How many narcissists does it take to change a light bulb?
Just one — but he has to wait for the whole world to revolve around him.
Blog watchers would have noticed a post at ClimateAudit where Steve has reprinted a comment by Ian Jolliffe on the form of PCA (decentered) used way back in 1998 by Mann et al. in the original hockey stick papers. (If you don’t understand all that you have some background reading at CA for homework.)
In a numerate science, statistical methods are standard, commonly applied and understood. Instead, Mann and cohorts represent at trend in environmental modeling that believes environmental science consists of creating and promoting the most obtuse methods to further their theories. Hence the joke above.
Apologies if this is not the correct place to make these comments. I am a complete newcomer to this largely anonymous mode of communication. I’d be grateful if my comments could be displayed wherever it is appropriate for them to appear.
It has recently come to my notice that on the following website, tamino.wordpress.com/2008/03/06/pca-part-4-non-centered-hockey-sticks/ .. , my views have been misrepresented, and I would therefore like to correct any wrong impression that has been given.
An apology from the person who wrote the page would be nice.
In reacting to Wegman’s criticism of ‘decentred’ PCA, the author says that Wegman is ‘just plain wrong’ and goes on to say ‘You shouldn’t just take my word for it, but you *should* take the word of Ian Jolliffe, one of the world’s foremost experts on PCA, author of a seminal book on the subject. He takes an interesting look at the centering issue in this presentation.’ It is flattering to be recognised as a world expert, and I’d like to think that the final sentence is true, though only ‘toy’ examples were given. However there is a strong implication that I have endorsed ‘decentred PCA’. This is ‘just plain wrong’.
The link to the presentation fails, as I changed my affiliation 18 months ago, and the website where the talk lived was closed down. The talk, although no longer very recent – it was given at 9IMSC in 2004 - is still accessible as talk 6 at www.secamlocal.ex.ac.uk/people/staff/itj201/RecentTalks.html
It certainly does not endorse decentred PCA. Indeed I had not understood what MBH had done until a few months ago. Furthermore, the talk is distinctly cool about anything other than the usual column-centred version of PCA. It gives situations where uncentred or doubly-centred versions might conceivably be of use, but especially for uncentred analyses, these are fairly restricted special cases. It is said that for all these different centrings ‘it’s less clear what we are optimising and how to interpret the results’.I can’t claim to have read more than a tiny fraction of the vast amount written on the controversy surrounding decentred PCA (life is too short), but from what I’ve seen, this quote is entirely appropriate for that technique. There are an awful lot of red herrings, and a fair amount of bluster, out there in the discussion I’ve seen, but my main concern is that I don’t know how to interpret the results when such a strange centring is used? Does anyone? What are you optimising? A peculiar mixture of means and variances? An argument I’ve seen is that the standard PCA and decentred PCA are simply different ways of describing/decomposing the data, so decentring is OK. But equally, if both are OK, why be perverse and choose the technique whose results are hard to interpret? Of course, given that the data appear to be non-stationary, it’s arguable whether you should be using any type of PCA.
I am by no means a climate change denier. My strong impressive is that the evidence rests on much much more than the hockey stick. It therefore seems crazy that the MBH hockey stick has been given such prominence and that a group of influential climate scientists have doggedly defended a piece of dubious statistics. Misrepresenting the views of an independent scientist does little for their case either. It gives ammunition to those who wish to discredit climate change research more generally. It is possible that there are good reasons for decentred PCA to be the technique of choice for some types of analyses and that it has some virtues that I have so far failed to grasp, but I remain sceptical.
Ian Jolliffe
Steve continues:
As an editorial comment, the validity of Mannian PCA is only one layer of the various issues.
For example, Wahl and Ammann approach the salvaging of Mann overboard from a slightly different perspective than Tamino. Their approach was to argue that Mannian PCA was vindicated by the fact that it yielded a high RE statistic and thus, regardless of how the reconstruction was obtained, it was therefore "validated". I don't see how this particular approach circumvents Wegman's: "Method Wrong + Answer 'Right' = Incorrect Science", but that's a different argument and issue. Also if you read the fine print of Wahl and Ammann, the RE of reconstructions with centered PCA are much lower than the RE using incorrect Mannian PCA, but, again, that is an issue for another day.
It would be nice if Jolliffe's intervention were sufficient to end the conceit that Mann used an "alternate" centering convention and to finally take this issue off the table.
