P W

![0_image_0.png](0_image_0.png)

$$P\ T,\,W\qquad\prod_{i\,=1}^{n}P\ t_{i-1}{\rightarrow}t_{i}\ P\ w_{i}|t_{i}$$
$$P\ \ w_{i}|t_{i}$$
$$\frac{P\left(t_{\mathrm{i}}|w_{\mathrm{i}}\right)P\left(w_{\mathrm{i}}\right)}{P\left(t_{\mathrm{i}}\right)}$$
$$P\;\;w_{i}$$

tag probabilities P t; transition probabilities P t;-1 → t; lexical probabilities P t | w

$$P\;\;t$$
$$\begin{array}{c c c}{{}}&{{}}&{{P\,\,t}}\\ {{t}}&{{}}&{{}}\\ {{t}}&{{}}&{{}}\end{array}$$
$$\begin{array}{l}w\end{array}$$ . 
$$P\ t_{i}\to t_{j}\ \ \ \ \ \ \ \ P\ t\,|w$$

$$5$$

## 6.2  Posterior Distributions For Multinomial Parameters

P a; a; S

![0_image_1.png](0_image_1.png)

![0_image_2.png](0_image_2.png)

$$\left\{\,u_{i}\,\right\}$$
$P$$t_{i}$$\rightarrow$$t_{j}$$S$$\left\{n_{i}\right\}$$u_{i}$$N$$\sum_{i}n_{i}$$\alpha_{i}$$P$$u_{i}$
$$\begin{array}{c c c}{{\alpha_{i}}}&{{}}&{{\alpha_{i}}}&{{}}&{{\frac{n_{i}}{N}}}\end{array}$$

![0_image_3.png](0_image_3.png)

