Wednesday
Mar172010
by 
Bishop Hill
Bishop Hill Statistical death-match
Mar 17, 2010 Blogs Climate: Statistics If you have a lot of time on your hands and get excited by tests for unit roots, do have a look at contributions the thread on random walks at Tamino's blog and the longer (much longer!) subsequent thread at Bart Vergheggen's.
VS, for that is his nom-de-blog, reckons that the temperature records are a random walk (or something like one) which means that many standard statistical approaches to measuring trends, including all the ones currently used in climatology, are invalid.
The thread is interesting on another level too, with several days of calm debate at Bart's site rudely interrupted by an invasion of trolls from Tamino's.
Statistics wasn't supposed to be this much fun.
Reader Comments (82)
I am ploughing through this and loving it! I am sure VS should write a book, he writes well and is easy to follow. Brilliant.
Most entertaining as the attack dogs flail around looking to apply the usual rebuttal.
I'm not quite sure why applying a couple of statistical tests is 'essentially demanding that a large percentage of known physics be thrown in the toilet', but hey it annoys the right people.
Hmm - isn't this a fancy way of saying that short-term trends aren't much use? Still, if it annoys the warmists, it can't be all bad.
A commenter remarks "I just don’t think it’s that helpful to torture the data with statistics". Hee, hee.
VS definitely took a piece out of Tamino and Tamino is now on the back-foot wielding new arcane statistical tests. It's sort of like two warlocks casting fiercer and fiercer spells against each other.
I have to say that the level of understanding of the Tamino attack dogs aka foot-soldiers is low. The basic argument of VS is that the historical records are indistinguishable from a random-walk. The acolytes assume that the record *is* a random walk - a not-so-subtle distinction.
There is also the erroneous assumption that a random walk is unbounded. In reality any random walk can have a function such that the further you are away from a mean the more likelihood you will randomly walk back towards the mean.
The final issue is physics bounding of the observed domain. The answer of course is: does the physics model the domain correctly and secondly does the physics model produce statistics indistinguishable from other models - such as random walks?
My oops
I said
What I should have said is the acolytes assume that VS said the record is a random walk - which is not the case. VS simply shows the statistics are totally compatible with a random walk hypothesis.
More interesting is the statistical analysis of other factors in climate change - discussed in the Tamino blog and the Bert blog - that shows the high correlation with solar parameters and lower/zero correlation with GHG
If the behaviour of a single plot can cause such disagreement, one has to wonder if the computer models stand any chance!
It also reminded me of Paul Klee's famous remark:
"A line is a dot that went for a walk”
Thank you your grace for giving the link. I have just spent a fascinating couple of hours going through that thread. It really demonstrates that a) the science is settled, and b) that there is a consensus!!
Actually, the discussion there does illustrate the potential for a properly moderated blog to host a reasoned discussion on important issues. Posters would only be permitted to post if a) they were able to demonstrate appropriate credentials/qualifications/experience and b) they committed to a professional level of discussion, appropriate between peers.
It might be possible to allow a separate but related/linked thread where observers could comment to their hearts content, provided that appropriate probity rules were observed.
A further interesting point. Tilde above says: "The basic argument of VS is that the historical records are indistinguishable from a random-walk.". I think that we can assume that VS is accepting the 'historical records' as presented by GISS, and NOT allowing for the many problems of "adjustments", delta UHI effects, questionable compliance of measuring stations with standards, and changing population of temperature stations over time that appear to reduce confidence in the veracity of the Global Mean Temperature record that we are asked to accept as valid. I would be interested in his comments about the impact that these sorts of issues would have on his conclusion.
@Tilde, You are absolutely correct about the 'useful idiots' completely misunderstanding what VS repeatedly tells them.
Totally focussed on defending the message at all costs, and oblivious to the science he is trying to discuss.
James P,
"Hmm - isn't this a fancy way of saying that short-term trends aren't much use?"
Exactly. I wrote to VS about that:
"“I would expect that VS would agree that if the 130 year record is merely a random walk, that the latest 12 years are by far not enough to draw any conclusions from. Perhaps VS will join us in fighting strongly against the erroneous “1998″ claim.”
He replied:
"While I’m not claiming that temperatures are a simple ‘random walk’ (again, thanks Alex for clearing that up, it got lost in the debate), I am claiming that the series contains a unit root.
In that sense, I will definitely join you in fighting the erroneous ‘cooling trend’ claim. However, you guys have to quit blindly calculating trends too, for the very same reasons :)"
(at http://ourchangingclimate.wordpress.com/2010/03/01/global-average-temperature-increase-giss-hadcru-and-ncdc-compared/#comment-1550 )
Also, he did seem to backpedal a little bit from initially claiming that it's all a random walk, and stochastic rather than deterministic, to now claiming merely the presence of a unit root.
