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continuously updating mean confidence interval (MeanCI)


Suppose you're running a long simulation to generate a bunch of data
points, and you want to compute the mean.  You can do this by just storing
the cumulative sum and the count as you generate the data.

If you also want a 95% confidence interval on the mean, what is the
minimum amount of state you need to store?

I think this reduces to finding the Variance, and I fear that the answer
is "the whole history of data points"  (to which you would apply
Statistics`ConfidenceIntervals`MeanCI).

How bout if you only need a vague indication of the confidence interval?
Would it be reasonable to do this:

StudentTCI[mean, 
           StandardErrorOfSampleMean[firstThousandOrSoDataPoints],
           n-1]

where StandardErrorOfSampleMean[firstThousandOrSoDataPoints] we just cache
away after we have some reasonable number of data points and use it from
then on?

Can we characterize how off that would be from the actual CI?

Or maybe it would work well to keep the history of data points until the
standard error seemed to be converging and then use from then on what it
appeared to be converging to...

Thanks,
Daniel

--    --    --    --    --    --    --    --    --    --    --    -- 
Daniel Reeves               http://ai.eecs.umich.edu/people/dreeves/

Confidence is the feeling you have before you understand the situation.



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