Questions and Comments for: Proof of the Optimality of Bayes Decision Rule
A slecture by Aaron Michaux
Please leave me comment below if you have any questions, if you notice any errors or if you would like to discuss a topic further.
Review by Anonymous
This video slecture is very clear, and concise. It can tainted a great Introduction to Bayes' decision rule and a very simple and clear definition of Bayes’ error and comparison to an arbitrary error obtained from an arbitrary decision rule. The layout of the slecture was very well done, starting with explaining that X be a random variable over space Ω, moving on to explaining the different partition of Ω as our classes and the hypothesis of deciding whether a member belonged to one of the partitions of Ω and finally the proof that using Bayes' rule as a decisions rule yields an optimal result.
The set up of the proof was quite simple and clearly explained, to show that Bayes’ rule is optimal in the 2 category case and can be extended to the n-category case. The simple proof of optimality by showing that bayes’ error can’t be beat was supplemented by Venn Diagrams, this made the proof much clearer especially when reference was made to the Venn Diagrams when explaining the subtractions inside of the integrals of set Ω1 an Ω2 to show that Bayes’ rule yields optimal decision when compared to an arbitrary decision rule.
Observation: One observation is that mention of decision tree was made at the beginning of the slecture for generalising the 2-category decision problem to an n-category decision problem but noting was shown on the screen at that point, a simple diagram of a decision tree at that point with very little explanation might have been useful, even if that was not precisely the point of the slecture.
