2005-05-30

binomial uncertainties

Blanton asked for error bars on yesterday's plot, so I calculated the uncertainties for binomial estimation, by taking two derivatives of the log likelihood for the "success" probability p given a sample of N trials in which there are M successes. (I used a flat prior on p.)

As expected (from the first derivative) I get that the maximum likelihood estimate of p is M/N, and (from the second derivative) I get that the (linearized) uncertainty on this is sqrt(pq/N), where q=1−p.

The clustocentric result of yesterday appears marginally significant.

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