I have read previously from an online draft of Huybers paper “Comment on Hockey Sticks, Principal Components, And Spurious Significance by McIntyre and McKitrick” linked here. I assume this is the paper on which you have based your oft posted negatively inclined observations about Steve M and Ross M in this matter. I will excerpt what I consider pertinent parts of Huybers’ paper and the M&M reply (that can be linked by going to the right side of this web page and clicking “reply to huybers”) and accompanied them with my comments — all in hopes of getting something more definitive out of you in your assessments of the situation.

My general take on this exchange as a nonprofessional outsider is that Huybers was on a less than whole-hearted mission to minimize the damage done to MBH and the HS by the previous M&M analyses.

Huybers questions the use of the covariance PC1, used by M&M in their analysis, versus the correlation PC1, the fully normalized PC1, that Huybers uses and calls it, that splits some of the difference between the MBH PC1 and M&M PC1 but lies closer to the M&M PC1. Huybers does not appear to me to make a case for his choice other than showing it matches, in his case, the averages derived without using PCA. I leave the M&M replies (which explain their choice of a covariance PC1 and by the way are much more detailed in my view than those of Huybers) to this for later, but suffice it for now to say that if Huybers used averages as a benchmark for PC1s why not forego this discussion and talk about why averages and not PCA should be used.

Huybers mentions in passing the questionable use of Bristlecones but seems too much in a hurry, in my view, to avoid any discussions of this critical issue in his comments and waves it off for consideration in future studies. This seems rather dismissive but it does allow the evidence door to open for M&M to present the MBH censored files that show the reconstructions without the bristlecones in their reply.

Huybers other point is the use of the mysterious and seldom used statistic, RE, to determine significance in cross-validation. His admission that the R squared statistic in MBH98 is very close to zero would, to this naive soul, stop most statisticians in their tracks right there for doing some serious thinking before going on to use and justify a less well defined statistic like RE. The variance re-scaling in the RE calculations was a misunderstanding that would appear to be directly attributable to Mann et al withholding code essential to the task of replicating his work. While M&M are able to reproduce Huybers’ results with his suggested calculation, when they fully emulate the MBH98 methodology, M&M obtain a 99% quantile that essentially agrees with their previous calculations –and that is the calculation that Huybers had questioned.

Here is how Huybers describes the purpose of his comments:

Having reproduced the statistical results of MM05, this comment is prompted by further questions regarding appropriate implementation of principal component analysis (PCA) and the presence of discrepancies in their estimate of significance levels.

While Huybers comments are aimed at questioning the MM05 analysis, he does make some comments, in agreement with M&M, on the MBH reconstruction that indicates problems that he sees with MBH. I have listed these excerpts below:

To further check the controls on tree ring variance, the variance of each NOAMER chronology is compared with that of the nearest instrumental temperature record using the Jones and Moberg [2003] instrumental compilation between 1870 and 1980. Because no meaningful relationship is discernible (there is actually a weak anti-correlation between the tree ring chronology and instrumental variances), the best approach appears to be to normalize the variance of the NOAMER records prior to performing PCA.

.. The reason for the bias in the MBH98 PC1 can be understood by considering that PCA maximizes the variance described by each principal component where variance is measured as the sum of the squared record, _2 = Pt x2t , and x is not necessarily zero-mean. The MBH98 normalization tends to assign large variances to records with a pre-1902 mean far from the 1902 to 1980 mean, and records with the largest variance tend to determine PC1.

.. Another point raised by MM05 is that many of the strongest trends in the tree ring chronologies may be unrelated to temperature change [Graybill and Idso, 1993] “¢’¬? in future studies this may warrant the exclusion or down-weighting of certain records, but this is an additional step which would have to be explicitly stated.

..The MBH98 normalization convention for a record, x, is xMBH = (x à⣃ ’ ‘ ¯x1902)/_01902, where ¯x1902 and _1902 are the mean and standard deviation computed between 1902 and 1980. MBH98 compute the standard deviation after detrending x, indicated as _0, an additional step that seems questionable but turns out not to influence the results.

.. To avoid ambiguity in future studies, it may be preferable to use simple averages rather than PCA when estimating spatial means such as Northern Hemisphere temperatures.

Here are excerpts on the points that Huybers is questioning about the M&M analysis and that I assume are relevant to the issues raised by TCO.

The pre-1902 values of the MBH98 PC1 are more negative than the corresponding record average. Conversely, the pre-1902 values of the MM05 PC1 are less negative, an observation somewhat at odds with the statement in MM05 that their PC1 is “very similar to the unweighted mean of all the series”. These off-sets between PCs and record averages further indicate that the MM05 results are biased in the opposite direction to those of the MBH98 results.

This is best illustrated by going to Huybers’ linked draft from above ” for the graphed results and explanations so we all can judge for ourselves what Huybers is saying.

.. The MM05 code generated realizations of x having roughly a fourth the variance of y, biasing RE realizations toward being too large. MM05 thus estimate a RE critical value substantially higher (RE=0.6) than that of MBH98 (RE=0.0) and incorrectly conclude that the AD1400 step of the MBH98 temperature reconstruction is insignificant. When the MM05 algorithm is corrected to include the variance adjustment step and re-run, the estimated RE critical value comes into agreement with the MBH98 estimate1.

