Perverse PCs

TCO has inquired about whether there is a legitimate purpose for using off-center PCs. I can’t think of any valid purpose. Here’s a good reason why not from our E&E article, where we showed how the MBH algorithm turned series upside down if it improved the hockey stick fit. Here’s how we wrote it up.

In response to a reader’s suggestion, we performed a sensitivity test in which we arbitrarily increased the ring widths of all non-Graybill (50 of 70) sites by +0.5 (index units) in the first half of the 15th century, and then re-calculated the PC1 under MBH98 methodology. The purpose is to evaluate how well the added variance is retained in the final temperature index. We provide the exact script here both to describe the calculation exactly and because the results are initially very counter-intuitive and have provoked some disbelief.

The results of this calculation are shown in Figure 2 together with the results from a centered calculation (all results smoothed). For a centered calculation, the increased ring widths for the first 50 years lead to an increase in the PC1 as expected. However, under the MBH98 de-centered method the increased ring widths for 50 non-Graybill sites in the early 15th century causes a significant decrease (!) in the early 15th century PC1. Carried forward through to Northern Hemisphere temperature calculations, these increased ring widths would be construed by the MBH98 method as evidence of colder temperatures in the early 15th century…

Under the MBH98 algorithm, the addition of the extra values in the first half of the 15th century causes the algorithm to flip the series upside-down so that they match as well as possible to the bristlecone pines, whose hockey stick pattern is imprinted on the PC1. This does not occur using a centered algorithm…

This rather perverse result nicely illustrates a problem of mechanically applying a numerical algorithm like PC analysis without regard to whether it makes sense for the underlying physical process.

Original Figure 2. North American AD1400 PC1. Above: PC1 using centered calculations; below: MBH98 PC1 using decentered method. Solid-base case; dashed — with arbitrary addition of 0.5 to non-Graybill sites from 1400–1450. 25-year smoothing is applied.


118 Comments

  1. TCO
    Posted Oct 31, 2005 at 11:41 PM | Permalink

    1. Can you provide an intuitive reason for why the PC1 is flipped?

    2. Is it relevant what the PC1 does or what the total reconstruction does?

    3. What is the story on this “off-center PCA is accepted in paleoclimatology as a field”? Who else does it other than Mann?

  2. Steve McIntyre
    Posted Nov 1, 2005 at 12:03 AM | Permalink

    1. The PCs are steered by the most hockey stick shaped series, in this case, the bristlecones. By flipping the series, they match the bristlecones better.

    2. If the Pc1 is used as a proxy in a regression-inversion analysis, it matters.

    3. No one else uses off-center PCs. It’s not accepted. VZ condemns it.

    An important argument against PCs which we include in our Reply to Ritson is that they “throw out” information on up-down orientation, which you’d think is important in proxy studies. If some are upside-up and some are upside-down, they are all re-oriented to get the maximum pattern-matching to a hockey stick shape.

  3. TCO
    Posted Nov 1, 2005 at 12:09 AM | Permalink

    How does it flip it??

    It seems to me intuitively that PCA is more useful for extracting signal from noise (signal processing) than for getting an average of what really happened. IOW it blows up the signal more than what physically occurred. that’s great if I’m running a sonar stack. But not so good if I want to keep track of average temp in the reactor.

    Or am I off?

  4. Louis Hissink
    Posted Nov 1, 2005 at 1:53 AM | Permalink

    I get the vague feeling that many of these proxy correlations seem like “suck and see” analyses and if they fortuitously re-enforce our belief in SGW then publish and make a hoo-ha over it. Whether or not the correlation is physically real or sensible probably does not come into it.

  5. Spence_UK
    Posted Nov 1, 2005 at 3:43 AM | Permalink

    Re #3

    How does it flip it? – I think you’ve got it covered, but I’ll try to embellish a little.

    PCA is a process for uncovering correlations, and it does not distinguish between direct correlations (positive, linear fit, y is proportional to x) and negative or inverse correlations (linear fit, y is proportional to -x). If y is proportional to -x the process negates x and adds the responses up, scaled proportionately to the degree of correlation.

    In an extreme example, consider a situation where we analyse a years gridded temperature data over the globe, sampled at (say) daily intervals. The dominant signal in this should be the summer/winter variation. But the summer/winter variation for the NH and SH would be in anti-phase. The PCA technique would (most likely) recognise this as a strong inverse correlation, invert (or flip) one half of the worlds’ temperature measurements – and then add them together in PC#1. You won’t know which got flipped (NH or SH) until after the analysis is complete!

    In this respect, you are correct, it will tend to exaggerate certain temperature variations. And of course the off centring technique gives the PCA method a hint as to exactly what it should be exaggerating ;) The theory goes that the exaggeration is bought under control by the normalisation process. But then signals that weren’t exaggerated in the first place are suppressed… as von Storch demonstrated in his paper.

    So the net result would be a strange mixture of some signals amplified and some suppressed… Messy, isn’t it? This is why interpretation of PCA output is so very important, because it dumps a reduced data set at your feet at the end of the process, but you don’t really know what that reduced data set represents. And that is before considering the problem that the underlying proxies are also correlated to things other than temperature, which might equally be hoisted out by the process…

  6. Louis Hissink
    Posted Nov 1, 2005 at 5:10 AM | Permalink

    Spence_UK,

    Spot on.

  7. TCO
    Posted Nov 1, 2005 at 6:46 AM | Permalink

    Why, how does the PCA flip things? Why would you want a technique that flips signs of correlation? least squares doesn’t do that.

  8. Posted Nov 1, 2005 at 7:09 AM | Permalink

    Hi,

    correct me if I am wrong. But PC analysis is principally good for looking for signals and correlations of any kind and for reducing data, remembering its gross features. In linear algebra, quantities can go in both ways and the sign of the correlation is more or less convention. The PC1 is defined to maximize a certain expression, and it is often maximized by taking negative weights for various data vectors. I completely agree that it is an unphysical result if our “leading approximation” is made of negative contributions of certain vectors.

    Concerning centering: the weights of different uncentered data vectors/proxies in PC1 depends on the choice of units etc. If you express your temperatures in kelvins, they will always be around 300K, and because it is more or less constant, the temperatures expressed in kelvins won’t contribute to your “major signal” too much. If you express them in Celsius degrees, they will matter a lot. If you first center your data so that the average of each “proxy” gives you zero, then it of course does not matter which units you choose.

    When i have time, I will look how PCA should be modified to eliminate these problems with the negative weights, units, and centering. Not sure whether there is a natural answer that would still convince someone that it is a good procedure to find the temperatures of the past.

    Best
    Lubos

  9. Dave Dardinger
    Posted Nov 1, 2005 at 7:29 AM | Permalink

    re #7

    It seems to me that when you’re trying to extract signal from a noisy record you’re interested in the size of the signal, not whether it’s a positive or a negative correlation. Thus if you’re looking at an individual’s net worth it might be positively correlated to age, negatively correlated to weight (only guessing there); who knows how it’s correlated to family size, etc. So if you have a set of individuals and a bunch of data on them and want to figure out which ones to hit up for a donation to your new charity, you’d want a table where you’d mixed together the data to create a new wealth proxy where the data was scaled, sign flipped if necessary and then all added together.

    Of course there are problems. Weight might be actually proportional to number of chocolate bon-bons eaten and in the 17th century this might be a positive measure of inherited wealth while in the 20th century it’d be a measure of time available to watch soap operas and more often be a measure of unemployment and lack of wealth.

  10. TCO
    Posted Nov 1, 2005 at 7:33 AM | Permalink

    Thanks Lumo,

    1. Still wonder what it exactly is good for, Wiki only says to “reduce a data set”.
    2. Seems like you all are saying that “false flipping” is a general concern of PCA, not just off-center PCA?

  11. TCO
    Posted Nov 1, 2005 at 7:35 AM | Permalink

    I don’t understand your example, Dave. I would think that non-physicallity would have exactly the same problem in your donation marketing scheme. If you go after fat people when skinny people are the best donors, you’re not targetting the right group.

  12. TCO
    Posted Nov 1, 2005 at 7:48 AM | Permalink

    BTW, I don’t think that my original question 2 was fully answered. (I may not have asked it correctly. I am always confused by the drawings or references to a specific PC and the general curve–which is some summation of PCs?)

  13. Spence_UK
    Posted Nov 1, 2005 at 7:53 AM | Permalink

    Re #10

    1. PCA is quite valuable in data mining type applications, when you have a massive data set and you are trying to extract salient information from the data. It is, in essence, a huge statistical trawling algorithm. Which is why the final interpretation is so important – just because you’re trawling for cod, doesn’t mean you won’t end up with tuna in your nets – if you take my meaning.

    2. Yes, the flipping thing (cough) is a general aspect of PCA, not just the non-centred case.

  14. Posted Nov 1, 2005 at 7:56 AM | Permalink

    Dear TCO,

    as far as I can say, you’re right, and PCA even without centering is designed in such a way that it can reflect the signs – much like everything in linear algebra based on vector spaces. ;-) It is a bad behavior if you think that you know what the true sign of the correlation between two quantities is.

