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

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该主题包含 0 条回复,1个帖子,最后由  zhaokai096 天, 9 小时 之前 更新。

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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.

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