# 求助：如何从MAP(maximum a posteriori)推出下面公式?

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zhaokai09
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As in probabilistic view of linear regression:
$$y_n|x_n,\beta\scriptsize{\sim}N(\beta^Tx_n,\sigma^2)$$
we now place a prior on the coefficients $$\beta$$:
$$\beta\scriptsize{\sim}N(0,1/2\lambda)$$
Then we can consider MAP (maximum a posteriori) estimation of $$\beta$$ under this model:
$$\hat\beta^{MAP}=arg\max_\beta{\log\Pr(\beta|x,y,\lambda)}$$
Until here all makes sense to me. The author states via the re-ordered chain rule we obtain:
$$\hat\beta=arg\max_\beta\{\log\Pr(y|x,\beta)\prod_{i=1}^p\Pr(\beta_i,\lambda)\}$$

I don’t understand how the author obtain this result. Can anybody explain it in details? Thanks!

Here is the link from which the above is.