#1




Q2.2/Hoeffding clarifications
A few questions regarding question 2.2:
 Is the question asking which statistics (v_1, v_r and v_min) fit the assumptions underlying application of the Hoeffding inequality for estimating the bias of an individual coin (i.e. mu = out of sample probability of a head)?  Is it fair to say that Hoeffding can be applied to any of these statistics as long as mu reflects the out of sample distribution of that statistic?  What is the appropriate value of N when applying Hoeffding to the average of 100,000 repetitions of the average number of heads realised by 10 coin flips? Is it 100,000 or 1,000,000? Seems to me that the overall process is equivalent to averaging the number of heads over 1,000,000 coin flips? Thanks in advance for your help... 
#2




Re: Q2.2/Hoeffding clarifications
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#3




Re: Q2.2/Hoeffding clarifications
Thanks for your reply Yaser, much appreciated.
Regarding my second question, I was trying to determine whether Hoeffding can be applied to v_min using mu = the expected minimum fraction of heads from 10 flips of 1000 coins (<< 0.5 for unbiased coins) rather than mu = the expected fraction of heads from 10 flips of a single coin (0.5 for an unbiased coin). I interpreted the question as assuming the latter but my understanding of Hoeffding is that it could be applied to v_min assuming the former. Does that make sense? And to clarify my final question, I was thinking about the case of v_1 where the expected value of the statistic in question is not affected by the number of coins or number of flips of each coin per experiment. Specifically, I would like to understand the difference between 2 approaches to estimating the probability of flipping a head from a Hoeffding perspective (1) averaging the fraction of heads realised by 10 coin flips over 100,000 experiments, and (2) the fraction of heads realised by 1,000,000 repetitions of a single flip. They are the same in terms of the calculation of the average statistic over 1,000,000 total flips but (2) gives a tighter Hoeffding bound. Presumably to calculate a simple statistic such as the probability of a head for a specific coin (vs a more complex statistic such as the min fraction of heads from 10 flips of 1000 coins), one would always frame the experiment as (2) to take advantage of the lower Hoeffding probability of error bound? 
#4




Re: Q2.2/Hoeffding clarifications
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#5




Re: Q2.2/Hoeffding clarifications
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Could the basic form of Hoeffding be used for (2) where the event is described as flipping a head on a single coin toss? 
#6




Re: Q2.2/Hoeffding clarifications
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__________________
Where everyone thinks alike, no one thinks very much 
#7




Re: Q2.2/Hoeffding clarifications
Thanks for your help in resolving my queries Yaser, it is very much appreciated. Fantastic course by the way and looking forward to reading the book when it arrives in my post box.

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