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Could someone please explain to me how and why can we go from equation $4.3$ to equation $4.4$:

$$\hat{c}= \arg\max_{c \in \mathcal{C}}P(c|d) = \arg\max_{c \in \mathcal{C}}\frac{P(d|c)P(c)}{P(d)}\tag{4.3}$$

$$\hat{c}= \arg\max_{c \in \mathcal{C}}P(c|d) = \arg\max_{c \in \mathcal{C}}P(d|c)P(c)\tag{4.4}$$

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We are trying to select the optimal $c$, here $d$ is fixed and hence $P(d)$ and $\frac1{P(d)}$ is just a positive constant.

Multiplying an objective function with a positive constant doesn't change the optimal solution, hence we can drop $P(d)$.

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Because P(d) is constant in terms of c, so it doesn't affect the location of the maximum (only its size but we don't care about that).

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