验概率与似然函数对后验概率的影响（${\displaystyle \propto }$符号代表“成正比”）：

${\displaystyle P(A\mid B)\propto P(B\mid A)P(A)}$

## 参考文献

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