Tilde Guillemet,
A higher correlation with solar parameters than with CO2? Not even close!
(eg http://www.eoearth.org/image/Solarforcings.jpg )
Fascinating little microcosm of the climate debate world. If anyone really didn't have an idea of the underlying tenor of climate debate then this would prove a good example to follow through.
All very enjoyably technical, even with various trips to Google to expand the understanding of what is said - at first, but then the stygian world outside intervenes and you don't need references ;)
Bart seems a reaonable chap, but he, like a lot of the others taking against VS, invoke the alleged truism that "CO2 goes up - it gets warm", and appear to say it's just the job of statistics to confirm that. VS is just putting the cool harsh glare of statistics from an angle they may not have selected themselves.
I liked his response to some of the defences for the tone of poor "put upon" tamino
I found the comments by VS very informative. Has anyone any idea who he is? He is clearly a serious academic. Also, who is Tamino? He seems to be a big name in GW. Forgive if I'm supposed to know.
I think Tilde's comments are spot on. A further argument used to refute VS is to state that temperatures are clearly bounded and therefore ergo the proposition is refuted. That is like saying that you cannot make assumptions about Gaussian pdf when talking about statistics of peoples heights because peoples heigths are clearly bounded whereas a Gaussian pdf is not.
On a further note, I have some carefully prepared data series using a method in my technical field. They are synthetic data. If you are out there VS (or anyone else), are you interested in running them through a statistical test to see if they contain a significant trend or not? I would then be happy to reveal the method.
jon - "Also, who is Tamino?"
Tamino has the same first name as I do. He is Grant Foster. He is one of "the team" or at least an appendage of that illustrious group and is referenced in the Climategate emails. He has less refereed (I refuse to use the corrupted terminology - peer reviewed) hard science publications than I do and is certainly not a big name in GW, or AGW, or MMGW, or....
It's a JOY! Thank you, Bish. This in particular is so blindingly obvious, and has been annoying me for ever.
"
Realclimate: “It is remarkable statistically that the 13 (now 14) warmest years in the modern record have all occurred since 1990. The fact that the 13 warmest years since 1880 could have occurred by accident after 1990 corresponds to a likelihood of no more than 1:10 000.”
This is clear and utter nonsense. That likelihood might (might!!) be correct, if the ‘random walk’ would have somehow referred to levels, and not changes (i.e. first differnces). But it doesn’t.
In time series analysis, one series is treated as a single sample realization from a given data generating process, so conditional on a given DGP, that probability up there is completely meaningless. Conditional on temperatures reaching their 1990 level, their observed 2000 level is very likely, assuming a random walk DGP.
"
reading on ......
Here's an idea. How about those Climate Scientists who want to get back into public confidence providing academic papers on how they adjusted their datasets to account for things like UHI, and having them published in, and peer reviewed by, statistical journals instead of climate science journals?
I am having a lot of trouble with the idea of a "global average temperature".
I also struggle with the idea of a "global atmospheric concentration of CO2". If it's being made in huge quantities in power stations and behind my SUV - and being absorbed / reprocessed in the Amazon rainforest - then how can measurements atop a Hawaiian volcano tell us anything?
Is it just me?
Steve2,
Since when is radiative physics a 'truism'?
http://www.aip.org/history/climate/co2.htm
You are not alone Jack.
Any averaging of recorded temperatures / CO2 / anything else at various points on the planet can only be a rough approximation of a mathematically true global average, which would require simultaneous measurement at every point in the atmosphere and integrated over time. At best the "global averages" only tell us the averages of the measured discrete (in location and time) data sets, and even then we don't necessarily know the added value, weightings, etc.
If anyone had told me last week that I would be spending an entire Tuesday afternoon reading a blog thread discussing statistical theory.... well, being as numerically challenged as I am, I would have dismissed the idea as quite unlikely. Yet I did. Kudos to Bart and I hope VS makes more frequent appearances: he would make a fine teacher.
@Bart Verheggen
Hmm, I said "alleged" trusim too, so I agree it wasnt clear what I meant. Radiative physics can have no arguments against it in the lab, you can easily reproduce the results, but those results don't scale up and transfer directly to explain the affect on Earths temperature by man made CO2. For instance during '45 - '75 the world cooled while CO2 went up.
Tamino's band of followers is worse than RealClimate, which has plenty of intelligent discussion, especially when the censors are weak.
