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I have a dataset consisting of 5 classes and the prior probability is $p(\omega_c)=\frac{|D_c|}{\sum_{i = 1}^{5}|D_i|}$. Suppose each class $c$ associated with the likelihood $p(x|ω_c)\,=\,\text{N}(\mu_c,\Sigma_c)$.

How can I derive a decision rule using Bayes' rule to assign a sample to one of the 5 classes? Moreover, how can I calculate $P(\text{error}|X)$ and $P(\text{error})$?

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  • $\begingroup$ Discriminant analysis $\endgroup$ Commented Oct 31, 2022 at 10:10
  • $\begingroup$ To build a decision rule one needs a loss or utility function to weight the consequences of a wrong decision and give a mathematical meaning to the "error". Without these, there is no clear meaning to constructing an optimal decision rule. $\endgroup$
    – Xi'an
    Commented Nov 3, 2022 at 8:52

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