#1




Question on the Selection of Samples from the Bin
In the multiple hypothesis section, we are presented the analogy of having let's say m bins, and a random sample of marbles of size N from each bin. My question is, are those m random samples the same marbles in each bin (only probably colored differently), or are they different for each bin (for example, randomly selected when we sample each bin)?
To clarify: suppose bins 1...m each contains marbles 1...M (M >> N). Let's say N = 4, and in the sample for bin 1 we select marbles # 2, 3, 4, 5 and color them. Then for bin 2...m, do we still sample marbles # 2, 3, 4, 5 or do we randomly select 4 probably different numbers for each bin? I tried to explain this myself, here are two contradictory explanations: 1. From the coin example give, we are randomly sampling for each bin, since the corresponding marbles in the bins are colored the same but the selected samples are colored differently. 2. From the training perspective, they are the same samples. If a bin corresponds to the entire population and a sample is the training set from the population, for selection of each hypothesis we are using the same training set (not generating new ones from the population). So which view is correct? Thank you very much!!!! 
#2




Re: Question on the Selection of Samples from the Bin
Your thoughts are correct. In the case that corresponds to multiple hypotheses and a given training set, the marbles are the same among different bins. This does not affect the calculation because (1) Per bin, the marbles are still picked independently of each other, and (2) Jointly, we apply the union bound that covers all possible dependencies between the different bins.
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#3




Re: Question on the Selection of Samples from the Bin
Thank you very much Professor! It makes me feel much safer to have this confirmation from you. It's very generous of you to spend time answering questions from us readers!

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