Comments on: Jones et al [1998]: Confidence Intervals

By: chiz

chiz — Thu, 21 Feb 2008 18:20:27 +0000

Good post. You make some great points that most people do not fully understand.

“There are some other frustrating aspects to this diagram. It turns out that the Jones et al [1998] version used in the compilation in Jones et al [2001] is not the same as the archived version for Jones et al [1998], but has been “re-calibrated”. I think that I’ve figured out the “re-calibration”, but it leads into more murky by-ways of the multiproxy underworld.”

I like how you explained that. Very helpful. Thanks.

By: john

john — Fri, 28 Dec 2007 01:00:49 +0000

Interesting thread (which I will have to study to understand better). I can only hope I am OT.

Reading it though, I was reminded of the teacher of my first statistical physical measurement class. Before telling us about errors, he talked about precision and accuracy. As I recall his example was “If you ask the billion Chinese the height of their chairman (whom they have never seen) you will get a very precise, but necessarily accurate answer”.

His point was be very careful when you use the term error since they can can result from many different source types.

By: TCO

TCO — Mon, 31 Oct 2005 23:24:08 +0000

I’m trying to disaggregate issues:

a. is there autocorrelation
b. how should autocorrelation be handled

I could imagine a case for instance where there is agreement on the method of dealing with autocorr, but disagreement on it being there. Or visa versa. Let’s drill down.

By: Steve McIntyre

Steve McIntyre — Mon, 31 Oct 2005 22:28:05 +0000

The autocorrelation can be verified simply by the time series. It’s not obvious that it’s been handled properly. I can’t come close to replicating their results, so I really don’t know what they did. I’m still working on it.

By: TCO

TCO — Mon, 31 Oct 2005 22:10:30 +0000

Steve, my question??

By: ruidh

ruidh — Mon, 31 Oct 2005 17:37:40 +0000

Dosn’t anyone here understand statistics? The SE did not “almost double” in 1400. The blue line pops up at most 50% of the pre-1400 value. Adding a series with a larger inherent variability will increase your SE. The red line shows a smaller step becuase it’s a completely different series. Red is “Annual mean land and marine temperature” while blue is “April to September mean temperature from land north of 20N”. The differences between these series is not readily apparent when expressing them as differences from the ’61-’90 mean. The appropriate meanis obviously different for the two series. Clearly, Arctic data (that added begining in 1400) affects estimates of temperature for part of the year above 20N more than it effects annual global mean temperatures. For one thing, it obviously has a much lower weighting in a global resonstruction than in a summertime reconstruction.

One might reasonably ask why include a proxy with a larger inherent variation? The answer is that it’s not proper statistics to deliberately exclude data just because it’s going to make your fit worse for a period.

By: Willis Eschenbach

Willis Eschenbach — Sat, 29 Oct 2005 23:36:04 +0000

re: 22, interesting point, Hans. And with tree ring temperature reconstructions, in addition to the error you point out in the surface temperature, there is an added difficulty.

This is that the most temperature sensitive series, those near the polar or elevational end of their range, are also likely to be a long distance (both in kilometres and temperature) from the nearest long-term ground station temperature record.

Consider, for example, two stands of trees, say they’re only 1 km. apart, but one is on the north slope of a mountain and the other on the south slope. We all know that both the average temperature and the changes of the temperature can be significantly different between the two locations.

To understand their changes in growth, we compare them to the nearest temperature record, which may be 30 km. away and down in a valley.

Now me, I’m not a brave enough man to attempt to numerically estimate the underlying error inherent in this calculation, but I can tell you one thing for sure …

It’s more than a tenth of a degree, the statistical error in the reconstructions above.

By: Hans Erren

Hans Erren — Sat, 29 Oct 2005 20:50:45 +0000

Just some thought about homogeneity corrections, station density and confidence intervals of the surface records.

A proper homogeneity correction can ONLY be carried out if there are sufficient stations within a radius of 1000 km. If this is not the case then the confidence interval of average annual temperature IMHO is as big as 1 Kelvin, being the approximate average station inhomogeneity.

I would therefore imagine that confidence interval of the surface record is inversely proportional to station density, and increasing dramatically in the 19th century.

Now the the proxies were calibrated against the surface record, was the confidence interval of the surface record ever taken into account.
In all the graphs I saw of the surface record I never saw an error bar….

By: TCO

TCO — Sat, 29 Oct 2005 20:21:24 +0000

Is autocorrelation of the record agreed on? Proven? Is it fundamental to your criticisms? Do others in the field use autocorr style stats?

By: Steve McIntyre

Steve McIntyre — Sat, 29 Oct 2005 05:27:09 +0000

Re #12 – in autocorrelated situations, errors do not average down with the square root. Beran points out that under the autocorrelation of long-run dependence (which occurs in geophysical systems, without necessarily taking a position on hte physical mechanism) you may need up to 10,000 measurements to achieve the confidence of 100 i.i.d. measurements.