Rule N revisited

PCA was also performed on certain proxy sub-networks (spatially dense regional networks of tree-ring data available separately in different continents) as means of dimensional reduction of the predictor network. In this case, the procedure was performed separately for each independent step of the stepwise calibration/reconstruction procedure described in “3” below. A decreasing number of PCs of these sub-networks are retained increasingly further back in time, as dictated by application of objective selection criteria (consideration of results of both Preisendorffers Rule N and Scree test).

MBH98 Corrigendum

We employed a standard, objective criterion for determining how many PCs should be kept for each region.

Michael E. Mann in his book.

Let’s continue with another housekeeping post.

When Steve and Ross uncovered Mann’s flawed PCA, Mann’s defence was that MM had failed to use Preisendorfer’s Rule N in the selection of the PCs in the NOAMER AD1400 step (for the background of this story, see here or read it from Montford’s excellent book). Steve observed immediately that the use of “Rule N” was not mentioned in MBH98 in connection to the tree ring PCA. He then emulated the claimed rule convincingly showing that it was pretty impossible that the rule was actually used. Further, up to now Mann has failed to reproduce any code or documentary evidence for the supposed use of the rule. It is hard to imagine, even in the context of the Hockey Stick, any other argument with so little support but which is still alive and well with the usual suspects. In fact, this fairy tale now seems to be the official story line in Wikipedia (citing Mann’s book, of course).

When I got my hands in the MBH9X file archive contained in the Climategate files, among the first things I checked was that if it contained the code for the selection rule, or even a file indicating the use of such code. Nope. Later I observed a curious thing in the files. MBH9X is a stepwise procedure, and in every step (if there were enough proxies), one supposedly (as the Corrigendum statement indicates) calculated the tree ring PCs. However, there were quite a few calculation steps missing from the archive. For instance, Stahle & Cleveland Oklahoma/Texas (STAHLE OK) precipitation chronologies had a single calculation step (AD1700) although they were also used in the later steps (AD1730, AD1750, AD1760, AD1800, and AD1820). I then checked the actual MBH98 data, and vola, I noticed that instead of calculating the PCs for the STAHLE OK network at, say, AD1820 step Mann had simply recycled the 1820-1980 part of the AD1700 step PCs (1700-1980)! The correspondence between the archive and the PCs actually used was almost one-to-one: every “missing” step in the archive matched the reuse of the PCs from the previous step in the MBH98 data. In other words, contrary what is claimed in the Corrigendum PCs were not calculated for every step.

So what has the above to do with the PC selection rule? Well, Steve had observed that there are three (*) cases (SOAMER AD1750, STAHLE SW AD1750, and NOAMER AD 1500), where MBH98 retains more PCs than in the previous step although the network does not change (i.e., the same proxies are inputs to the PCA). But it was not only that the network was (supposed to be) the same … the PCs were exactly the same as in the previous step! Of course then, it is impossible for any “rule” to retain different number of PCs. The most striking example comes from the NOAMER AD1500 step, which is using PCs from the AD1450 step. Mann is keeping 2 PCs in the AD1450 step, but in AD1500 step 6 PCs are retained from the same PC set!

As Steve has said several times, MBH9X is the gift that keeps on giving! When now preparing for this post, I discovered yet-another Mannian mystery. There is a single exception to the above mentioned correspondence between the archive and PCs actually used. Namely, PCs are calculated for the SOAMER AD1450 step, but no SOAMER PCs are used prior the AD1600 step. The corrigendum text cited in the beginning continues

PCs were no longer calculated back in time once a given network contained fewer than 7 available series (with the exception that PCs were calculated for the ‘Stahle Southwest U.S./Mexico network’ with 6 series available). Thus, although some series may be available further back in time, they may not have been used to calculate PCs. For example,there are 110 series available back to 1400, but only 95 are used because PCs were not calculated on 6 Australian and 6 South American ITRDB series and 3 ‘Vaganov’ series.

SOAMER contains 7 series in the AD1450 step. Why were none of those PCs used?

(*) Actually there is a fourth case (AUSTRAL AD1750), which is immaterial here as it has the corresponding calculation step in the archive.


  1. bernie1815
    Posted Sep 3, 2014 at 4:35 PM | Permalink

    Is there a way of determining when a PC represents a signal within/across a number of different proxies and when the PC is essentially a signal from a single proxy?

