continuously updating mean confidence interval (MeanCI)

*To*: mathgroup at smc.vnet.net*Subject*: [mg24596] continuously updating mean confidence interval (MeanCI)*From*: Daniel Reeves <dreeves at eecs.umich.edu>*Date*: Tue, 25 Jul 2000 00:56:28 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

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.