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What is Bayesian decision theory explain 2 category classification?
Bayesian decision theory refers to the statistical approach based on tradeoff quantification among various classification decisions based on the concept of Probability(Bayes Theorem) and the costs associated with the decision.
How the decision error for Bayesian classification can be minimized?
We will show that the Bayesian classifier is optimal with respect to minimizing the classification error probability. This suggests that the probability of error is minimized if R1 is the region of space in which P(ω1|x) > P(ω2|x). Then, R2 becomes the region where the reverse is true.
What is optimal decision model?
An optimal decision is a decision that leads to at least as good a known or expected outcome as all other available decision options. It is an important concept in decision theory. In order to compare the different decision outcomes, one commonly assigns a utility value to each of them.
Is it natural to seek a rule that minimizes the probability of error?
If errors are to be avoided it is natural to seek a decision rule, that minimizes the probability of error, that is the error rate. (4.17) This loss function assigns no loss to a correct decision, and assigns a unit loss to any error: thus, all errors are equally costly.
This loss function assigns no loss to a correct decision, and assigns a unit loss to any error: thus, all errors are equally costly. The risk corresponding to this loss function is precisely the average probability of error because the conditional risk for the two-category classification is
Which is the minimum risk in the Bayes decision rule?
Thus, the Bayes decision rule states that to minimize the overall risk, compute the conditional risk given in Eq.4.10 for i=1…a and then select the action ai for which R(ai|x) is minimum. The resulting minimum overall risk is called the Bayes risk, denoted R, and is the best performance that can be achieved.
Which is an example of a Bayesian decision rule?
This form of decision rule emphasizes the role of the posterior probabilities. As being equivalent, the same rule can be expressed in terms of conditional and prior probabilities as: Decide w1 if p(x|w1)P(w1) > p(x|w2)P(w2); otherwise decide w2 (4.7)