At one point, his group was all echoing the talking points about why code should not be made public in climate science. RealClimate had no problem putting up a post titled Show us the Code. Still wondering if the author who was not providing code, was just echoing the climate scientists. He said you should take a course in wavelets, when before Steig said you should take a course in Matlab.
Tamino and his followers are thugs, nothing more. The discussion on Bart's site was very civil until the Tamino thugs arrived.
Many thanks for the link. It was an enjoyable way to spend the morning, though VS could have been more straightforward in explaining the initial presenting issue of why you cannot statisticallly prove a causal relationship between CO2 and global temperature when (a) both variables appear correlated with some third unspecified variable (autocorrelation) and (b) the relationship between the changes in the two variables appear to vary considerably across time(non-stationarity) . Or at least that is my takeaway from the discussion.
As you noted , the initial discussion was very civilized but then some rather obnoxious types, RC regulars by and large, arrived and created what was little short of a food fight or in VS's vernacular - a spit fight. Methinks VS is a Brit. However, lVS seems capable of looking after himself.
It is astounding the reaction such a largely arcane post wrought. It seems to be matter not whether the topic is the correct way to look at time series data with high inter-period variability or the reasonableness of Santer's charge that Steve McIntyre should publish more when Jones, Santer and others were endeavoring to prevent his publications (on Andy Revkin's blog ). In both instances the tone of the comments from pro-CAGW folks is amazing.
There's something I don't understand (or actually I think I do and others don't, but maybe I'm wrong).
To me it's obvious that nothing will be done globally to reduce CO2 emissions in the next two decades or so - probably longer. I'm not getting into the issue of whether or not something *should* be done - I mean that nothing *will* be done. Or, more accurately: individual nations, like the UK, the rest of the EU, US etc etc may well do something. But whatever they do will be neutralized by increased carbon emissions by other countries - not only China, India, Brazil, South Africa but also Mexico, Indonesia, southeast Asia generally, etc.
This is someting I'm willing to make any bet on - that, in twenty years, global CO2 emissions will be no lower than today. And yes, if that means that there will be a tipping point and mankind will be destroyed, etc, that's exactly what's going to happen. Short of the world becoming an Orwellian dictatorship, there's no way that global CO2 emissions will be reduced or even stopped anytime soon.
(Of course, countries like the UK or Australia etc may well hurt themselves economically in the attempt - like Spain has already done - but that won't change a thing.).
What I don't understand, honestly, is how anyone can think that anything or anyone can actually make the world, as a whole, take such drastic actions, in such short times. It simply won't happen.
Given the above, I would ask -- can we assume that in 20 years - or hopefully just 10? - that issue will be solved, in terms of the "science"? One way or the other?
Steve2,
There are more factors influencing climate than only CO2. Aerosol went up a lot in concentration during the 40s-70s (to a large extent due to soaring SO2 emissions).
Yes, there's a lot of uncertainty in the (historic) aerosol forcing.
And no, uncertainty is not the same as knowing nothing,
TG,
So in other words he didn't say it was a duck, he just said it (random) walked like a duck, quacked like a duck, etc?
Well, that changes everything.
Oh look lads, it's a (random) fly-by Duck O'Dwyer. Anything useful to contribute to the conversation Frank?
I feel sorry for VS, he thought he was involved in a scientific debate with people who would welcome his undoubted expertise in statistics, and where he might be able to have an intelligent conversation.
He was not to know that Tamino, dghoza and Eli Rabbitt to name but three do not go in for intelligent conversation they simply indulge in loud mouthed bovver boy tactics, honed on RealClimate on the bsais that if you can't argue the case you can at least shout down the other party.
Some of the simple questions that VS asked were like a breath of fresh air and his critique of climate models was spot on (well at least agreeing with my own views)
I thoroughly enjoyed most of the thread - one of the most informative I've read
The short of it appears to be that AGW physicists regard econometric statistics as irrelevant, or at least inapplicable, when it appears to transgress physics, while econometric statisticians regard the variants of statistics commonly used by AGW physicists as naive and potentially misleading. At this point, my view is that this impasse is the result of an incomplete and messy database
It's interesting that the temperature plateau of the last 15 years is now the battleground, with neither side being convincing - and indeed disagreeing amongst themselves ... this is how Science should progress. The AGW people now shy away from the MWP (ie. the battleground has shifted) but until a convincing explanation for this period is forthcoming they remain on the edge of the razor - no ifs or buts
Dhoggie-boyo is a thug, although erudite. He doesn't mind this, of course (pig-in-mud comes to mind). Moderator BV, try as he may for at least the appearance of impartiality, implicitly encourages him with faint moues of displeasure. This is a pity as it disrupts the thread (as it is meant to do, of course)
Nonetheless, a good robust discussion - using the word "robust" in its' proper sense - with some excellent references supplied along the way. I hope there is much more of this
Quidnunc, your comment would seem a little less hypocritical if you'd actually engaged the topic yourself - as far as I can see your sole contribution consists of calling me names.