    Jean S: Yes, PCs are just linear combinations of the proxies.

  2. kim
    Posted Sep 3, 2014 at 5:05 PM | Permalink

    I’m tellin’ ya; a jury can understand this.

    • stan
      Posted Sep 4, 2014 at 10:50 AM | Permalink

      Agree with caveats. An articulate expert witness in statistics with a well prepared attorney could keep things from getting lost in details.

      • Bill_W
        Posted Sep 4, 2014 at 11:28 PM | Permalink

        The way juries are picked is typically to NOT allow anyone on the jury who has any expertise in an area related to the trial OR anyone who has any knowledge that may bias them. Having ever clicked on a skeptical website might suffice. I have been on a jury and so has my wife and a friend. In both of our cases, we had a few people on the jury with any sense and that actually knew that we were supposed to follow the law. The rest of the jury had their mind made up well before deliberations and did not try to follow the law, despite the judge’s instructions to do so. I am not so confident a jury could follow it. They could understand Climategate e-mails and anything that sounded like a cover-up. Those e-mails probably won’t be allowed into evidence. Possibly the fact that a majority of the public is skeptical about AGW could help.

        • bernie1815
          Posted Sep 5, 2014 at 8:30 AM | Permalink

          Bill W: I am with you on how juries are selected and the critical thinking capacities of juries due to a painful experience with a civil suit. A senior partner from a very respected Boston Law Firm who we used to review our lawyers’ approach to our case said that with juries, if you have a winning case you still only have a 70% chance of the jury deciding in your favor. If you have a losing case, you have a 30% chance of the jury deciding in your favor. Better to settle than to put your fate in the hands of a jury.
          In our case, fortunately, the judge vacated most of the jury’s findings.

  3. Skiphil
    Posted Sep 3, 2014 at 7:29 PM | Permalink

    “SOAMER contains 7 series in the AD1450 step. Why were none of those PCs used?”

    hmmmm…. an “Inconvenient Question” ???

    Could it lead toward “An Inconvenient Truth” ???

    Jean S: Don’t know … PC1 seems to be rather hockey stickish (no surprise as the Mannian PCA is used) so from that point there should be no problem of using it … this is why these Mannian puzzles are fun to solve 😉 P.S. I got your email. Will reply when time permits.

  4. BallBounces
    Posted Sep 3, 2014 at 8:18 PM | Permalink

    PCA = principal component analysis

    PCs = principal components

    “MM” = Steve McIntyre and Ross McKitrick

    • Jeff Alberts
      Posted Sep 3, 2014 at 9:19 PM | Permalink

      That’s a double Big Mac. 😉

      • kim
        Posted Sep 3, 2014 at 10:05 PM | Permalink

        This post is a Big Mac Attack and something frosty from the ice cold Jean Machine.

  5. pohakea
    Posted Sep 3, 2014 at 10:49 PM | Permalink

    pp 8 and following, today’s 50 page pdf: very sad arm-waving …

    Click to access legal-20623990v1-2014-09-03-brief-of-appellee-michael-mann.pdf

  6. Paul Baverstock
    Posted Sep 3, 2014 at 11:22 PM | Permalink

    Wow, just read Mann’s latest documents to the Court re his case with Steyne. Just………wow.

    • jeff taylor
      Posted Sep 4, 2014 at 8:54 AM | Permalink

      I especially liked the idea that resolution of this matter doesn’t “involve a search for scientific truth”.

      • Pouncer
        Posted Sep 4, 2014 at 10:51 AM | Permalink

        I see that Mann’s lawyer’s pleadings include a direct assertion of fact: that Edward Wegman of George Mason University was investigated for plagiarism and misconduct — and was NOT sanctioned for misconduct _per se_, but was nevertheless reprimanded for plagiarism.

        Plagiarism is a serious academic offense. I would venture to say such an accusation is defamatory.

        But the George Mason investigated, to use Mann’s language, “exonerated” Wegman of that charge. Surely Mann, and his attorney’s know or should have known that Wegman’s assistant in a non-statistical portion of the topic paper was found to have made improper and inadequate attributatation, (to over simplify).Of course Mann’s assertion also makes the implicit accusation that because the topic paper was “plagiarized”, the statistical conclusions must, somehow, be invalid — if not “tortured”, “manipulated”, “bogus” or “fraudulent”. Despite such restaint Mann asserts that Wegman’s work (in his area of expertise) showing statistical problems with Mann’s own work (in a discipline well OUTSIDE Mann’s expertise) can not be relied upon by defendants because … well, plagiarism. To so distort the facts and baldly assert that Wegman himself, without other parties, was guilty of the serious and unprofessional academic offense of plagiarism while implicitly dismissing Wegman’s statitical competence is malicious, libelous, and actionable.