    On the other hand, if you don’t know, it may be actually helpful if the method is able to revert them. Once this possibility is allowed, then it also may happen that you obtain the results that are just the opposite of the true ones.

    You should however notice that PCA is designed to help you with many things that would otherwise be difficult to analyze. Imagine that you’re missing the datasets from the polar regions in some period of time. Then you could not just take the average of your data to find the global temperature – missing polar data would obviously mean that your average temperature will be higher in this period of time.

    PCA is kind of able to fix the holes by “reasonable” numbers that reflect the correlations and typical difference between the polar temperatures and other temperatures, as reconstructed from the rest of the data.

    Well, I would still not use a method like that – centered or uncentered – to reconstruct numbers that should normally be nothing else than the average of available data weighted by their reliability.

    All the best
    Lubos

  15. Dave Dardinger
    Posted Nov 1, 2005 at 7:57 AM | Permalink

    re: #11

    Well, TCO, that’s what I’m trying to say. Something which may match a given measure in one point of time, and may not even be doing it because of what the comparer is looking for, may not therefore match it at a different time. That’s why looking for proxy sets which show rising values in the early 20th century, whether the reason is temperature or not, will throw you off in other time periods.

  16. Jean S
    Posted Nov 1, 2005 at 8:22 AM | Permalink

    TCO and others still wondering the effect of “MBH’s robust PCA” with biased records (e.g. bristlecones):
    I wrote a simple Matlab program that generates 70 white noise “proxies” with the first-order statistics close to the avereages in the NOAMER set. Then one of the series (the bad apple) is slightly corrupted (some extra mean added to the end). The “proxies” are then processed with the standard and MBH’s PCA, smoothed, “adjusted to the instrumental record”, and plotted for the comparison.

    Just cut the code from below and place it in any .m file.
    Have fun! (BTW, I didn’t bother to orient the pc’s, so sometimes you get an inverse “hockey stick” :)

    (hopefully cut&paste works here…)
    ———- cut here ———-
    % Demonstrate the effect of “MBH’s robust PCA” with a single biased record
    % (not to be confused with PCA or anything robust :)

    % Number of “proxies”
    proxies=70;
    % “Proxy” time
    start_time=1400;
    end_time=1980;
    timeline=start_time:end_time;
    samples=length(timeline);

    % “Proxies” (white noise)
    %
    % STD & mean
    sigma=0.01;
    mu=1;
    proxy(:,1:proxies-1)=sigma*randn(samples,proxies-1)+mu;
    % The bad apple follows
    biased_samples=78;
    % Indecies of Interest :D
    IoI=samples-biased_samples:samples;
    extra_mu=0.01;
    proxy(:,proxies)=[sigma*randn(IoI(1),1); ...
    sigma*randn(biased_samples,1)+extra_mu]+mu;

    % “MBH’s noncentralized robust PC1″ aka “Perverse PC1″

    noncent_mu=mean(proxy(IoI,:));
    % Detrending has almost no effect, but that’s part of the original…
    % …maybe it will be useful sometimes :D
    noncent_sigma=std(detrend(proxy(IoI,:)));
    MBH_stand=(proxy-repmat(noncent_mu,samples,1))./…
    repmat(noncent_sigma,samples,1);
    [U S MBHPC1]=svds(MBH_stand’,1);

    % True PC1
    normalized_data=(proxy-repmat(mean(proxy),samples,1))./…
    repmat(std(proxy),samples,1);
    [U S PC1]=svds(normalized_data’,1);

    % Smooth
    wlength=21; % odd
    h=hanning(wlength);
    h=h/sum(h);
    MBHPC1=filter(h,1,MBHPC1)./filter(h,1,ones(samples,1));
    PC1=filter(h,1,PC1)./filter(h,1,ones(samples,1));

    % “Normalize to the instrumental record”
    inst_mu=-0.1251;
    inst_sigma=0.1521;
    MBHPC1=(MBHPC1-mean(MBHPC1(IoI)))*inst_sigma/std(MBHPC1(IoI))+inst_mu;
    PC1=(PC1-mean(PC1(IoI)))*inst_sigma/std(PC1(IoI))+inst_mu;

    figure; clf;
    subplot(2,1,1); hold on;
    plot(timeline,MBHPC1,’r’);
    plot([start_time end_time],[0 0],’k–‘);
    xlabel(‘MBH Robust PC1′);
    ylabel(‘anomalies’);
    grid on;
    axis tight;
    subplot(2,1,2); hold on;
    plot(timeline,PC1,’b’);
    plot([start_time end_time],[0 0],’k–‘);
    xlabel(‘True PC1′);
    ylabel(‘anomalies’);
    grid on;
    axis tight;

    ———- cut here ———-

  17. Steve McIntyre
    Posted Nov 1, 2005 at 8:35 AM | Permalink

    #14. Lubos, I’m venturing a little in the following statement so don’t ridicule me too much if I’ve over-reaching. The problem with PCs is not that they are signed, but that you don’t know the direction of the sign – it’s that they are essentially unoriented.

    I’m trying to remember my group theory from 1967. Here’s some inflated language to describe what I think I mean: the PC is a coset of the upside-up and upside-down version. The PC “space” doesn’t appear to be a vector space, but a factor space of the vector space/{-1,1} if that makes sense.

    I think that we’ve shown convincingly that the MBH method will produce simulated PC1s that look just like the MBH NOAMER PC1 with respect to bend, shape and look. But there’s a big difference between the two: the main contributors to the simulated PC1 have a random distribution of signs, while the main contributors to the MBH PC1 all are bristlecones and all have the same sign. However, it wouldn’t have mattered if they had the same sign – it would have got the same answer.

    The MBH method is simply too powerful in findng hockey stick shapes. From a scientific point of view, you’d have to say that this was a goofy methodology and should never have been used in the first place.

    But it’s a great way to scan a big data set for hockey stick shaped series. It also emulates simple cherry-picking. If you simply take an average of the bristlecones, you get a series that looks like the PC1. (This would not be the case in a simulation due to the cancelling signs.)

    I did an experiment to emulate Jacoby’s picking of the 10 most “temperature sensitive” sites from 35. The “few good men” approach to paleoclimate. If you simulate a data set of 35 red noise series, then pick the 10 most hockey stick shaped series and average them, you get a hockey stick shaped “reconstruction”. The amplitude of the shaft averages down while the amplitude of the blade stays about the same. If you add in a cherry-picked series like Gaspe, you can enhance the effect even more. This is a much more plausible explanation of the attenuated amplitude of reconstructions than von Storch’s regression theory – which does not explain the change in amplitude from calibration period to historical period,as the above does.

  18. Steve McIntyre
    Posted Nov 1, 2005 at 8:38 AM | Permalink

    Re #16: the MBH99 PC1 is upside-down as archived. Look at the WDCP website, contributors Mann, MBH99.

  19. TCO
    Posted Nov 1, 2005 at 8:59 AM | Permalink

    Yeah,

    1. I think some weighting scheme makes more sense. I don’t see why there can’t be a method that takes care of the missing polar time data while not flipping signs. And we obviously do know the sign of the stuff with reasonable physicality. I mean the tree rings were measured with a frikking ruler.

    2. I think Steve’s comments (in EE) would be more “interesting” if he tied in the GENERAL issue of flipping by PCAs and if he made some GENERAL inferences about how offcentering increases that flippability aspect. Actually as I think about it, it would be best written up as some general comments on the PCA method (in a stats methods journal) with a passing reference to the MBH and paleo work (to show that it impacts some fields). More of a generalist method note, than a “drive a stake through Mann” paper in slant.

  20. Steve McIntyre
    Posted Nov 1, 2005 at 9:26 AM | Permalink

    This post notes up an amusing article on PC-type methods. Looking back at this post, I can see that I’ve modified my posting style a lot. Now I give much longer quotations to give a better feel of the article. http://www.climateaudit.org/?p=107

  21. John Hekman
    Posted Nov 1, 2005 at 12:36 PM | Permalink

    The signal-to-noise ratio on this site is getting a bit low lately. I think that if more visitors are coming here looking for enlightenment, there should be a prominent heading that says something like “the essence of M&M”. The “What the Hockey Stick Debate is All About” article is good, but given current developments, a new summary is needed. The reader should hear a single tune, not a symphony of sounds.

    What is the one fact that you would use to get the attention of someone who reflexively believes that the hockey stick is still valid? It would be this: MBH say that their method is “robust” with respect to the different proxies they used. But M&M have shown that their result is driven almost exclusively by the bristlecones, a tiny segment of the proxy series. MBH have provided NO answer to this criticism. MBH completely contradict their claim of robustness by saying that to test the model for its sensitivity to bristlecones is to “throw away data.” END OF STORY. Their results have been shown to be unreliable to any reasonable person unless and until they can answer the bristlecone challenge. There is nothing to debate here. The challenge has gone unanswered.

  22. Jeff Norman
    Posted Nov 1, 2005 at 3:50 PM | Permalink

    “TCO has inquired about whether there is a legitimate purpose for using off-center PCs.”