As it is, I already commented on the topic. If there is a difference between saying that something IS something and that it cannot be told apart from one, it seems rather metaphysical to me. A difference that makes no difference is no difference.
Tamino's Thugs: Don't wrestle with pigs: ya'll get all muddy and the pigs will love it.
Their discussion technics is well known. Get personal, discuss trivial matters and make that the main subject, spam the thread with multi posts so that everybody forgets the main subject, throw in some ad homs, wait until the opponent gets aggrivated and start whining "Mommy, they're after me!". VS was doing fine until he fell into the trap the Tamino gang was setting up. Methinks Hansen's Poodle..oops Pitbull has a script for that.
PS That single rodent comment was IMO the best example of a tamino troll, which unfortunately sent VS into orbit. From there things went south and the troll army had a field day all under the (closed) eyes of a friendly referee.
Luboš Motl addressed the Tamino random walk discussion in an excellent manner on the Reference Frame. Here is an excerpt:
http://motls.blogspot.com/2010/03/tamino-vs-random-walk.html
Ian:
I believe the database issue is a separate concern completely. Even a much improved database will not affect the statistical problems raised by VS - unless of course the new temperature db is not plagued by autocorrelation.
Now I've had longer to go over the VS proposition - and brushed up on my rusty maths/stats - I've come to the conclusion that the VS proposition is not good news for climate realists.
My position - and I guess that of many other disbelievers on AGW - is that there are powerful negative feedback processes presently reacting to the challenges we are making to the atmosphere and oceans. The theory being that, given the long term narrowly bounded range of temperature, negative feedbacks must predominate.
Because VS has found no sign of non-random effects in the last 150 years this means that there is no sign of negative feedbacks kicking in. The only consolation is that VS has not found any signature of AGW forcings, nor any signature of positive feedbacks.
Further research in this area is obvioulsy needed. For instance analysis of other time-series data related to climate that may show signs of non-random walk behaviour.
Amazing how a single commenter/ has injected a new term into climate vocabulary - 'non-random walk'.
Dhogoza, BV etc wont accept that there can be no fundamentally true but statistically/mathematically non-derivable physical realities. They keep trying to cut down his 'non-physical' statistics down with their double edged swords but cant they see that they are killing climate models in the process?
Tilde:
"Because VS has found no sign of non-random effects in the last 150 years this means that there is no sign of negative feedbacks kicking in. The only consolation is that VS has not found any signature of AGW forcings, nor any signature of positive feedbacks."
Wouldn't you suppose that the feedback effects might be coincidental with the temperature series, and of similar or lesser magnitude, and thus share randomness characteristic?
If you want an insight into Foster's credibility, read his posts on Principal Component Analysis, and pay particular attention to the misrepresentation of Joliffe. This was all in aid of defending the Mannian Hockey Stick to the last gasp.
The technique used is a simple one. When you come to the difficult point, fill your post with equations, and shout loudly. Your acolytes, unable to understand the tricky bits, will then all cheer and congratulate you on being a brilliant mathematician.
However, all you are really saying is that if a statistical procedure calls for use of the mean of a series, it is OK, if you are a climate scientist, to use the mean of a subset of that series. How you pick the subset? Who knows? Who cares? What matters is that Obama is the greatest thing since JFK, Exxon is evil, all skeptics are in denial, probably also Creationists and anti-evolution and have bad personal hygiene, and we have to save the planet for the children.
Starting now.
j Ferguson
There is certainly feedback processes occurring and what we are seeing is the resultant. The problem is how strong the effect is and over what time scale.
I now place myself on pretty shaky ground WRT stats - it was so long ago. I understand that the analysis process takes first differences of the time series and assumes it has a known statistical distribution - perhaps Gaussian. The analysis looks at month by month *differences* not absolutes.
The stationary assumption is that at any point in time the statistical distribution for the first differences is the same - e.g. with temperature, if it's Gaussian with a standard deviation of 0.5C in 1900 then it will be Gaussian with standard deviation of 0.5C in 2000.
With the postulated strong feedback effects you would expect to see a change in the shape of the distribution or a changes in the standard deviation at different times. The VS analysis says there is no detectable change, so we can only assume that the feedbacks are not affecting the short-term variability because they are not actually very strong, or they occur over much longer time scales than century scales.