M&M’s reply can be found by linking as directed above, but for sake of talking points I have excerpted the following:

On Principal Components — Covariance or Correlation:

Relative to the MBH98 PC1, the differences between the covariance PC1 and correlation PC1 are trifling and both confirm the bias reported in MM05.

..6] a) Tree ring chronologies are typically autocorrelated, especially the controversial bristlecones. For autocorrelated series, the ordinary least squares sample variance (used by Huybers) is a biased (under-) estimate of the long-run variance, so the bristlecones will tend to be over-weighted this way. An “”unbiased fully normalized” PC1 can be obtained using an autocorrelation-consistent variance estimator [e.g., Andrews, 1991]. This bias correction yields a result (Figure 1g) very similar to the covariance PC1.

[7] b) Huybers argues that the correlation PC1 captured a “”robust feature of the NOAMER dataset” based on its similarity to the mean of the 70 series in the AD1400 network scaled by their standard deviation (Figure 1f). If the purpose of PC analysis is merely to predict the mean, then there is no reason not to simply use the mean. As for the robustness of the feature, only 70 of 212 series in the NOAMER network extend back to AD1400. Using all 212 NOAMER series scaled by their standard deviation (Figure 1d) yields a network mean closer to the covariance PC1 than the correlation PC1″¢’¬?by this criterion “”full normalization” adds bias to the PC1.

On Bristlecones and their effects on PCA:

[8] The differences among these PC series can be traced to differing weights for bristlecones.

.. [9] Bristlecone impact can be seen directly by comparing the MBH98 PC1 (Figure 1a), which is weighted almost entirely from bristlecones, with an unreported PC1 from Mann’s FTP site (Figure 1b), which Mann obtained by

applying MBH98 PC methodology while excluding 20 bristlecone sites…

On the RE Benchmark:

]]>[14] The variance re-scaling step called for by Huybers was not mentioned in MBH98. However, recently-released code… shows that MBH98 included a re-scaling step. If simulations are done with variance rescaling on a simulated tree ring PC1 without constructing a full network of other proxies and calculating a NH temperature index, we agree that the 99% quantile is _0. However, Huybers’ [2005] simulations do not fully emulate MBH98 methodology, as his simulations did not replicate the effect of a proxy network.

[15] We did new simulations in which we took 1000 simulated PC1s saved from the simulations described by MM05; for each PC1 in turn, we made a “”proxy

network” of 22 series with the other 21 being white noise (replicating the 22 series of the MBH98 AD1400 network). We then used MBH98 methodology on the proxy network, including inverse regression of the proxies. After calculating the reconstructed temperature principal component (RPC), we scaled the variance of the RPC to the “”observed” variance of the temperature principal component prior to calculating a NH average, from which we calculated an RE statistic. The 99% quantile was 0.54, down slightly from 0.59 as found by MM05.

If you ask a tough question and the other person starts blustering, calling you a fool for asking, etc. there is a decent chance that you are hitting a little close to something relevant that needs to be explored. If you find a ball of yarn has a little string attached, give that string a tug. You’ll get an explanation. Give a couple more tugs. If everything is cool, you will just learn something. But it’s amazing how often that string will unravel the whole ball of yarn, how often your gut suspicion of a problem will bear something out.

TCO, I am now firmly convinced that tugging at that ball of yarn has become the be all and end all to your modus operandi. You post incessantly about how you do not have to be very conversant in a subject matter to ask the “right” questions of those more expert than you in order to drag the truth from their sealed lips and frozen keyboards. Then you refer, in very vague and general terms, over and over and over again to some character flaw that your questioning revealed or how some flaw in a person’s thinking was revealed. Do you ever spend significant time on detailing and summarizing the specifics of your supposed accomplishments in terms that other posters here would comprehend? Not that I have seen while posting here, but maybe someone will come to your rescue and remind me.

Usually it’s Steve, but (broken record), wrt West Pointer (Huybers), Steve had a lot of sturm and drang misdirection when Huybers actually had a valid point. I learned that when I reread the Huybers paper. (/broken record)

So prove me wrong, by pointing to excerpts from Huybers and MM papers and explaining your accusations from above in some detail and with the clarity and succinctness that you would use in publishing a paper. I would much prefer that you limit your findings to substantive issues and exclude or at least identify inconsequential debating points. I will not accept any excuses because if you take just half the time and space that you regularly spend expounding on virtues of the TCO methods of discourse you should cover the matter in detail and thoroughness in a reasonably short time period.

]]>Only speaking for myself, but it is **how** you push your points not **that** you push them that is a little hard to take.

I sometimes get the sense you wouldn’t mind applying a ruler to the backside of the less cooperative types here. That attitude generally doesn’t fair too well in a group such as this. Were you ever a headmaster at a public school in Britain by chance?

]]>Very true….to a point.

The trick is knowing the difference between when we are hitting close to something relevant or on the otherhand, having actually received an adequate answer, being called a fool for a perfectly sound reason.

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