If someone here has access to the Encyclopedia of Statistical Sciences , they could post their definition of Inverse Regression here.

Also see the new http://climateaudit101.wikispot.org/Glossary_of_Climatology_Terms — a work-in-progress.

Cheers — Pete Tillman
ClimateAudit 101 team
http://climateaudit101.wikispot.org

For the climate science is important the consensus, not the facts!

The number of proxy records successively increases for the four scenarios (95, 139, 378, 405).

Then, data is run through MBH98 machine, and not much differences are found, except that offset in verification mean rises 0.1 degrees.

If so, nice result, but degrees of freedom should be taken into account. As in Brown’s multivariate calibration confidence formula,

which takes this kind of overfitting (large amount of responses) into account in the uncertainties.

I previously commented that Wahl and Ammann had been engaged in “academic check kiting”. In this case, they seem to have realized the absurdity of citing a rejected paper and tried to cooper up the situation. From my perspective – and I’m used to business situations, I would have said that any “acceptance” of Wahl and Ammann 2007 must surely have been conditional on the rejected companion article being accepted somewhere and that it is false to say that it was “accepted” on March 1, 2006. (This matters only because they were already being cute with IPCC publications deadline.) IPCC “needed” this article because otherwise there was no journal article that could be used to argue against our criticisms.

Their emulation of MBH exactly matches ours, as I observed in May 2005 and most of our results, given the same assumptions, are virtually the same.

I;ve reported a lot on this – see http://www.climateaudit.org/?cat=20 . Not much has changed here.

As I reported earlier, in late 2005, I suggested to Ammann that, rather than engaging in further controversy, we try to write a joint paper summarizing what we agreed on. Ammann said that it would be bad for his career advancement and thus the controversy continues. On an earlier occasion in June 2005, they tried to trick Stephen Schneider about the rejection of the GRL article. They only included the failed verification r2 statistics after I filed an academic misconduct complaint.

I guess that I’ll have to bestir myself to respond to this dreck formally. Ammann and Wahl make so many misrepresentations of the issues that it’s hard to write a journal response without being tedious and yet there are a lot of spitballs that need to be picked off the wall.

The submission and acceptance dates of the articles.

From abstract:
«Altogether new reconstructions over 1400–1980 are developed in both the indirect and direct analyses, which demonstrate that the Mann et al. reconstruction is robust against the proxy-based criticisms addressed.»

Excuse me if I’ve resumed this ancient post!

Kendall and Stuart (Chap 29, “Advanced Theory of Statistics,” vol 2, 4th ed.) devotes a whole chapter to this problem (“functional and structural relationship”). My reading is that things are a mess, particularly if one recognizes the existence of measurement error in both X and Y variables.

There is also a section on Calibration (32.76-32.77), (6th edition)

Two cases emerge, which have sometimes been confused in the literature. We refer these as the unconditional and conditional models, respectively, the terms being used in a manner that is consistent with our earlier description of regression methods in these chapters. Also, we refer to the general question of estimating as a calibration problem, rather than one of inverse regression, as the term ‘inverse’ seems open to misinterpretation

For the multivariate calibration case, the reader is referred to Brown 1982 (the same as in #3) .

In circumstances where the proxies have considerable orthogonality – if one can talk this way – Partial Least Squares regression approaches Ordinary Least Squares regression. OLS rotates the PLS-coefficients in n-space by the matrix . The proxies in (say) the MBH98 network are surprisingly orthogonal. Mixing Partial Least Squares regression with prior processing using Principal Components is not an obviously consistent procedure – the prior Principal Components operation generates orthogonal series, which are exactly what you “shouldn’t” want for Partial Least Squares regression.

In the case of the MBH98 network (and I suspect that it’s also true for the MBH99 network), the PLS regression coefficients are surprisingly close to OLS coefficients.

Kendall and Stuart (Chap 29, “Advanced Theory of Statistics,” vol 2, 4th ed.) devotes a whole chapter to this problem (“functional and structural relationship”). My reading is that things are a mess, particularly if one recognizes the existence of measurement error in both X and Y variables.

The problems vanish if all the error variances are sufficiently small. But I’m not sure that’s the case when dealing with climate reconstructions.

respectable interval provided the t-test of the hypothesis is rejected

and

The practical man’s answer that one should not attempt calibration when one is not confident that might be countered by the argument that if the procedure is obviously suspect in some circumstances then the solutions may be far from ideal in the other cases where there is no obvious flaw.

I’m sure this applies to multivariate case as well, i.e. 1) in calibration make sure a priori that there is a (linear) physical relationship between x and y 2) Don’t use calibration residuals for evaluating the model.

1) P.J. Brown (1982) Multivariate Calibration. Journal of the Royal Statistical Society. Series B, Vol. 44, No.3. pp 287-321