This is an intellectually confused post. It is so unclear and muddled that only a charitable reader would suppose the author understands the mathematical and modeling issues here. I’m surprised the author published it in this form - you don’t want to jump into a controversy like this with such an unclear discussion.

As just one example, the whole digression on a “decision boundary” is conceptually mistaken. Once you report a posterior probability, it’s up to the user to establish a simple real number threshold for placing a bet (if we’re talking about means to put skin in the game). The posterior you just learned holds all information, your only action is to threshold it. That’s the Neyman-Pearson lemma.

If you allow generalizations to interval-valued probability, which might be sensible under these conditions, the situation gets more complicated. But the writer of the post did not mention this.

Another place this came out is his initial discussion of aleatory vs. epistemic uncertainty — this can be done clearly, but here we read:

> Aleatory uncertainty is concerned with the fundamental system (probability of rolling a six on a standard die). Epistemic uncertainty is concerned with the uncertainty of the system (how many sides does a die have? And what is the probability of rolling a six?).

This is just not helpful. He has said “probability of rolling a six” twice.

Source: do UQ in day job.