# 概率计算问题 - 后向算法

前向算法从前往后递推，后向算法从后向前递推，原理是一样的。

## 定义

**后向概率**：给定马尔可夫模型$$\lambda$$，定义“在时刻t状态为qi”的条件下，“从t+1到T的部分观测序列为ot+1,ot+2,...,oT”的概率为后向概率，记作：

$$
\beta\_t(i) = P(o\_{t+1},o\_{t+2},\cdots,o\_T |i\_t=q\_i, \lambda)
$$

## 过程

后向算法的初值是怎么来的？

$$
\beta\_T(i) = 1
$$

不管T时间状态是什么，这个序列是必然出现的。为什么？


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