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Old 04-06-2013, 01:24 PM
scottedwards2000 scottedwards2000 is offline
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Join Date: Jan 2013
Posts: 9
Question Re: Is the Hoeffding Inequality really valid for each bin despite non-random sampling

Originally Posted by yaser View Post
Now if you reuse these numbers to do something else somewhere else, that will not alter the applicability of Hoeffding to the bin we started with, right? You can now view the multiple-bin experiment as starting with any given bin, then reusing the numbers you got in sample from that bin for the rest of the bins. Hoeffding still applies to that original given bin, regardless of which one it is. Since that bin is arbitrary, Hoeffding must apply to all of the bins individually.
Actually, now that I re-read this part (I'm taking the course again!), I realize that I don't really follow this logic. Can you please expand on your last sentence above? How does the fact that the first bin is arbitrary help us, when we have no idea if the bin we choose is the first bin? I can see how if we ran the experiment an infinite amount of times, we would eventually choose the first bin, where Hoeffding applies, but we aren't running it an infinite amount of times are we?

Thanks for your help!
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