    I have been wondering for some time if there might be a correlation between the way Mann used off-center PCs and the way temperature differentials are calculated.

    You cannot(*) simply take a randomly changing number of temperature records and average them together to get an overall regional, hemispheric, or global temperature trend over time because there are too many confounding biases that could impact your average (elevation, prevailing winds, seasonal impacts, large bodies of water, moves, truncations). Therefore they calculate a temperature differential.

    The individual temperatures for each time period is compared to some arbitrary average temperature for an extended arbitrary period of time to see if the temperatures were different at that time. If I recall correctly the arbitrary period of time was (at one point) 30 years between 1961 and 1990. All annual records were compared to the average annual temperatures during this period. Differential trends were averaged together using some careful weighting algorithm that compensates for relative area coverage. Or so it is claimed. I did not mention UHI.

    There are all kinds of problems with this approach (given the number of records that do not completely overlap this period or extend much beyond it), but is it not pretty much the same as using “off centered PCs” for tree rings?

    Jeff

    (*) This is actually different from the approach being taken by Junkscience were they have identified specific weather stations for use in calculating a “global average temperature” which is specific to the specified stations.

    I’ll have to read this again when I am awake.

  23. Steve McIntyre
    Posted Nov 1, 2005 at 4:16 PM | Permalink

    Re #22: Jeff, no matter how much you may complain about these averages, they don’t flip some of them upside-down if it “works” better.

    Actually MBH98 ends up doing this in its regression phase with some instrumental records. Some of the instrumental series are not hockey stick shaped and have a negative correlation to the temperature PC1. They are assigned negative weights in MBH98. Thus a high temperature for some sites in the 18th century leads to a lower reconstruction.

    It’s hard to itemize all the horrors of MBH.

  24. TCO
    Posted Nov 1, 2005 at 4:22 PM | Permalink

    Why is there a site that advocates junk science?

  25. Dave Dardinger
    Posted Nov 1, 2005 at 4:43 PM | Permalink

    re: 24 TCO,

    Surely you’ve been there, haven’t you? Clips and links to articles and papers which illustrate junk science are listed there daily and where he feels like it comments are made. Some links are also to anti-junk articles, but it’s assumed that the reader is bright enough to figure out which articles are junk and which ones point it out.

    You might argue that you see plenty of junk science just reading the paper and don’t need a Readers Digest version, but some of us don’t have as much time to find out what’s going on.

  26. TCO
    Posted Nov 1, 2005 at 4:47 PM | Permalink

    Yeah, I been there. This site is better. Plus they got all their skirts ruffled when my f***ing alpha tree rose on the scene.

  27. Jeff Norman
    Posted Nov 1, 2005 at 5:57 PM | Permalink

    Steve,

    I think I meant to suggest that the idea for “averaging” part of the tree ring data series instead of the whole data set might have been inspired by the way temperature data sets are treated.

  28. Posted Nov 1, 2005 at 6:37 PM | Permalink

    Dear Steve,

    in some sense, you are right that one uses the projective vector spaces in PCA – which means that the physical space is a quotient. You’ve convinced many of us that the MBH procedure emphasizes the hockey sticks but still, it does not have to be the only subtlety one needs to know when he tries to analyze this data.

    Maybe it’s time for you to think as a positive climate “historian” and try to develop your own method, realize your own reconstruction that actually gives more justifiable results than the magic in the literature. I hope that you are ready if you happen to obtain another hockey stick. ;-) Mann et al. have argued that even with the naive average, the bristlecones make the average look hockey-like.

    You have a lot of this data from the proxies, and you may develop a method that gives them reasonable weights etc. In your work, I am sure that you would have a control over how much different things affect the results etc.

    I am interested what data – and variability – one gets if the data is analyzed by a much more reliable person like you.

    Also, you may try to construct an anti-hockey stick argument – for example an artificial justifiable algorithm that does something to suppress the hockey sticks and bristlecones. How far from the graphs found in literature you may get? You know the RC-like people asking for models that don’t predict warming etc. I am also interested how hard it is to obtain results that look very differently.

    All the best
    Lubos

  29. Paul
    Posted Nov 1, 2005 at 9:05 PM | Permalink

    Steve,

    I’ve used PCA many times but I’ve had a hard time understanding what Mann is doing from your many descriptions here. I think of it in geometric terms. Suppose we have a lozenge shaped cloud of data points in 3D. Then the standard method is to subtract the average of the data points to move the origin to the center of the cloud. The principle component analysis would then produce an eigenvector that is along the longest extent of the cloud. The second eigenvector would be at right angles to the first and along the second widest direction, and the third PC would be at right angles to the other two. Any point in the cloud can then be described by projecting it onto the three axes formed by the eigenvectors. If the cloud is long and thin, it’s enough to project on PC1. So what’s Mann doing in these terms?

  30. TCO
    Posted Nov 1, 2005 at 9:15 PM | Permalink

    That’s (I think) what I’m used to hearing it about. Or for instance Nate Lewis at Cal Tech with the “chemical nose” that gets 14 factors of data…but then he projects it onto 3 axes which best define the overall response of his sensor. That makes sense, since your trying to get the smallest number of vectors which give you the most info. But I’m not sure why you would use it with time series or with regressions.

  31. Ross McKitrick
    Posted Nov 1, 2005 at 9:38 PM | Permalink

    Re #29: Paul, the geometric picture is a bit weak for understanding PCA since you have data in 3 dimensions and you use 3 axes, so you don’t actually reduce the dimensions. But, in terms of your example, Mann’s method doesn’t center on the origin. It repositions each observation such that the hockey stick-shaped series get placed far out to one side. Then the first PC axis is oriented to pass through those points, creating the impression that they represent the dominant pattern in the data set. It does this by centering each series on its 20th century mean and scaling by the 20th century variance. For series whose 20th century mean differs from the whole-sample mean they get preferentially placed farther from the origin, hence the preference for hockey stick series.

  32. TCO
    Posted Nov 1, 2005 at 10:00 PM | Permalink

    I think a tilted 2-d object in 3 dimensions is a better example. By extension then, you might have an object in 14-d space and you pick the 3 orthogonal vectors (or more) that best summarize the object’s shape.

  33. James Lane
    Posted Nov 1, 2005 at 11:13 PM | Permalink

    Au contraire, TCO. Ross’ summary above is by far the best conceptual explanation of the effect of the MBH non-centered PCA I’ve seen to date. Get thee to a PCA primer.

  34. TCO
    Posted Nov 1, 2005 at 11:33 PM | Permalink

    I was agreeing with him ya numskull. I’m pointing out how a 2 D object tilted in 3-d land can be analyzed to reduce the number of vectors (with the trivial case of 3 to 2). Ross didn’t like the 3 dimensions without reduction example from before.

  35. Louis Hissink
    Posted Nov 2, 2005 at 8:05 AM | Permalink

    The whole issue of PCA depends on whether the two factors are physically reasonable.

    I suspect that a PCA of cat’s legs versus dog’s legs would be signficant, and this cats = dogs.

    Mathematically this might be obscure, leading to new insights.

  36. Paul
    Posted Nov 2, 2005 at 9:58 AM | Permalink

    #31, Ross, thanks that’s a very clear explanation of what’s happening. Pictures are easier for me to understand.

    “For series whose 20th century mean differs from the whole-sample mean they get preferentially placed farther from the origin, hence the preference for hockey stick series.” I take it that to mean noise has a mean of zero but hockey stick shaped series don’t so they get placed preferentially further out on PC1 and hence larger weight. If this is the case, shouldn’t any series that has a large bump in it anywhere be treated preferentially? And why don’t series with a negative hockey stick get large negative weights? BTW, in all the series I’ve seen published on this site I’ve never seen a negative hockey stick in the raw(er) data. Don’t they exist?

  37. Paul
    Posted Nov 2, 2005 at 10:04 AM | Permalink

    Correction to #36. You said “20th century mean” so the large bump comment should be revised to a large bump in the 20th century, which could be U shaped and doesn’t have to be the blade of the hockey stick.

  38. Steve McIntyre
    Posted Nov 2, 2005 at 10:07 AM | Permalink

    Re #36: the MBH99 North American PC1 is an upside-down hockeystick. Now PCs do not intrinsically have an orientation -so hte term upside-up or upside-down doesn;t really have a meaning for a PC series. But as plotted, it’s upside-down.

    The proxy series that intrigue me the most are the records of treeline changes, and I’ve posted up some interesting examples.

  39. Posted Nov 2, 2005 at 11:18 AM | Permalink

    I find Ross’s explanation sits rather oddly with his claim that you can’t average temperatures because they are intensive variables. How can he even talk about the 20th century mean if you can’t take means of temperatures?

  40. Dave Dardinger
    Posted Nov 2, 2005 at 11:31 AM | Permalink

    Well, Tim, since Halloween is just past let me give you an example. If I made a list of witches and had one of the variables associated with each one be his/her ‘spell index’, you could surely calculate a mean spell index without necessarily agreeing that there is such a thing as the ability to cast spells. Or perhaps we could catagorize them as white witches or black witches and then calculate an average degree of grayness of witches. This wouldn’t demand that we agree that there can be such intermediate ‘colors’ for witches, would it? So I think Ross can deal with the statistical properties of something without having to agree that the result has any physical meaning.

