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Imagine I want to randomly sample how fast a driver is going on a highway. And for this purpose, let's assume that the distribution is normal with the mean as the speed limit. Now if I take a sample, that would give me a single speed that a driver might be going. But what I'd like to do is repeatedly sample how fast one specific driver is going. My thought process is to first sample on the previously mentioned distribution to get that specific driver's average speed, u1. Then perform many samplings on the new normal distribution with mean=u1.

Please look at comments for a better example.

My feeling is that for repeated samples, each driver has their own individual mean, which the first sample gives us, and then further samples should be around that mean and not the global mean.

I feel like this is the right thing to do, but I can't express the idea well to get any hits on google. Is this the correct way to do this (and if so what's the name for this technique)?

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This appears to be related to Bayesian statistics (as you seem to want to find the speed distribution of a single driver). Key words appropriate are "Bayesian statistics" and "posterior distribution". It may also be more accurate to center the distribution of a sample at the speed obtained at the previous sample. This strengthens the connections with the mentioned key words. – Lord_Farin Oct 16 '12 at 7:42
Like @Lord_Farin said, the keyword you might want to use in the search is "posterior distribution". However, upon reading your post, I cannot figure out what you want to know about. – Tunococ Oct 16 '12 at 8:08
@dbachrach - Welcome to math.SE! try clarifying your question a bit more: what can you sample and what do you actually want to measure? – nbubis Oct 16 '12 at 19:46
Here's a better example: Measure the height of a person's jump. Across the global population the height of a person's jump can be sampled from a normal distribution. But what I'd like is to sample heights for a specific individual. So I'd first sample the global distribution to get an individual's average A jump height. Then I'll assume that that individual will jump on any specific jump around the average A. For further samplings for this individual I would sample from a normal distr with mean=A. – dbachrach Oct 17 '12 at 5:50
This seems like a frequent sampling issue: use the global distribution to get the mean for the individual. Then sample on a new distribution around that sampled mean for specific instances. Is this a common statistical technique? If so what is it called? If not is there a better technique? This sounds intuitive to me, so I'm really looking for keywords or terms so I can research further. I just can't get my search started because I don't know the right names. – dbachrach Oct 17 '12 at 5:55

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