The last possibility is that the feedback processes are highly non-linear. That is they are almost non-existent within a particular range but cut in with a vengeance at a set level - a top-hat function.
The last possibility is that the feedback processes are highly non-linear.
Don't you think that is quite likely, at least for the last 2000 years, given the behaviour of the climate in recorded history? That either cooling or warming provokes feedbacks which revert to the mean? We have somehow to account for the fact that there was a RWP, MWP and LIA, and that in each case we had a fluctuation which appears to have slowed and reversed direction before going too far one way.
Bernie
It is hard for me to see how the quality of database-past can be much improved, so my point seems moot in any case
But VS and Tamino wrangled in a 3rd-party fashion (wry smile - "I did not have statistics with that man!") over cherry-picking, or not, data to eliminate unit roots. Seems like a data wrangle to me
Nonetheless, the status is uneasy draw; doubtless more rounds to come ... let us fervently hope, as I found it very interesting
Tilde: You say (and perhaps correctly) "The last possibility is that the feedback processes are highly non-linear. That is they are almost non-existent within a particular range but cut in with a vengeance at a set level - a top-hat function."
It has been a while for me, too, but what about the effect of feedbacks lagging behind the initial forcing by periods varying from months to years?
jorgekafkazar said :
I'm absolutely certain that feedbacks are occurring on all time scales. What I'm not sure about is whether they are positive (amplification) or negative, or a mix of many types.
These feedbacks are compatible with a random walk hypothesis assuming they are 'linear' in the range and there are enough different types that they tend to cancel each other out.
However I do see examples of time lag - 800 years between temperature and CO2 levels - from the ice-core records.
One thing did occur to me though is that the earths temperature has been basically bistable - a high temperature - now and a low temperature - ice age. In between were rapid transition periods.
The theory of random walk / unit poles is not compatible with the bistable state. An outcome of a random walk in the data is that the system can be pushed to a new state and will randomly carry on from that point. It will not revert to some original level or trend line. If this were the case on very long time scales we'd see the climate stabilise at several distinct levels.
In the very long scale we see clear evidence of bounding, no evidence of unit poles, and no evidence of multiple stable states nor of any random walk.
In the short period of the VS analysis we see essentially random data which has been shown to have a unit pole.
The question again arises - at what time scale does climate stop being stochastic and start behaving like a normal feedback system? Perhaps this is the difference between weather and climate? Or perhaps it is a much longer period?
TG,
"My position - and I guess that of many other disbelievers on AGW - is that there are powerful negative feedback processes presently reacting to the challenges we are making to the atmosphere and oceans. The theory being that, given the long term narrowly bounded range of temperature, negative feedbacks must predominate."
The long term history of the earth would appear to refute the notion that the earth is any way predisposed to maintain temperatures to our liking. Furthermore present observations show heat acumulating in the earths systems so there is no evidence of a negative feedback predominating, while there is evidence of positive feedbacks.
Not only that but even if we allow for some unknown feedbacks we must also allow that they are as likely to be positive as negative. And as you say they may be non linear.
All adds up to good reasons not to mess with the system by pushing hard on it with GHG forcings that are unprecedented in millions of years, doesn't it?
FOD said
The Vostock ice-core data shows average earth temperature is bounded roughly in a 10C range. We are at the higher end right now but not the maximum in any way.
If VS is right on a long enough time-scale then you will get your catastrophe.
It is almost amusing to see how much energy is being spent on rebutting VS when his arguments fully support the notion of tipping points and step changes in climate - which is what AGW FUD is all about.
A random walk unit pole system can have an major step changes in climate that will persist at whatever level they are pushed to - and then randomly walk based on that level and not on any historical value.
So Mr FOD. Is your theory that we are about to reach a tipping point correct? Or is the statistical genius of Tamino in rebutting VS to prevail?
FO'D: Where is the evidence of heat accumulating in the earth's systems? The current El Nino is releasing energy stored in the Pacific Ocean into the atmosphere, from whence it is radiating to space. When the El Nino terminates, the atmosphere will cool as the Pacific recharges. The atmosphere contains very little energy in comparison to the oceans, so it is the oceans that matter.
Has Steve McIntyre commented on this yet?
A post by whbabcock (March 17) at the VB site summarises the situation.
He simply points out that cointegration of a specific time series (in this case, temperature differential and atmospheric CO2 ppm) has shown that statistically these two elements cannot be reliably correlated
Not that the AGW physics is wrong - simply that on our existing database, correlation cannot be demonstrated
My first post. I understand very little statistically. Do not know if VS is right, but it was fun as he destroyed Tamino. He was hallucinating! "you copy-pasted" was awesome!! :):):):)