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I am new to Bayes theorem; In Naive Bayes, we assume that events are independent. How does Bayes theorem modify if the events are dependent ?

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The theorem stays the same. The term Naive Bayes is short name for Naive Bayes classifier. Here, while calculating the posterior probability, we assume conditional independence over the input dimensions: $$p(\mathbf x |C_k)=\prod p(x_i|C_k)$$

So, we have the class posterior as below: $$p(C_k|\mathbf x)=\underbrace{\frac{p(\mathbf x|C_k)p(C_k)}{p(\mathbf x)}}_{\text{Bayes Classifier}}=\underbrace{\frac{p(C_k)\prod p(x_i|C_k)}{p(\mathbf x)}}_{\text{Naive Bayes Classifier}}$$

Without the naive assumption, Bayes classifier directly calculates the class conditional probability, $p(\mathbf x| C_k)$. So, the theorem has nothing to do with the naive assumption we make. See here for more on terminology.

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    $\begingroup$ The misconception in OP seems to be that naive Bayes = Bayes theorem, I'm not sure if your answer is clear enough on this. $\endgroup$
    – Tim
    Aug 20 '20 at 11:35
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    $\begingroup$ @Tim tried to elaborate more on the topic $\endgroup$
    – gunes
    Aug 20 '20 at 14:38

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