    BTW, I’m neither in agreement or disagreement with Ross’s opinion as I haven’t read the book. It sounds dubious on the surface, but I might change my mind if I read what he had to say.

  41. Ross McKitrick
    Posted Nov 2, 2005 at 11:33 AM | Permalink

    Tim – I’m just reporting what they did with their data. No endorsement is expressed or implied. Paul – if the bump is U-shaped (ie a spoon rather than a hockey stick) the 20th century mean will depart less from the series mean than if it were a hockey stick, so it won’t get as heavily overweighted. “Why don’t series with a negative hockey stick get large negative weights?” They do.

  42. Paul
    Posted Nov 2, 2005 at 12:57 PM | Permalink

    #41. I see. The negative weight then flips the negative hockey stick so that it adds to the positive hockey sticks instead of subtracting and averaging them out. Correct?

  43. Ross McKitrick
    Posted Nov 2, 2005 at 1:14 PM | Permalink

    #42 – Yup.

  44. Steve McIntyre
    Posted Nov 2, 2005 at 1:31 PM | Permalink

    In the case of the bristlecones, the hockeysticks are all upside-up. This is a piece of information that is actually not used in the PC algorithm – yet consistency of orientation seems a pretty fundamental point in a multiproxy study.

    There are a variety of different ways that you can "get" a hockeystick shaped composite index when you’ve got the bristlecones in the mix. That’s why we’ve never said that MBH hockeystickness is simply an artifact of the PC method, although people repeatedly put those words in our mouths. There’s an interaction of data and mathods.

    People then try to say – oh, now you’re trying to change the focus from methodology to data? That’s not true either. We have been intensely focused on data from the outset – look at the dry issues in MM03. But, as we repeatedly say, if you see what the methodology does in MBH, it picks out and overweights the bristlecones – so a logical question is: if the flawed methodology picks out these proxies (which are already known to be problematic), what happens without them?

    We know the answer to this: there is no hockeystick. Mann did the calculations in his CENSORED directory and not only failed to report the adverse results, even claimed that his results were robust to the presence/absence of all dendroclimatic indicators when they knew that they were not robust if you "threw out" the bristlecones.

    This also does not mean that you can’t “get” a hockey stick shaped reconstruction using selected proxies. But then you have to show that each of the other reconstructions has not cherrypicked proxies, meets standards of statistical methodology and robustness, etc. etc.

    Gavin has censored this information in a different way. While he has let a couple of posts from me pass on to realclimate recently after we complained, he has not passed through a post about bristlecones, specifically refuting his own claim (not Mann’s) that the bristlecones could be removed and still yield a hockey stick with enough PCs. The refutation of Gavin’s comment is in the CENSORED directory. No bristlecones, no hockey stick shaped PCs. No hockey stick shaped PCs, then the 15th century reconstruction under MBH98 methods runs hot and no 20th century uniqueness.

  45. Posted Nov 2, 2005 at 2:01 PM | Permalink

    IMX the geometrical interpretation of PCA is the most useful. It makes it clear what PCA does (and does not) do: it simply selects a rotation of the underlying data, which might or might not provide you with a different perspective or insight. The rotation PCA selects puts the highest “variability” as the leading component, but transformations of the data beforehand (by ensuring zero offset, normalizing variance etc) gives different definitions of variability, which provide different rotations. This makes it easy to see when you would or would not want to center the data: if you’re not interested in the offsets, force a zero center and they will be ignored, etc. By normalizing against 20th century averages, MBH indicate that they are interested in offsets against 20th century averages. That’s their choice, it gives them a particular rotation to look at, and anyone else can choose to look at a different rotation. But because PCA simply selects a rotation, and the rotation is arbitrary, if an interpretation of the data relies on which rotation is selected, there’s something wrong. This kind of thing should come out during the fitting process.

    As an aside, the practice of PCA followed by truncation, called principal components regression, is used but isn’t that popular in multivariate calibration. In chemometrics, more typical would be PLS, which is designed precisely for where you care more about predictions than views of the data. It would also be interesting to see what a standard stepwise selection procedure ended up with. Again, though, any reasonable procedure should produce about the same answer.

  46. Steve McIntyre
    Posted Nov 2, 2005 at 2:07 PM | Permalink

    That’s where the bristlecones come in. From a PCA point of view, they are pretty much orthogonal to everything else and yield a distinct pattern – in the PC4 under a conventional algorithm and the PC1 under the MBH method (which is NOT a principal components method within Preisendorfer’s definition). The results in the regression-inversion dowwnstram of the PCA are NOT the same with and without the PC4 – even Mann agrees with this. He however characterizes any procedure without the PC4 as being “mathematically incorrect” or “throwing out data”. The results are NOT robust – that’s one of our key points.

    Does that “matter”? Well, they warranted that they were robust and people relied on that warranty.

  47. Michael Jankowski
    Posted Nov 2, 2005 at 2:08 PM | Permalink

    Re#44 – I tried to respond to Gavin’s censorship of a post of yours on RC. It’s been 24 hrs without appearing, so I assume at this point that mine has been censored entirely. Gavin’s remark in question:
    “[Response: Absent a public apology regarding your remarks about my ethics, I will not be drawn into a personal discussion with you. Discussion regarding upcoming papers is best left to after they have appeared. -gavin]”

    My post stated that I agree with Gavin’s last point. No harm done there, obviously. I guess my post went awry when I pointed out that RC has had main articles with “discussion regarding upcoming papers” concerning the satellite discrepancy, cheering at the press release of Wahl and Amman’s article submission (later rejected), etc, and that one of RC’s main contributors – Mann himself – has on a number of occasions used unpublished works as references to defend his works and attack yours.

    The inconsistency and hypocrisy is astounding.

  48. Brooks Hurd
    Posted Nov 2, 2005 at 2:48 PM | Permalink

    Steve, Ross, and others,

    Based on reading a lot on PCA, it appears to me that PCA is a poor tool for the sort of data analysis which MBH performed. If MBH had perfomed PCA on temperatures in degrees K, rather then anamolies, do you think that the results would have been different?

    I have a more basic question. What is an example PCA being used in a way where it aids the data analysis?

  49. Steve McIntyre
    Posted Nov 2, 2005 at 3:06 PM | Permalink

    Re #36: You said: “BTW, in all the series I’ve seen published on this site I’ve never seen a negative hockey stick in the raw(er) data. Don’t they exist?”

    You also have to watch what happens in the “adjusting” of the data. For example, the density data at Tornetrask declines in the 20th century. Look here as to how Briffa and Jones “adjusted” the data:
    http://www.climateaudit.org/?p=150. Or the Briffa MXD reconstruction goes down after 1960. Look at how they truncated this series at 1960 in the IPCC (and all other) spaghetti graphs.

  50. TFox
    Posted Nov 2, 2005 at 5:49 PM | Permalink

    RE #46. Any truncation is throwing out data, the question is whether that data is signal or noise, which in a calibration context is defined by how well it correlates with the training set. Any reasonable variable selection procedure ought to produce reasonably similar results, regardless of which rotation it’s handed to start with. Remind me again what variable selection procedure you’re using?

    As an aside, a geometrical interpretation removes mysteries about the changing sign — it’s just an inversion in the rotation.

  51. Ross McKitrick
    Posted Nov 2, 2005 at 6:52 PM | Permalink

    #50: The question in this case is not signal versus noise, it is whether a fraction of data known on prior grounds to be flawed should be allowed to exert a pivotal influence on the conclusions. The bristlecones were introduced in a paper by Graybill and Idso who said the growth spurt is not a temperature proxy. Subsequent papers looked at them and said the same thing. Mann put them in knowing (by his own sensitivity analysis) that they force a hockey stick-shaped result whereas the entire rest of the data set does not. The hockey stick conclusions rest on the inclusion of the bristlecones, and with their removal the conclusions of the paper unravel. This would make the results non-robust even if the bristlecones were known to be good proxies, but the fact that they’re known to be invalid as temperature proxies makes it even worse. The other way of stating it is, if you are going to allow 16 out of 400+ data series to override the conclusions, why even use the other 400 series? They’re just there for show in this case.

  52. James Lane
    Posted Nov 2, 2005 at 7:35 PM | Permalink

    #48 Brooks, PCA is used quite extensively in applied social sciences, especially psychometrics. For example, you might have respondents rate their agreement with a large battery of statments, e.g.

    “I am more a follower than a leader”
    “I feel relaxed in most social situations” etc etc.

    PCA is used to reduce such a list of statements to a set of basic underlying dimensions, or in this case hypothesised underlying personality traits.

    If you’ve ever undergone recruitment testing, you’ve been through this. Your responses asssign you a position on “introversion – extroversion’ “independent – cooperative” etc. scales. These tests would have been originally designed, in part, using PCA.

    PCA is also used extensively in market research, for example using product-attribute rating data.

    When i first came across MBH, I was quite surprised to see it deployed in a “phyiscal” science.