        Were, that is, Wegman an academic of Mann’s miniscule character.

        Steve: Wegman was exonerated of plagiarism in the Wegman Report, but was reprimanded in connection with a different paper in which a grad student had copied boilerplate text. At the time, I looked for cases in which a non-plagiarizing senior author was considered responsible for plagiarism by a coauthor and was unable to find any precedents. There are many cases in which an innocent author was not held responsible for plagiarism by a coauthor.

        • MikeN
          Posted Sep 4, 2014 at 1:03 PM | Permalink

          I think there are instances of a celebrity writer who has uncredited secret coauthors who engage in plagiarism for which the celebrity writer got the blame.

        • Steven Mosher
          Posted Sep 4, 2014 at 1:53 PM | Permalink

          maybe we should start a fund for wegman to sue mann

        • Pouncer
          Posted Sep 4, 2014 at 2:02 PM | Permalink

          Thank you, Steve, for correcting my mis-remembered and poorly summarized review. I think your correction may amplify the point. Mann, in my experience seems to routinely accuse his critics using factual assertions of fact that, if literally true, would ruin that critic’s career. Some opinion columnist is (quotes approximate) “a shill for the oil company”; this statistician is “a plagiarist”: that meteorologist is “blinded by religious zealotry”; another dendrochronologist is “ignorant of basic physics”; a politician has “sold his office” and so on. It’s not that there is no room in any debate for such claims, but that a certain oblivious hypocrisy and one-sidedness in a debate, after a while, calls for every assertion of fact the debater might use to be subject to extra scrutiny.

          If someone shows willingness to lie about a statistician, would that same one scruple to lie about the statistics?

    • Posted Sep 4, 2014 at 12:30 PM | Permalink

      Wow indeed! He’s doubled down again. It seems that Mann is continuing to pursue a strategy that, if continued, will lead to the case going to court. While Mark Steyn and others will continue to be financially impacted by this strategy, they should also have the opportunity to present their case, proceed with discovery, and ideally place the appropriate focus on the specifics of Dr. Mann’s research as well as the inquiries that were done in the wake of “Climategate”.


  7. James Perth
    Posted Sep 4, 2014 at 1:45 AM | Permalink

    Thank you Ball Bounces for refreshing my memory on the meaning of those abbreviations. Best practice for technical writing is to write out the words in full the first time they appear and then immediately follow with the abbreviation. It greatly assists the understanding of an amateur statistician like myself to have those abbreviations spelled out.

  8. Posted Sep 4, 2014 at 3:34 AM | Permalink

    Apologies for being off topic but I thought this would be the best way of getting in touch. I hope you are well. I thought your readers would be interested in this puzzle as set out on DeSmog UK. I know how much they enjoy a climate related conundrum. Lord Lawson has considerable influence over the British government through his close relationship with the chancellor, George Osborne. Therefore I think the public are rightly very interested in where his funding comes from. I am attempting to encourage readers to help in this research – although it’s very early in the life of a website to try such an initiative. This is very much inspired by the success you have enjoyed by encouraging others to obtain information you feel should be in the public domain. Warm regards, Brendan:

    • Posted Sep 4, 2014 at 5:54 AM | Permalink

      funny thing Brendan, is that you are probably the only person commenting here, or any sceptic blog that is funded….. (ie you are payed to work at Desmog Blog, and Request Initiative…

    • Kenneth Fritsch
      Posted Sep 4, 2014 at 10:30 AM | Permalink

      BM, sniffing for funding is a lot different than the technical sniffing/analyses done here on published papers, and thus you might be addressing the wrong crowd in your recruitment efforts.

    • Steve McIntyre
      Posted Sep 4, 2014 at 11:54 AM | Permalink

      Brendan, of immediate topical interest in our discussion of Mann v Steyn is who is funding Mann’s lawsuit against Steyn et al. Perhaps you can illuminate us on that topic?