6 responses so far ↓
“You can learn a lot from listening to people talk. Why everything I know today I’ve learned from listening to myself talk about things that I knew absolutely nothing about.”
— Gracie Allen
This really is too funny. Tamino apologizes for misrepresentation and then truncates to create an AGW-supporting quote:
[I certainly agree with this statement from your comment: "... the evidence rests on much much more than the hockey stick. It therefore seems crazy that the MBH hockey stick has been given such prominence ..."]
instead of
“the evidence rests on much much more than the hockey stick. It therefore seems crazy that the MBH hockey stick has been given such prominence and that a group of influential climate scientists have doggedly defended a piece of dubious statistics. “
David,
I guess he didn’t want to get kicked completely out of the club. Just a demotion.
I ran a few graphs of the data before and after sorting on my blog link below. It was an obviously confusing method to pick those with the highest slope in recent times and decrease the amplitude of reconstructed data in the process.
http://noconsensus.wordpress.com/2008/09/08/manns-statistical-amplification-of-local-data/
Hi Jeff, Nice work. It seems to me that the more general problem is to determine what the confidence interval should be, when you take into account the process of filtering for high correlations. Anmy thoughts on how you would do this?
Cheers
Please snip if this is high school stuff.
Let’s take some numbers that we will call “pure” because they are generated from rolls of a dice or flips of a coin. They carry no past history. From such numbers, wise people have derived a multitude of everyday terms like variance, correlation, distribution etc. The language of mathematics.
Now take a physical variable like temperature. We know that the coldest record on the surface of earth is about minus 85 deg C and the hottest is about 55 deg C. So temperature observations at surface Earth are between these 2 bounds. But, if we take a location like Melbourne, we know that the min temp is about minus 3C and the max about 46C. So the distribution curve is narrower. Then, we can select the max and min temp for Jan 1st each year, to find that the distribution is even narrower. So although we are measuring temp each time, we have different widths to the distributions.
Then we measure human temperatures and find they are bounded even narrower, otherwise you die. Yet, it is plausibe that there is a correlation between a Melbourne human body temp on 1 Jan each year and the Melbourne max/min/mean on 1 Jan. Ditto for the other examples.
So the physical temperatures have a history, a past form that has to enter the stats somehow. Yet it seems to me that some stats treatments regards temp as a pure, unbounded number with a roll-the-dice type of distribution.
Then some maths people use these temps of the earth in models and create CIs that do not seem to include the distributions and error bounds of temp data. They use correlations between datasets with different distributions, even ignore that some distributions pre-exist. I’m not absolutely sure about this, so correction welcomed.
The feeling is that one should not do stats on number sets that have already have stats done on them. The HS is an example.
Having followed the increasing complexity of maths debate from plane to next higher plane, I’ve some to heteroskedacity. Are there many more higher planes of understanding above that, or is there light at the end of the possible tunnels?
David,
Sorry for the huge delay in responding.
If the data were pure, (not too many influences outside of temperature) you would be correct but because of the nature of proxies this is not the case.
Imagine though what would happen if you took the data in a tree ring proxy where many tree ring widths increase in the last 100 years. If we assume the ring width is sensitive to both temperature and CO2. Both having a positive relationship with temperature.
If the CO2 rise is linear or near linear in the 100 year period and temperature has a variation similar to measured data the addition of these curves will make an uprising slope in ring spacing which is greater than either individual effect. If the temperature slope variation is reflected in the ring spacing, it will correlate well using a PCA algorithm to center and correct for magnitude of the data.
What’s more if this were true the CO2 is assumed to have a positive linear or near linear change in ring spacing it will amplify the slope at the end of the data.
Since the proxy is then amplified at the end, the correlation will pull the curve down to fit temperature and therefore de-amplify the prior historic data.
The correlation will only reveal that there is some temperature signal, not that the signal is entirely temperature.
The thing which strikes me about this whole situation is that all that is required for this to happen is that some “low frequency” influence (over 100 years) other than temperature needs to add to the data. Gradual rain pattern variation, nutrient scarcity, CO2, a neighbor tree growing next door.
Negative low frequency local influences are removed by allowing only a single sided analysis of the data. This sorts the data for only positive influences which are guaranteed to include other things than temperature!!
Thus we have a statistical amplification of local (recent)data over the proxy history!
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