  53. TFox
    Posted Nov 2, 2005 at 7:42 PM | Permalink

    #51 — Do I understand this right — your variable selection procedure is based on what Graybill and Idso attributed their growth spurt to, and nothing in the statistics? Have you asked Graybill and Idso to be coauthors?

  54. James Lane
    Posted Nov 2, 2005 at 10:21 PM | Permalink

    #53 TFox, you don’t understand it right. The statistics show that the MBH reconstruction is totally dependent in the presence/absence of the bristlecones. No bristlecones, no hockeystick.

    Graybill & Idso are the guys that actually collected the bristlecone data used by Mann, and at the time ruled out the anomolous 20th century growth spurt as being due to temperature change. Graybill, sadly has passed on. Idso is not in the “warmers” camp.

    Hughes has described the 20th century growth spurt as a “mystery”. And yes, that’s the Hughes of MBH.

    So you have a situation where a 1000 year reconstuction of the planet’s climate variability is based on a handful of high altitude North American tree ring sites that nobody thinks is a valid temperature proxy in the 20th century (and there are good reasons for being suspicious of tree rings as a reliable temperature proxy in any century).

    I strongly suggest you read both of M&M’s 05 papers to put the bristlecones into context.

  55. Paul Penrose
    Posted Nov 2, 2005 at 10:27 PM | Permalink

    Re: #26
    TCO, we really don’t need that kind of language here. I’m not a wide-eyed innocent, but come on, this is a public place. Let’s not be vulgar.

  56. TFox
    Posted Nov 3, 2005 at 1:37 AM | Permalink

    Re #54. James, thanks for the suggestion to look to the papers. I can now admit to having read the GRL paper without having understood the philosophy or algorithm of variable selection it supports. To me it seemed solely concerned with the effect of differing normalization on PC1 (ie. the statement that different rotations look different, when projected down to the first dimension) without commenting on why PC1 is the only component of interest, particularly after changing rotations. I didn’t see cross validations by number of components, selection statistics, a scree plot, a decision procedure, or any of that kind of thing. While I only skimmed the E&E paper, I didn’t find anything there either. Is there a statistical, cross-validation type reasoning that I could follow? I’d appreciate a pointer. Or is it just that the bristlecones ought not to predict temperatures (even if, empirically, they seem to)?

    Thanks again,

  57. TCO
    Posted Nov 3, 2005 at 2:39 AM | Permalink

    Thanks for engaging on the issues, TFox.

  58. fFreddy
    Posted Nov 3, 2005 at 3:29 AM | Permalink

    Re #56, TFox

    Or is it just that the bristlecones ought not to predict temperatures (even if, empirically, they seem to)?

    TFox, I think the idea is that there is a weather station quite near to the bristlecone sites which provides a good observed 20th century temperature record. This record is nothing like the hockey-stick shape of the bristlecone tree rings.
    This is why everyone agrees that the bristlecones are no good as a temperature proxy : it is not based on any clever statistical treatment, just good old-fashioned observed data.
    Or am I missing your point ?

  59. James Lane
    Posted Nov 3, 2005 at 6:48 AM | Permalink

    #56 TFox – apologies, I now realise you are addressing a more specific point than I thought. I believe that you are seeking a decision rule or “philosophy of variable selection” that justifies excluding the bristlecones (for example as PC4 in the centred PCA), perhaps along the lines of a scree test, eigenvalue rule or P’s Rule N?

    To my mind the question is a little beside the point for reasons discussed above. To my mind the problem with the bristlecones is logical rather than purely statistical. However I’m sure that Steve will have a view on this, and rather than try and second-guess, I think I’ll hand-pass it to him!

  60. Steve McIntyre
    Posted Nov 3, 2005 at 9:19 AM | Permalink

    TFox: James Lane has represented our views on this accurately.

    Our objection to the MBH98 PC method is that it is wildly biased towards mining hockey stick shaped series, that this methodology was not disclosed. If you go through the ancient history of this dispute, even decoding this methodology required considerable effort. In a way, this issue is important only because it leads to the bristlecones and it’s important in several different ways than you are thinking: (1) the non-robustness of MBH results to the presence/absence of bristlecones. (2) that the bristlecone pattern is not the “dominant” component of variance as represented by MBH.

    You say:

    Or is it just that the bristlecones ought not to predict temperatures (even if, empirically, they seem to)?

    Based on the specialist literature, the bristlecones do NOT empirically predict temperature. Per Hughes, their 20th century growth is a “mystery”. Others attribute it to CO2 fertilization, but it could also be airborne nitrate fertilization, airborne phosphate fertilization (they are in nutrient deficient soils), precipitation (they are in arid climates), etc.

    They are a distinct pattern in a PC analysis but that does not make them a temperature proxy. Reconstructions relying on bristlecones have high RE statistics and ~0 cross-validation R2 statistics.

    You cen get RE reconstructions as good as MBH (actually better) by replacing bristlecones with dot.com stock prices; I’ve shown this in a post. There are important issues in the MBH regression involving spurious regression. I’ve posted some notes on this topic in August and have been meaning to pursue the matter more, but have got taken up with other issues recently.

  61. TFox
    Posted Nov 3, 2005 at 10:49 AM | Permalink

    Hi Steve,

    Thanks for taking the time with my questions, I appreciate it. So the PC/statistics argument is relevant for understanding the history, but once we’ve understood that the bristlecones are high leverage, the exact PC algorithm doesn’t matter anymore? I guess I can accept that, but then to understand the gist of the story, I think I need to hear more about bristlecones.

    You write:

    the bristlecones do NOT empirically predict temperature

    I’ll have to take the word of the experts for the reasons bristlecones are useless, but I still haven’t seen a clear demonstration their lack of utility. My apologies in advance if this has been covered time and again. By how much do cross-validations improve when bristlecones are left out?

    Thanks again,

  62. Brooks Hurd
    Posted Nov 3, 2005 at 6:36 PM | Permalink

    Re: 52,
    James,
    Thanks for the explanation.

  63. Steve McIntyre
    Posted Nov 3, 2005 at 7:25 PM | Permalink

    TFOx, the issue of CO2 fertilization was cited in IPCC [1996] as an issue as well. So they shouldn’t have adopted a series dominated by the type CO2-fertilization series through the backdoor.

    As to statistics, it depends on the statistic. The cross-validation R2 is about 0 with or without the bristlecones, but the RE statistic increases. We’ve shown that it’s easy to get spurious RE statistics. Some of the underlying statistics on RE (which is a quirky statistic) presume that it is necessarily less than the R2 statistic – which is not the case here, but not discussed in MBH98.

    You have very high autocorrelation in the bristlecone PC (the MBH98 PC1 or covariance PC4) and in the temperature PC1. You have a high calibration period correlation between the bristlecone PC (also the non-updated Gaspe cedar series) and the temperature PC1, but not to the gridcell temperature series. The regressions in the calibration step have all the hallmarks of a spurious regression.

    My other big beef with the bristlecones is robustness: Mann said that his reconstruction was robust to the presence/absence of ALL dendroclimatic indicators, but it’s not robust to the presence/absence of bristlecones. He knew this because he studied this case in the BACKTO_1400-CENSORED directory.

  64. TCO
    Posted Nov 3, 2005 at 10:42 PM | Permalink

    I think there is more of a methods issue than is being addressed. that’s because there are so many bristlecone series, that they are overweighted even in a pure average. In an area-weighted pure average, they would not be.

  65. TCO
    Posted Nov 3, 2005 at 10:55 PM | Permalink

    Paul Penrose, sorry–I was drinking.

  66. Steve McIntyre
    Posted Nov 3, 2005 at 11:20 PM | Permalink

    Re #64: TCO, if they are no good as a temperature proxy, why use them? Any valid result should be robust to their exclusion and not provoke hysteria about “throwing out data”.

  67. TCO
    Posted Nov 3, 2005 at 11:36 PM | Permalink

    They map the global field. hehe! ;-)

  68. TFox
    Posted Nov 4, 2005 at 8:56 AM | Permalink

    Re #63. Thanks for that data, Steve. These cross-validation numbers are based on the temperature reconstructions either with or without bristlecones, right? Is this calculation still based on a truncated PC series, or does it include everything (except with or without bristlecones)?

    Thanks!

  69. Paul Penrose
    Posted Nov 4, 2005 at 7:16 PM | Permalink

    TCO,

    Ah, PWI (posting while intoxicated)! Probably shouldn’t post after drinking those “adult beverages”. Don’t sweat it – unless you make it a habit.

  70. TCO
    Posted Nov 5, 2005 at 8:53 PM | Permalink

    I have PWIed a lot. I’ve just been sober (relatively so) for last 3 months.

  71. TFox
    Posted Nov 8, 2005 at 7:27 PM | Permalink

    Hm, no answer to #68. I guess if I can’t understand the story from the published papers, and questions go unanswered, I’ll have to wait until new experts are convinced, and maybe one of them can explain it to me.

