# Determining Bayesian Classifier

Consider a 2-class Pattern Recognition problem with feature vectors in $$R^2$$. The class conditional density for class-I is uniform over $$[1, 3]×[1, 3]$$ and that for class-II is uniform over $$[2, 4] × [2, 4]$$.

Now I have two questions.

1. Suppose the prior probabilities are equal. In such a case, the Bayes classifier is given by $$x + y = 5$$.
2. If the prior probabilities are changed to $$p1 = 0.4$$ and $$p2 = 0.6$$, what is the Bayes classifier now?

I solved the first part kinda "graphically" and intuitively, but I don't know how to solve the second one. Any help, hint or a solution, will be appreciated. Thanks!

• Express the conditional probability using Bayes theorem as $p(y=1|x) \sim p(x|y=1)p(y=1)$ and $p(y=2|x) \sim p(x|y=2)p(y=2)$ . To find the Bays classifier , think about the points that separates the region in the plane where the first quantity is greater the the second one . – Popescu Claudiu Feb 7 at 8:22