How does Naïve Bayes relate to decision theory under asymmetric misclassification costs?

Naïve Bayes can be adapted to cost-sensitive decision theory by modifying posterior thresholds based on misclassification costs.

In Bayesian decision theory, the optimal decision minimizes expected risk rather than simply maximizing posterior probability. For Naïve Bayes, this means comparing P(C|X) weighted by cost matrix C(i,j). Instead of argmax P(C|X), we choose class minimizing expected loss. This is critical in domains where false positives and false negatives have different costs, such as fraud detection or medical diagnosis.