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Old 02-18-2021, 09:39 AM
Roelof Roelof is offline
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Join Date: Feb 2021
Posts: 4
Default Re: The concept "h is fixed before you generate the data set" is extremely vague

Actually this is more intuitive than it may seem. Going back to the bin model: What you need to remember is that the choice of any hypothesis h determines the color of the marbles in the bin (h(x)=f(x) then green otherwise red).

So suppose you've chosen a particular h, after that you then select a sample out of the bin (this is what is meant with "generate").

Because of probability properties we know that the contents of the bin will be similar to the sample with a certain likelihood.

Now, however, suppose we change the h after we have selected (generated) the sample. What this means is that we are recoloring the marbles in the bin according to the new h.

The sample that you had previously selected knows absolutely nothing about (has absolutely no relation to) this new recoloring. The marbles could be all green or all red or anything else in between depending on the new h. So for example if they were all green and you selected a new sample then that new sample would be all green.

In short, you can't do a selection out of the bin, change the contents of the bin arbitrarily and expect that selection to be able to say something about the new contents of the bin.
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