http://cstpr.colorado.edu/prometheus/?p=4419#comment-10097

One commenter, perhaps slightly off topic suggested winnowing out the models consistently producing the trashier forecasts but what kind of heresy is that? That’s a direct attack on the alarmism! Consistency has to be defined in a way that all manner of garbage is carried along!

That was complicated but the results were straightforward. This climate modeling seems to be so much different.

I’ll just have to study this more.

It’s an important statistical subtlety, but the two sets of trend estimates should not be expected to have the same variance.

If we were comparing the heights of Swedish men (per lucia’s analog), this would be the difference:

The 5 observations are 5 measurements of *one* Swedish man’s height. The 55 models are single measurements of each of 55 different Swedish men. Both sets of data attempt to determine the average height of Swedish men. The variance is not the same.

So the appropriate scaling for the difference is .

But of course the SE’s are much smaller than the SD’s (by a factor of sqrt(N)), so equality of the means is a very easy reject.

It does appear that Megan’s internet test is based on the equality of the two SDs, while in fact they are obviously very different. There is a long literature on the “Fisher-Behrens” problem of testing the equality of two means when the variances are unequal, e.g. http://projecteuclid.org/DPubS/Repository/1.0/Disseminate?view=body&id=pdf_1&handle=euclid.aoms/1177697509 . It seems that there is no exact test, but a lot of good approximate tests. In the present case, however, it’s not even a close call, so any reasonable statistic would give an easy reject.

Yes I am suggesting the **inter-model** variability is too high. As discussed here we can make it as high or low as we want by adding or subtracting models, bogus or otherwise. In addition as I explained, they should all be designed to produce future histories – ie they are trying to do the same thing. If they differ wildly as to future histories, compare them to the data and pick the best model.

As my example above shows, it seems suspiciously like the ensemble approach is designed to “not reject” the models, while also not providing the inherent stochastic variability that would do anything but allow the 100 yr projections to essentially just have a drift term.

It’s looks like another bogus statistical approach from the climate scientists.

A credibility or (or “credible”) interval is the Bayesian equivalent of a confidence interval. From the posterior distribution of a parameter (ie the distribution given the data and the prior) take the interval that includes 95% of this distribution.