    Just to make it clear where I get lost: I’m having a hard time understanding what is meant by statements like “bristlecones empirically do not predict temperatures”. If they don’t predict temperatures, then cross-validations should improve without them, and the reconstructed temperatures will be essentially unaffected by their inclusion or exclusion. Since (as I understand it) this isn’t the case, I think that the term “predict” is being used in some sense I’m not familiar with.

  72. John A
    Posted Nov 8, 2005 at 8:06 PM | Permalink

    TFox,

    Steve is travelling at the moment. If you could wait a few days, I’m sure Steve will respond.

  73. TCO
    Posted Nov 8, 2005 at 9:10 PM | Permalink

    Tfox (Steve really knows this stuff and please hold his ass to the fire for answers). I think part of the issue is that the bristlecones have not been independantly (for instance in a lab or controlled field studies) been shown to correspond to temp. Also, even now, they don’t vary with the actual closest temp readings. Instead, they according to Mann mimic the “global climate field”. That just seems bizarre to me.

    I’m not sure what you mean by the cross-validation statistics and effect of leaving the cones out. Could you elucidate for simple me. Serious.

  74. James Lane
    Posted Nov 10, 2005 at 2:46 AM | Permalink

    TFox,

    I’m also struggling to understand what you mean by cross-validation in this context.

    Also, we seem to have a semantic problem here. You introduced the word “predict” in post #56. The bristleconces do not “predict anything”. They’re being touted as a proxy i.e. wide tree ring = warm, narrow tree ring = cold. Thus they are being used to reconstruct past temeratures.

    There are all number of problems with TRs generally as temperature proxies, because ring width is influenced by a number of factors, especially precipitation. Also, it is possible that many species have an “optimum” temperature for ring growth, making the response to temperature U-shaped around that optimum.

    The problem with the bristlecones is more specific. The hockeystick “demonstrates” a dramatic rise in temperature from the late 19th century, driven by the bristlecones, which exhibit dramatic ring growth in the 20th century. However nobody in the literature believes that that growth spurt is due to temperature. Finally, if you take out the bristlecones, the hockeystick in the reconstruction disappears. I don’t think I can make it clearer than that.

    (The bristlecones also inluence aspects of the reconstruction further back – with out them the 14th-15th century is warmer.)

    Finally, reading between the lines, I think you might have got the wrong end of the stick on another part of the argument. Steve and Ross don’t argue that the reconstruction without the bristlecones for the “handle” of the hockeystick is “better” than MBH – they conclude that they both fail. This point is consistently misrepresented over at realclimate. Steve is currently developing a more general case against the paleo-proxy reconstruction papers.

    Hope that helps. I’m sure Steve wil reply to your post when he gets back, but in the meantime it might be helpful if you clarify what you mean by cross-validation in this context. Cheers.

  75. Jean S
    Posted Nov 19, 2005 at 9:01 AM | Permalink

    The Mann himself is teaching PCA in March, see Data Analysis in the Atmospheric Sciences. Maybe some “skeptics” should attend to see how PCA is done “right” :)

  76. McCall
    Posted Nov 19, 2005 at 11:06 AM | Permalink

    It’s hard for me to believe that Dr. Mann hasn’t become a better and wiser teacher during this intense debate. Given the visible and well-documented criticisms of his early PCA methodology, I believe this class would be a fair synthesis of generally accepted methods and practices — interesting too! At worst, I would hope that it’s not a example of “burn me once …?”

  77. McCall
    Posted Nov 19, 2005 at 11:19 AM | Permalink

    I am disturbed to see an editorial(?) position to “limit skeptic press coverage,” over on RC. Other than the obvious “big brother” issues, it begs the question of whether a mathematical/statistical criticism of a paper make one a skeptic, or a critical mathematician/statitician?

    http://www.realclimate.org/index.php?p=218#more-218

    Since Dr. Mann appears to be leading/authoring much of the imbalanced topic post and some of the comments, perhaps I should reassess my more balanced and hopeful outlook for his course.

  78. Dave Dardinger
    Posted Nov 19, 2005 at 11:24 AM | Permalink

    re #76

    I don’t know. One would have thought that Dan Rather and Mary Mapes would have learned something about how to judge whether a document is fake or not, but they still somehow believe the Rathergate documents are legit.

    If Mann does too good a job on PCA isn’t it likely to to reflect negatively on his own early work?

  79. TFox
    Posted Nov 21, 2005 at 5:30 PM | Permalink

    Re #74,

    Hi James,

    I believe I’m using the phrases “predict” and “cross-validation” in their ordinary senses in multiple regression. I’m data-oriented: the reasoning you provide about why tree rings ought not predict temperatures is what I’d call a hypothesis, something to evaluated by testing against the data. Thus the importance of cross-validation procedures and prediction statistics against thermometers. I believe the hockey stick consensus is that cross-validations improve with bristlecones; I have not seen clear statements on this from the skeptics. The clearest statement I’ve seen is comment #63 on this thread; unfortunately, the numbers provided seem to support the opposite conclusion to the one being drawn, so I’m still not sure that I understand the position being taken. I also don’t understand your comment that M&M do not believe their technique superior — if it doesn’t matter, why the seven-year quest? Perhaps the future publications Steve is working on will clarify the story.

  80. Steve McIntyre
    Posted Nov 21, 2005 at 5:43 PM | Permalink

    Re #79: I’m writing on my account. If you feel that I’ve been unclear, please feel free to blame me rather than some omnibus term like “skeptics”.

    Mann and Wahl-Ammann say that the RE statistic increases if you use bristlecones; this is true. However cross-validation “statistics” do not improve in general, as the R2 and other statistics DO NOT IMPROVE. We’ve stated this quite clearly. If you use dot.com stock prices, you also improve the RE statistic – this does not demonstrate that dot.com stock prices are a valid proxy. We’ve also shown that you im[prove the RE statistic using PC1s simulated from red noise using the erroneous Mann method. So just because the addition of bristlecones increases the RE statistic, it does not increase cross-validation statistics across the board and is simply “spurious” in the statistical sense that I’ve used in a number of posts, as opposed to Mann’s use of “spurious” as a debating adjective.

    I don’t know what you mean by the “M&M technique”. We’ve never presented a reconstruction as being “our” reconstruction.

  81. TFox
    Posted Nov 21, 2005 at 5:58 PM | Permalink

    Re #73,

    Hi TCO,

    If you haven’t already, you might find it interesting to work through some material on multiple regression and variable selection. I like the discussion in Draper and Smith, _Applied Regression Analysis_. If it’s got to be free, Julian Faraway has a web book using R at http://www.stat.lsa.umich.edu/~faraway/book/.
    For discussions of cross-validation and similar issues, you may find the PLS literature helpful, as PLS has the same need to select variable after the transformation. One entrypoint is a nice little review from SAS called An Introduction to Partial Least Squares.

    Have fun, it’s an interesting area.

    And oh, one final comment about your original question about off-center PCA. In comment #45, I said why I thought off-center PCA could make intuitive geometrical sense, and could well be useful in certain circumstances. If you prefer literature references, check out the discussion in Edmund R. Malinowski, _Factor Analysis in Chemistry_ (which I skimmed for free on Amazon). A variety of normalizations are discussed, including off-center ones. They aren’t seen as novel or unusual, and the literature reference provided is thirty years old.

  82. TCO
    Posted Nov 21, 2005 at 6:23 PM | Permalink

    I think the point about “standardness” has to do with adequate description of the methodology by Mann. He did not tell anyone how he had done the calculation (making his math unreapetable). Other than that “standardness” is a semantic argument.

    WRT its effect on correlations. Are you stating affirmatively that it does not have a distortive effect?

  83. TCO
    Posted Nov 21, 2005 at 6:23 PM | Permalink

    P.s. I will check out the refs. Takes me a while though. But hold me to it…

  84. TCO
    Posted Nov 21, 2005 at 6:26 PM | Permalink

    Re #79, this is either tendentious or stupid. I can show that proof of a geometric thereom has a flaw without having my own proof of the thereom. Are you really not understanding this point?

  85. Steve McIntyre
    Posted Nov 21, 2005 at 6:29 PM | Permalink

    TFox – the citations for uncentered methods tend to be about 30 years old; there were some discussions in ecology. However, in time series applications for meteorology and climate, centering is assumed (per Preisendorfer discussions) and this is what Mann cited. Mann acknowledges in a post at realclimate that centering is “standard”. But as TCO says, “standardness” is ultimately semantic; the real issue is the effect of the method which in the present circumstances is to mine for hockey stick shaped series. If you are INTENTIONALLY applying this methodology, you need to declare it and attach warning labels, not hide it. If he’d declared in advance that he was using a non-standard PC methodology that mined for hockeysticks, surely someone would have raised a question about it long ago.

  86. TCO
    Posted Nov 21, 2005 at 6:34 PM | Permalink

    Even if he’d called it standard, and not made the mining comment…if he’d just said that he’d done it off-center. That would have been how you properly write a paper and show your method. Remember, this is a mathematical paper!

  87. TFox
    Posted Nov 22, 2005 at 12:10 PM | Permalink

    Re #83 and #84,

    Hi TCO,
    Please work through the variable selection references, see if your comments make sense in those contexts, and then come back to paleoclimate. You include a variable or you don’t; it’s a binary choice.

