Zero-width confidence intervals are not necessarily wrong. They are rather unconventional, perhaps, but that doesn’t make them incorrect.

Man, that’s just plain and fancy footwork. I can’t offhand think of any physical measurement that has a confidence interval of zero. Examples, anyone?

w.

Zero-width confidence intervals are not necessarily wrong. They are rather unconventional, perhaps, but that doesn’t make them incorrect.

Steve M,

The URL for the Hegerl paper is a bit off. It looks to be http://data.climateaudit.org/pdf/Hegerll07.jclim.pdf

if you tell me which part you find hard to understand, I can send you an algorithm. The records are processed by a number of programs. Tom;s teaching is over for the semester so I think you’ll get more detail out of him soon.

Just so that I meet the requirements of other readers, UC and bender, can you summarize any questions? BTW I got a copy of the Hegerl J CLim article as published posted up here Ther references ot an SI have been removed and there is no SI at the J Climate website.

where A, B are regression parameters, each with standard errors, and Proxy P is subject to sampling error.
Then the error in the inference T is the quadrature sum of the errors in A*P and B, and the error in A*P here is the straight
sum of the relative errors in A and P.

Is that not the correct way to compute the confidence level for a quantity inferred from an error-prone calibration? That’s what I learned in high school physics, anyways.

TLS uses first principal component, minimizes perpendicular distances from data points to the line ( a new line to my calibration-line-plot ) ?

In Hegerl J. Climate paper

Note that if the uncertainties in the paleo reconstruction are much larger than in instrumental data, an alternative is the use of inverse regression, neglecting error in instrumental data (Coehlo et al., 2004).

I think this is an misunderstanding. IMO Coehlo explains CCE and ICE quite well, and Hegerl et al didn’t read carefully. ICE requires prior distribution for temperatures, and another viewpoint of ICE was just developed in http://www.climateaudit.org/?p=1515#comment-108922 and following comments. If I were a reviewer, I’d stop reading that manuscript right there, page 7. ( I don’t have the final version, was anything corrected? ). I’m not surprised that their CIs went wrong..

Am I the only one perplexed with the confidence interval around 1400, 1650, and 1750?

The new SI (which starts from 1505) shows the CI’s around 1650 and 1750 to be very wide.

Still, as Annan argues, the CI’s are wrong. In order to get the uncertainty on the inferred value, the uncertainty in the observed value (the proxy value on which the temp reconstruction is based) has to propagate through the uncertainty in the regression coefficients. It makes no sense to assume all the uncertainty comes from the standard errors in the estimated regression coefficients. Some of it must come from sampling error from the estimation of the means.

It is very important to know exactly what these folks are doing.

Anyways, this is probably why reviewers never caught the error. But it would be nice to know to what degree this deception was intentional.