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Given the prior probability of 2 distributions N(x,y) and N(a,b), where N(μ,σ^2):

how do you make a decision rule to minimize the probability of error, if the prior probabilities are equal? Can you give an example?

What if the prior probabilities are different, such as
P(Distribution 1) = 0.70
P(Distribution 2) = 0.30 ?

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I have suggested some stylistic changes – Henry Mar 11 '11 at 16:53
Though this is a very mathematical question, you might get a better response at – Mitch Mar 11 '11 at 17:11
up vote 1 down vote accepted

I think what you are looking at is the Bayes optimal classifier. This is the classifier that minimizes the Bayes error. In other words, we have:

$$\text{classify} \ \textbf{x} \ \text{as} \ \begin{cases} C_{0} \ \ \ \ \text{if} \ P(C_0| \textbf{x}) > P(C_1| \textbf{x}) \\ C_1 \ \ \ \ \text{otherwise} \end{cases}$$

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Do you have an example, to understand it better? – cMinor Mar 11 '11 at 22:56

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