    Hi Steve,

    I’m going to give up here, without ever really understanding your point. I think that in order to make progress in communicating with people like me, you will need to stake out a clear, affirmative position about paleoclimate reconstructions. You’ll have to start with standards for data acquisition and selection, lay out and justify in detail the data analysis procedures you advocate, carry it through and produce the best reconstruction you think can be made with the available data, compare it to other reconstructions, identify and analyze the differences, and put the new work into the context of what’s known about climate; past, present, and future. Once two (or more) alternatives are on the table, it’s possible to discuss them and make progress; until then, it’s not.

    Just to tell you my story: I came to this topic because I’d understood (not from anything you said, of course) that the entire case for AGW rested on a single, unreplicated paleoclimate study which itself was fatally flawed by a coding error. Since then, I’ve learned that many groups have gotten similar results from a variety of data sources with a variety of methods, that the “coding error” is rather a question of fashions in PCA centering, and that no one thinks paleoclimate is relevant to AGW anyway. Given the story I was first told, this is all kind of a shock, and given that my interest is in climate policy not ancient trees, my attention is waning. Nevertheless, I’ll be interested to read about your reconstruction when it appears.

    Thank you for your time, attention, and willingness to answer questions. I wish you every success in your work.

  88. Paul
    Posted Nov 22, 2005 at 2:05 PM | Permalink

    TFox,

    You’re asking much from Steve…and I don’t think you’ve grasped all of what’s happening with Steve’s work. I’m going to attempt to summerize what I’ve learned on this site. I’m sure others will correct me if my understanding is incorrect.

    First, Steve saw the hockey stick and said “My! That’s interesting. I wonder how they got that.” So, he started to do some digging. First, he ran into the problem that Mann didn’t want to give him the data OR the code. I’m sure there were some red flags for Steve when Mann doesn’t just hand over the stuff.

    Second, Steve started delving into what Mann did. First, he found some interesting things happening, which are to be found in his and Ross’s paper. There were apparent “code errors” (which in reality appear to be non-standard methods).

    Third, Steve started looking at what the proxies were, and why they were selected. This was in relation to trying to figure out how Mann had got his hockey stick. He discovered that not only did Mann’s methods mine for hockey sticks (even using red noise) but that if he pulled out a particular proxy (the bristlecone pines), the hockeystick virtually disappeared. Why would he remove the bristlecone pines? Because they’re not a good temperature proxy. What about the other proxies? Apparently, there are issues with most of the proxies used by Mann & the rest of the hockey team.

    The discussion is more than just a about PCA centering methods, but about the validity of the code and the proxies. Searching this site will show that there are all sorts of questions regarding proxies and their validity. It appears that many, if not most, of the paleoclimate studies are based on the same proxies which all have issues. It’s no longer about a single flawed study.

    The next issue is if the past is of any importance to the future. The proponents of AGW say that our creation of 2xCO2 is the cause. The “skeptics” say “Hold on! The earth as been warmer in the past. Why? Is it a function of CO2? If so, why did CO2 rise in the past? If not, what was it? Are those same things causing the perceived warming today?” I think most “skeptics” would say that if there was strong evidence that AWG is happening, they might also be able to say that we might need to do something about it (this begs the questions of “what is the ‘correct’ temperature for the earth?” or even “is a warmer earth a bad thing?”).

    Is Steve going to do a “reconstruction?” I don’t think so. I don’t think he has confidence in the proxies. Until there is robust data, there’s not much of a point in reconstructing it? It’s like re-building a house on fractured footings. The second house won’t stand any better than the first one did.

  89. Peter Hearnden
    Posted Nov 22, 2005 at 2:17 PM | Permalink

    Paul, how can you both know the recons are wrong and also know it, the earth, was warmer in the past [1000/2000 years I presume]? Is there some undisclosed recon only you have access to? Or is it your view of the bit’s and pieces of data you like the look of? Probably.

    The correct temperature of the earth is the one minus our bu**ering up of it’s atmosphere’s properties. Not much yet, more to come though.

  90. andre bijkerk
    Posted Nov 22, 2005 at 2:42 PM | Permalink

    Hi Peter

    Don’t you think that finding hippo and turtle fossils in the Thames, dated roughly 100,000 years wouldn’t that be a little hint that the UK was a wee bit warmer back then?

  91. Brooks Hurd
    Posted Nov 22, 2005 at 3:08 PM | Permalink

    Peter,

    All the multi-proxy reconstructions can not be correct because there are differences between them. Some of them are no doubt correct, where as some of them are off a bit. Some of the reconstructions may show local conditions and others may show global conditions.

    I find it hard to accept the AGW proponents who toss out every multi-proxy reconstruction that differs from their notion of paleoclimatology as being local not global. This is particularly hard for me to accept when I can see raw data from the other studies, but not from the AGW proponents’ “global” climate reconstructions.

    Personally, I am a crusty old engineer who wants to see the data. When people are not forthright about providing the data to support their positions, I have to ask why?

  92. Paul
    Posted Nov 22, 2005 at 4:41 PM | Permalink

    RE #89: Peter,

    I don’t know anything. That’s the point. The more information about the proxies that comes out, the more information about how temperature reconstructions comes out, the less I trust things. I have no proxies or reconstructions hidden…but those proxies that are available are suspect – bristlecones, Polar Urals, ice cores, glaciers…none appear to be robust enough proxies.

    One other issue: What is the “correct” temperature for the earth to be?

  93. TCO
    Posted Nov 22, 2005 at 6:59 PM | Permalink

    Tfox, I looked through the refs. Not clear what you wanted me to get from them. How do they connect to time series measurements with proxies? the spectrum paper was not at all evident that they had the same sort of problem. Not really disagreeing…yet. Just asking what I’m supposed to get out?

  94. Peter Hearnden
    Posted Nov 23, 2005 at 3:28 AM | Permalink

    Re #90, locally that proxy might well indicate that, but globally? Nah, you’d need a (wait for it, easy boys…), recon based on many proxies then and, well you all know what you all think about them!

  95. Peter Hearnden
    Posted Nov 23, 2005 at 3:35 AM | Permalink

    Re #91, Brooks, I want to be an engineer becuase I don’t trust what you lot ‘the engineering team’ put out – I think it’s propaganda – probably commie led ;). Please send me ALL the data you have on engineering. If you don’t respond to this very resonable request, and despite me being an rank amateur, I’m going to cast aspersions on your integrity and call you a commie (LOL again). Don’t dally either, the same response will ensue. Just what have you to hide? Send me ALL you data, (we can arrange e mail contacts I’m sure) every bit – I demand you do! ;)

  96. TCO
    Posted Nov 23, 2005 at 5:52 AM | Permalink

    How do you know something is a valid proxy, Peter? How do you validate and calibrate it, before using it in your compendium?

  97. Peter Hearnden
    Posted Nov 23, 2005 at 7:33 AM | Permalink

    Tco, for those promoting the views of this blog it seem to me you validate it by asking ‘does it suit my ends’ if it does you accept it, if it doesn’t you dismiss it. Since most proxies of the recent past don’t suit this places ends, most get dismissed. Proixies that show the recent or more distant past to be warmer than now are OK though :). See several post’s in this blog for examples.

    Me? I honestly don’t think I’m qualified to decide. Ask a climatologist if you really want to know :)

  98. Dave Dardinger
    Posted Nov 23, 2005 at 7:43 AM | Permalink

    re#45

    Uh, Peter, why is asking for the data / methods used to produce a particular result equilivent to asking for everything a person knows on a subject? I’m afraid your tour de farce is too typical of your failure to understand the problem under discussion.

  99. Peter Hearnden
    Posted Nov 23, 2005 at 7:51 AM | Permalink

    Dave, you take things a bit too literally. However, if Brooks want me to stick to one piece of work he’s produced as an engineer, then I’m sure he wont mind if we go through all the work relevant to that piece of work (details of which I presume he’s kept), and publically. I mean, what would he (or for that matter you) have to hide?

    Oh, and surely you’ve noticed this site has gone just a teeny weeny bit beyond asking for the data and methods of one M. Mann?

  100. Peter Hearnden
    Posted Nov 23, 2005 at 10:47 AM | Permalink

    Re #100 TCO, my answer in #97 was honest. I think, given my knowledge (and I’m most certainly not a qualified meteorologist or climatologist – they’re not interested in CA) that the experts have it about right. I certainly don’t think I know better than them – as most here seem to. Again, imo, you need to ask the experts.

    Now, is, imo, everything M. Mann or any of the rest of them produce without error, faultess, perfect, the last word? Of course not! Are they dishonest, lefties, greenies, or even, LOL, commies? NO they are not! But my view is the general idea the recons give is, despite all the bruhaha, standing the test of time. ATM it’s warm, it’s almost certainly historically warm, and it’s most likely going to get warmer – perhaps a lot. Nothing else adds up.

  101. McCall
    Posted Nov 24, 2005 at 2:12 AM | Permalink

    ATM it’s warm, it’s almost certainly historically warm, and it’s most likely going to get warmer – perhaps a lot. Nothing else adds up.

