> Sturla > > P.S. Personally I am not convinced "unbiased" is ever a valid argument, as > the biased estimator has smaller error. This is from experience in > marksmanship: I'd rather shoot a tight series with small systematic error > than scatter my bullets wildly but "unbiased" on the target. It is the > total error that counts. The series with smallest total error gets the best > score. It is better to shoot two series and calibrate the sight in between > than use a calibration-free sight that don't allow us to aim. That's why I > think classical statistics got this one wrong. Unbiased is never a virtue, > but the smallest error is. Thus, if we are to repeat an experiment, we > should calibrate our estimator just like a marksman calibrates his sight. > But the aim should always be calibrated to give the smallest error, not an > unbiased scatter. Noone in their right mind would claim a shotgun is more > precise than a rifle because it has smaller bias. But that is what applying > the Bessel correction implies. > > I agree with the point, and what makes it even worse is that ddof=1 does not even produce an unbiased standard deviation estimate. I produces an unbiased variance estimate but the sqrt of this variance estimate is a biased standard deviation estimate, http://en.wikipedia.org/wiki/Unbiased_estimation_of_standard_deviation.
Bago
_______________________________________________ NumPy-Discussion mailing list [email protected] http://mail.scipy.org/mailman/listinfo/numpy-discussion