      • Tom
        Posted Sep 4, 2014 at 1:44 PM | Permalink

        As I have pointed out before you can be held liable for legal defense funds if said funds are closely connected to those who have an interest in the outcome of the case. Donative intent is broken and the fund is taxable income. The most clear cute case of this is when the employer of the individual is involved in the fund s Carro May Audigier v. Commissioner , 21 T.C. 665 is the controlling legal authority on the issue. Since the creator of Mann’s fund is an alumni of his employer this is of interests me.

        Quick can anyone tell me what 36.9% of $2,000,000 is?

        Steve: if people can get tax receipts for donations, doesn’t that affect taxability of payment of legal fees as well? I can see how gifts can occur if people are donating using after-tax income, but not if they are getting tax deductions.

        • Tom T
          Posted Sep 4, 2014 at 3:09 PM | Permalink

          I’m not so sure about that. Donations to legal aid are tax deductible and use of legal aid is tax free. I used it myself when I was a poor college student fighting with my landlord. However, in no way did those donating to legal aid or legal aid itself have anything to gain from me winning the battle against my landord. The issue is donative intent. If those behind the fund have an interest in the outcome of the case then the donative intent is broken and the aid is considered income.

        • Posted Sep 4, 2014 at 3:15 PM | Permalink

          In the United States, donations to a legal fund are only tax deductible if that legal fund is a charity. In that case, it is governed by the same rules as any charity. That includes a number of restrictions on how the money can be spent.

          I’d expect it to be known if a charity was financing Michael Mann’s case so my guess it someone else is financing it as a “gift.” That means it isn’t tax deductible.

      • pohakea
        Posted Sep 4, 2014 at 3:14 PM | Permalink

        Priceless thread, comments, here and over here, too:
        ” … Mann’s legal defense fund, via Public Employees for Environmental Responsibility (PEER) and GAP’s Environmental program ( …” (David Ross)

        h/t to Bishop-hill comments,
        Feb 18, 2013 at 12:34 PM | Unregistered (Anonymous) Commenter deepthroat,

      • Tom T
        Posted Sep 4, 2014 at 3:46 PM | Permalink

        FYI its 30% reward of recovered taxes to whistle blowers. Quick what is 30% of 39.6% of $2,000,000.

    • David S
      Posted Sep 4, 2014 at 5:25 PM | Permalink

      Whoever it is, they can’t be less disinterested than Deutsche Bank, if you excuse the double negative.

  9. Grant B
    Posted Sep 4, 2014 at 4:40 AM | Permalink

    Thankyou Brendan Montague. Bishop Hill tells us all we need to know about you.

    • kim
      Posted Sep 4, 2014 at 11:32 AM | Permalink

      Hah, from that thread: ‘Hired gun, shooting blanks’.

  10. Kenneth Fritsch
    Posted Sep 4, 2014 at 10:25 AM | Permalink

    Is not Mann’s later published reconstruction work free of using PCA? And if so, why?

    Of note to even laypersons is that much of Mann’s published reconstructions include methods that allow subjective selection to influence the outcome. Selecting the retained PCs is a controversial part of PCA and I judge to be beyond the pale of complete objectivity. There are different approaches to retaining PCs as noted in Steig et al. (09) and O’Donnell et al. (2010). Some selections appear to be grasped out of thin air with perhaps some hand waving rationale, while others appear to have some underlying thought and reason connected to the selection process.

    And speaking of selection allows me to reiterate that the basic flaw in Mann and others temperature reconstructions is selection of proxies without an a prior criteria for selection and instead using the biased method of selection based on correlation with the instrumental record.

    • None
      Posted Sep 4, 2014 at 1:15 PM | Permalink

      The whole PCA thing is a joke when applied to paleoclimatic data. It finds sets of squiggles that minimise the variance in the data – the jump to claiming that one (or more of these datasets when grouped together) must actually record variations in a single seperable physical effect, never mind specifically temperature, is just an astronomical one.

      To quote Joliffe on the matter “Of course, given that the data appear to be non-stationary, it’s arguable whether you should be using any type of PCA”.

  11. pohakea
    Posted Sep 4, 2014 at 3:18 PM | Permalink

    Priceless thread, comments, here and over here, too:
    ” … Mann’s legal defense fund, via Public Employees for Environmental Responsibility (PEER) and GAP’s Environmental program ( …” (David Ross)

    h/t to Bishop-hill comments, Unregistered (Anonymous) Commenter deepthroat (BM thread linked by Grant B, thank you!)

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