    One has one of two choices for reply to 101:
    1) Very scientific — so what do you remember most in our warm summer of 1998, when you were 3?
    2) At your advanced age, it’s nice to know faith has become such a big part of your life. Like Mr. Dano, you’re mathematically and scientifically unprepared to understand what is an essentially statistical critique of MBH by M&M (exception: M&M’s BCP vs. temp proxy criticism); from which I can only say, “see you in church!”

  102. Posted Nov 24, 2005 at 3:09 AM | Permalink

    ftp://ftp.ncdc.noaa.gov/pub/data/paleo/contributions_by_author/oerlemans2005/oerlemans2005.txt

    ORIGINAL REFERENCE: Oerlemans, J. 2005.
    Extracting a Climate Signal from 169 Glacier Records.
    Science, Vol. 308, No. 5722, pp. 675-677, 29 April 2005.

    ABSTRACT:
    I constructed a temperature history for different parts of the world
    from 169 glacier length records. Using a first-order theory of glacier
    dynamics, I related changes in glacier length to changes in temperature.
    The derived temperature histories are fully independent of proxy and
    instrumental data used in earlier reconstructions. Moderate global
    warming started in the middle of the 19th century. The reconstructed
    warming in the first half of the 20th century is 0.5 kelvin.
    This warming was notably coherent over the globe. The warming signals
    from glaciers at low and high elevations appear to be very similar.

  103. Peter Hearnden
    Posted Nov 24, 2005 at 5:40 AM | Permalink

    Re #102. Nice ad homs.

  104. TCO
    Posted Nov 24, 2005 at 5:47 AM | Permalink

    They’re not ad homs. He’s making the point that the criticism of the proxies is statistical. They are involved and statistical to start with. So examination of them must be statistical in nature.

    I also wonder if you are confusing looking at how we have warmed over last 100 years (when we had instruments) with warming relative to times when we did not. To look at those historical times, you have to use proxies. Meaning you have to look at quality and relevance of proxies and the statistics and all that.

  105. Peter Hearnden
    Posted Nov 24, 2005 at 6:10 AM | Permalink

    Well, OK TCO, little boy, then you just have faith you’re right and this place is YOUR church? Such slinging gets us nowhere.

    Whatever, I think the recons have it about right. Otoh I think most here are desperate for them to be wrong and are only looking for problems. They’re looking for anything, however minor, wrong with the recons not what’s right or how to advance them (remember what science is?). NO ONE is claiming the recons are perfect, I’d say they’re on the right lines and I’m not convinced we can dismiss it as being very warm atm, indeed I think the evidence that it is very warm atm is good.

    But, you don’t have faith do you ;) SO presumably you don’t dismiss all the proxies that show it to be colder over the last couple of millenia but accept all the ones to show it to be warmer. Perhaps…

  106. TCO
    Posted Nov 24, 2005 at 6:29 AM | Permalink

    You’re weaving man…

  107. Dave Dardinger
    Posted Nov 24, 2005 at 7:25 AM | Permalink

    re:#103

    Hans, does this paper show the correspondence with local temperatures? And does it take into consideration precipitation? AFAIK glacier length is a function of both temperature and precipitation.

  108. Steve McIntyre
    Posted Nov 24, 2005 at 8:51 AM | Permalink

    Peter, I have not requested any data that should not have been archived in the first place either under NSF policies or journal policies. When I’ve suggested to non-Hockey Team scientists to archive unarchived data (and I’ve had such correspondence with Hughen and Kameda for example), they have promptly and courteously archived their data at WDCP. My issues pertain to a small core of scientists (the Hockey Team) who produce these multiproxy studies.

    The justification of my requests is indicated by the fact that any requests that I’ve made to journals have in nearly all cases so far led to the recognition by the journal of a problem and an attempt by them to obtain more data from the authors, with varying degrees of success. I have not had any luck so far with NSF, but I think that NSF will ultimately be forced to change its practices.

    I realize that these people like to say tht they should not have to deal with an “amateur”. But that’s not the issue. They should have buttoned everything up when they did it. For what it’s worth, now that I’m an invited IPCC 4AR reviewer, do you think that means that I’ve lost my “amateur” status and that requests for data should no longer be a problem?

  109. Posted Nov 24, 2005 at 9:09 AM | Permalink

    re # 108
    Hans Oerlemans is a leading expert on glacier mass balance so I assume he takes precipitation into account.

  110. Paul
    Posted Nov 24, 2005 at 10:46 AM | Permalink

    Peter,

    You’re still ducking most of the questions. You result to “ask the experts” (#101), which is weak…as the opinion of the “experts” is what is being debated.

    You argue that warming is very well documented. The problem is that it isn’t very well documented. We have some evidence of warming. And, we still have the issue as to the cause of the warming. Is it because I love my SUV and chainsaw and snow blower (alas, haven’t had a chance to use it…and this morning when I woke up, it was -13C, so as for it being a “warmer” winter, I’m reserving judgement)?

    Peter, the challenge is learning what happened in the past, the cause and then is that same cause active today? Is this warming part of a geologic cycle? Is it caused by man? Is the warming and 2xCO2 a coincidence or is there a cause & effect relationship? The AWG crowd has convinced most the politicians on the plant that there is a relationship. But there is no evidence of this. We have theory, we have conjecture, we have flawed proxie studies, we have lots of things, but we don’t have evidence that human activity is causing the apparent warming trend.

    Let’s keep studying it, but let’s not make global policy based on preliminary, inconclusive science.

  111. Peter Hearnden
    Posted Nov 24, 2005 at 4:04 PM | Permalink

    Re #111. Paul, I ‘duck’ because *I’m* not going to pretend to be an expert when I’m not. I’ll give you one thing though, you’re good at patronising comments.

    There IS plenty of evidence of of the human pertubation of climate, and it’s plain as a pikestaff the extra CO2 is anthropogenic in origin – do some ruddy background reading!

  112. TCO
    Posted Nov 24, 2005 at 8:47 PM | Permalink

    Pete, I don’t “pretend” to be an expert. But I do try to think through things and question them. That is part of the critical thinking of being a good Ph.D., heck of being a good B.S.

  113. Peter Hearnden
    Posted Nov 25, 2005 at 3:50 AM | Permalink

    Re #113, and, TCO, part of what goes on here is to try and implant the idea people like me don’t do the same…

  114. David H
    Posted Nov 25, 2005 at 6:38 AM | Permalink

    Re 109 Steve, I’ve written to Mr Morley asking him to give you key to the Soap cupboard but I would not hold your breath.

  115. Brooks Hurd
    Posted Nov 25, 2005 at 12:30 PM | Permalink

    Peter,

    I would be happy to send you data on one of the topics that I have discussed on this site. Trace gas analysis. I have a very good understanding of this subject and therefore I have lots of data. Just provide me your email address or an FTP site.

    Saying that you don’t trust engineers is building a nice straw man. Engineers display their successes and also their failures. They will provide the data and their methodolgies that led to their designs. When an engineering design fails, it is studied to find out what happened so that future designs can be improved. All engineering assumptions are constantly questioned. Climate scientists operate in much different ways.

    I still can not understand why so many in climate science want to keep their data and methods secret. Furthermore, I can not understand how they can maintain this attitude and continue to be published in peer reviewed journals with data archiving policies.

    Most of the people working in climate science could not show you a “success” because their work produces predictions which can not be verified for many years. We know of the many failures of climate models to predict recent climatic events, but we are told not to worry because the new models have all the problems fixed.

    Many of the people in climate science continue using the same methodologies long after people have pointed out problems with them. The explanation as to why they continue using flawed techniques because “they have always done it that way” can hardly be considered scientific.

    Have you seen any indication of the climate science community testing some of their basic assumptions? Here are two key assumptions: Many proxies are assumed to be good temperature indicators. Ice core CO2 measurements assume that all gas is trapped in bubbles. Can you direct me to any studies which test the validity of these assumptions? If these two assumptions are not substantially correct, then the AGW arguments become very weak.

  116. TCO
    Posted Nov 25, 2005 at 1:08 PM | Permalink

    Which is it, Pete? If we say that you don’t (with a sneer on our face), we’re mean and wrong. But when you say that you do, it’s ok? I mean seriously, you got me confused. Leave aside the positive or negative connotations. To what extent are you deferring to expertise and to what extent trying to understand and examine the claims and think them through? I’m not even saying one is right or wrong…

    BTW, you gotta give Steve-O some credit for a math brain…and willingness to dig into things and think and try to get right math answer…and share the details, gorey and otherwise, with the hoi palloi, no? Steve is the type of teacher that I always had in the sciences in HS and College. The RC style thing is bizarre to me. And even weirder coming from liberals as I remember the liberals in HS and College being very geared to complete freedom and let it all hangout discussion.

  117. Allan Ames
    Posted Mar 24, 2007 at 1:46 PM | Permalink

    For PC analysis, try transforming to ranks.
    I think this solves the red noise problem,
    and guarantees centering.

  118. Posted Feb 19, 2010 at 6:10 PM | Permalink

    thank for this great contribution to knowledge

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