The Bayes Optimal Classifier is a probabilistic model that uses Bayes theorem to make the most accurate classification of a new instance by considering the predictions from all possible hypotheses, weighted by their posterior probabilities.
Difference from MAP Hypothesis:
- MAP (Maximum A Posteriori) selects one single most probable hypothesis.
- Bayes Optimal Classifier considers all hypotheses and combines their predictions using posterior probabilities.
Classification Equation:
Where:
Given Table:
Since 0.4 > 0.3, the Bayes Optimal Classifier predicts: COVID Positive
It is more reliable because it considers all hypotheses, not just the most probable one.