Another Interesting Correlation Graphic

In my last post, I observed an interesting bimodality which almost certainly appears to originate in Mann’s pick two procedure on low-correlation tree ring networks. Some readers may recall the interesting bimodal distribution that we reported in MM 2005 (GRL); the introduction of bimodality into a distribution seems like a sure sign of a picking operation like the absmax procedure (“pick two”).

The next graphic shows a further remarkable bimodal aspect to Mann’s correlation coefficients – this time, we’re dipping our toes in the murky waters of “low frequency” correlations. The x-marginal distribution is the rtable correlation (“high frequency”) calculated in a usual method (given Mannian RegEMed proxies and temperatures); the y-marginal distribution are the rtable “low frequency” correlations, calculated after smoothing somehow. (See also Matt Briggs’ recent thoughts on this.) I’ve color coded this to show the truncated Briffa correlations in green and the ring width correlations in red and orange – red showing ones that in the Passing 484, orange are Failing. Some points we’ve already noted e.g. the very high reported correlations of the truncated Briffa data. We also previously observed the bimodality of the high-frequency rtable) correlations which I am currently attributing primarily to the pick two effect.

The new point here is that the bifurcation of the low-frequency correlations is noticeably more pronounced than the bifurcation of the high-frequency distributions. I presume that this is related somehow to the Slutsky-Yule effect (a well-known effect in economics time series, where repeated averaging makes series increasingly sinusoidal), but I’m still experimenting. For now, I merely observe that these bifurcated distributions are definitely not the sort of thing that you want to see in sound statistical practice and that there is an eerie deja vu developing, since we’ve already seen weird bifurcated distributions in connection with MBH that even Jolliffe hasn’t grappled with.

This is the same plot for the odds-and-ends series (only 104 of them). At a first glance, the relation between low-freq and total correlation seems straightforwardly linear, but when you look at the x- and y- marginal distributions, you see that the y-distribution (low-freq) has developed a noticeable bimodality not present in the x-distribution.


10 Comments

  1. Steve McIntyre
    Posted Sep 25, 2008 at 12:32 PM | Permalink

    A further example on this. Yule 1926 calculated correlations between sine series sampled more frequently than their period, but with random displacement one to another. The correlation distribution was strongly bimodal as shown below. (This is the famous paper on spurious regression with the example relating C of E marriages to mortality – one which has remarkable RE statistics (so I guess it must be a validated relationship [Wahl and Ammann 2007].

  2. Posted Sep 25, 2008 at 2:51 PM | Permalink

    The pick-two effect should be present at both high and low frequencies. The apparent difference may just be due to the size of the histogram bins, relative to the spread of the correlations. The high-frequence correlations have a higher sample size, and hence a tighter distribution. If the high freq. bins were made proportionately smaller, they might show similar bimodality, especially for the TR graph.

  3. stan
    Posted Sep 25, 2008 at 7:42 PM | Permalink

    I suppose you have seen this, but just wanted to pass it on in case you haven’t. http://www.projo.com/news/content/URI_Honors_Colloquium_25_09-25-08_LUBN73R_v12.1607f3c.html

    Mann doesn’t seem to like you.

  4. Posted Sep 25, 2008 at 9:46 PM | Permalink

    Stan #3 quotes the Providence (RI) Journal to the effect,

    Michael E. Mann, a Nobel Prize-winning scientist, had just spent an hour explaining why he thinks there is virtual scientific consensus that people are causing the earth to warm and sea levels to rise, when a self-described “left-leaning, pro-environment person,” a meteorologist, rose to angrily dispute him.

    Umm, Al Gore won a Nobel Peace Prize for passing Mann’s HS off as Lonnie Thompson’s Ice Core data. But that’s not quite equivalent to Mann having won a Nobel Prize himself. Or did I miss something?

  5. sean egan
    Posted Sep 26, 2008 at 12:32 AM | Permalink

    What is RegEMed and can we add it to the list of Common Acronyms used on this blog.
    Are there any onff island uses/references

    • Jean S
      Posted Sep 26, 2008 at 1:47 AM | Permalink

      Re: sean egan (#5),
      RegEM stands for “Regularized EM algorithm” by Tapio Schneider, see here. Not that I’m aware of.

      The problem with RegEM is that very little is known of its properties. However, one should stress that again (see old posts in CA and check publications here) Mann is using a modified version of RegEM as I observed here. If I were Tapio Schneider, I’d be quick to check that this unreported modification does not change the intended behavior of the algorithm…

  6. Arthur Dent
    Posted Sep 26, 2008 at 1:44 AM | Permalink

    Note that the IPCC won the Nobel Prize and I have seen many contributers to the IPCC referred to as ‘Nobel Prize Winners. Just another way of dumbing down the Nobel prize.

  7. Steve McIntyre
    Posted Sep 26, 2008 at 4:34 AM | Permalink

    a Nobel Prize-winning scientist

    Isn’t the proprietor of Climate Audit a “co-winner” of whatever prize that Michael Mann won? Maybe we can have a parade together.

  8. Pete Stroud
    Posted Sep 26, 2008 at 5:00 AM | Permalink

    Surely Mann’s defence of Gore’s snows of Kilimanjaro claptrap that was judged completely erroneous by a British high court judge, must make even a rabid alarmist doubt the ‘Nobel Laureate’s’ scientific competence.

  9. ChrisJ
    Posted Sep 27, 2008 at 12:23 PM | Permalink

    Sidebar- Could some explain the meaning of the bi-modality? Thanks. -chris

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