By the way, I think that the attempts by Mann et al. to do a comprehensive reconstruction of historical temperatures from proxies were somewhat original and admirable, or at least a strong push of past attempts, in providing “real” world support for the climate computer models. The lack of proper statistical guidance, the authors hurry to get their message out on what they saw as a critical problem needing immediate attention and the advocates of immediate AGW mitigation suspending normal judgments of the works because it fit their needs so well are what I see as being problematic for this sequence of events.

Agreed. It was premature to take the paper and run with it the way people did. It’s truly unfortunate. In the normal course of things, perhaps others would try to replicate the results, would find problems, would question the use of proxies, methods, etc. and the science would move towards some better certainty about the issues. The paleo recons could then be viewed with better confidence as saying something useful about past climate change and ultimately, about current.

Steve: There was nothing original about the idea of a proxy reconstruction. Bradley and Jones 1993 had done one and Jones et al 1998 somewhat preceded MBH98. Even Groveman and Landsberg 1979 – discussed previously. Mann’s key innovations (and this is from a Bradley interview) were 1) his mathematical methods for extracting a faint signal (which turn out to be Mannian PCs); 2) and this is perhaps due to Hughes, the introduction of BCPs into climate reconstructions, which previous people had steered clear of. Of course the Team quickly got addicted to crack once Mann legitimized the use of BCPs.

I then compared verification statistics for the different reconstructions as shown below. OLS yielded much the “best” fit in the calibration period, but the worst fit in the verification period.

If OLS is equivalent to ICE, it actually finds the best fit (minimizes calibration residuals), and in proxy-temperature case makes the most obvious overfit. Let me try to get an understanding of the methods applied. As we know, core of MBH9x is the double pseudoinverse, in Matlab

RPC=P*pinv(pinv(TPC(1:79,T_select))*P(903:end,:));

where P is standardized (calibration mean to zero, calibration de-trended std to 1) proxy matrix, TPC target (temperature PCs) and T_select is that odd selector of target PCs. After this, RPCs are variance matched to TPCs, and brought back to temperatures via matrix multiplication. As you can see, I can replicate MBH99 reconstruction almost exactly with this method:

Differences in 1400-1499 are related problems with archived data, and in 1650-1699 they are due to unreported step in MBH procedure. Steve and Jean S have noted these independently, so I’m quite confident that my algorithm is correct.

I’ve considered this method as a variation of classical calibration estimator (CCE) and Steve’s made a point that this is one form of PLS. These statements are not necessarily in conflict. Original CCE is (with standardized target)

where matrices and are ML estimates of and , obtained from the calibration experiment with a model

By setting , I get exactly the same result as with double pinv. Which verifies my observation that MBH9x is CCE with special assumption about proxy noise and with incorrect variance matching step after this classical estimation.

Back to OLS (ICE) estimate, which is obtained by regressing directly X on Y,

this is justified only with a special prior distribution for , which we don’t have. Thus OLS is out of the question. Yet, it is interesting to observe that OLS is actually a matrix weighted average between CCE and zero-matrix (Brown82, Eq 2.21) :

It would be interesting to compute MBH99 results with real CCE, but S does not have inverse for AD1700 and later steps. But results for up to AD1700 are here, CCE:

http://signals.auditblogs.com/files/2007/11/ad1600_rec_cce.png

ICE:

http://signals.auditblogs.com/files/2007/11/ad1600_rec_ice.png

As you can see, variability of ICE is lower, as it is weighted towards zero. But hey, where did that hockeystick go ?

Lucia, I would have to say that Steve M’s notation on my reply is valid for any number of visiting real climate scientists that I have observed here, but before departing they frequently key on critiquing those critiquing the Hockey Team papers without revealing much in the way of judgments on the critiqued papers. The follow on to this departure can sometimes come from other visiting real climate scientists stopping in to implore the participants here to be more polite to these visitors in the future or do without their potential contributions to the knowledge base here. These exhortations run counter to my blogging experiences where I have found those visitors (often with a counter POV to that of the majority of the blog participants) who come to inform avoid general comments on the participants or their POVs like the plague.

Since in my view, JEG is more aggressive in these regards than other visiting climate scientists and his web site indicates he wants to “teach” the world about AGW and its repercussions, he might remain a bit longer. I, however, do not see these more politically oriented climate scientists doing much critiquing of papers providing evidence for AGW. I think the problem there lies in the split personalities of the scientist and policy advocate and hearing the policy dominated personality, not the scientist, making the decisions of what and what not to critique – at least on a blog such as CA.

By the way, I think that the attempts by Mann et al. to do a comprehensive reconstruction of historical temperatures from proxies were somewhat original and admirable, or at least a strong push of past attempts, in providing “real” world support for the climate computer models. The lack of proper statistical guidance, the authors hurry to get their message out on what they saw as a critical problem needing immediate attention and the advocates of immediate AGW mitigation suspending normal judgments of the works because it fit their needs so well are what I see as being problematic for this sequence of events.

Since peer reviewers are generally anonymous, the public will have little information other than “It was published in a reputable journal”. That would be sort of a shame — particularly if the paper does contain useful interesting information. (And it well may. Most papers contain some useful information even if that information is not definitive or may be flawed.)

It appears the discussions would require more than a comment after Steve’s post, so I wondered if Judy or JEG would post at a blog, web page etc.

If past reactions are predicitive in these matters, I suspect that a reply from Judy and/or JEG will concentrate on Steve M’s critique of the paper without concluding, in any detail, much about the paper’s results and conclusions.

Steve: I disagree. If past reactions are predictive, this is usually the point where real climate scientists disappear.

So, evidently Steve accepted their invitation to talk about it. Having expressed an interest to talk about Mann et al 2007, are Judy and JEG going to give their points of view on Mann 2007 somewhere now? If they did , those of us not entirely up to speed on these statistical issues could read what Judy and JEG think.

It appears the discussions would require more than a comment after Steve’s post, so I wondered if Judy or JEG would post at a blog, web page etc.

estimating a covariance matrix as a sample second moment matrix when data are not centered would obviously be problematic

Yes, it is exactly what is happening in Rutherford et al (2005) as you can see from the link I provided (Steve’s post also has a link to a backup of the original code, if you want to check yourself). IMO, this is not only “problematic”, it practically destroys the algorithm. Notice also that the mean parameter is directly affected. This is what I wanted to have your opinion about. After all, bad reputation of Rutherford et al (which is claimed and understood as being an application of the RegEM algorithm) affects directly the reputation of your RegEM algorithm.

Thank you also for the indsider’s comment on the RegEM algorithm and interesting reference. Just a quick question: have you (or anyone) considered using RegEM on integrated climate data as it seems to be relatively nonstationary?

Well, there’s red snow. There’s white snow. And then there’s the snow where the huskies go!