I mentioned a few days ago that a serious discussion had threatened to break out at realclimate, where Demetris Koutsoyannis had posted up some astute commentary. He has recently dropped in here as well. I was unfamiliar with his work prior to this recent introduction. He has written extensively on climate, much of which has been from a statistical viewpoint much more advanced than poor old Rasmus.I began writing a commentary on his realclimate post, but instead have simply reproduced it below as it deserves to be read in its entirety, following some short introductory comments.
You can consult a list of his publications here . He emailed me the following two articles not posted up his website, which may interest others. (They are more accessible to non-statisticians than some of the other articles on the website): Koutsoyiannis, D., Climate change, the Hurst phenomenon, and hydrological statistics, Hydrological Sciences Journal, 48(1), 3-24, 2003. Koutsoyiannis, D., The Hurst phenomenon and fractional Gaussian noise made easy, Hydrological Sciences Journal, 47(4), 573-595, 2002.
I’ve obviously been intrigued by persistence issues for some time and have briefly discussed Mandelbrot and also Vit Klemeà’¦à⟼/a>, who has encouraged Koutsoyannis. In light of Rasmus’ insistence (persistence?) for i.i.d. (independent identical distributions), I repeat the following from Klemeà’¦à⟬ which applies nicely to Rasmus and his ilk:
Somehow the operational attitude toward mathematical modeling, the exaggerated strife for mathematical tractability and convenience ("Oh Lord, please keep our world linear and Gaussian") has blurred our sense for reality…
I’ve discussed Rasmus together with Cohn and Lins in a number of recent posts, commencing here . Rasmus argued that consideration of statistical persistence "pitched" statistics against physics, in effect claiming that statistical approaches perhaps made sense at a quantum mechanics level, but not at a terrestrial scale. Doubters should re-read his post at realclimate, but here are a couple of excerpts:
In fact, one may wonder if an underlying assumption of stochastic behaviour is representative, since after all, the laws of physics seem to rule our universe….
On the very microscopical scales, processes obey quantum physics and events are stochastic. Nevertheless, the probability for their position or occurrence is determined by a set of rules (e.g. the SchràÆàⵤinger’s equation). Still, on a macroscopic scale, nature follows a set of physical laws, as a consequence of the way the probabilities are detemined…
The nature is not trendy in our case, by the way – because of the laws of physics.
If one pursues his references a little further, one finds that MBH99 has become not merely an icon, but may even be one of the “laws of physics” referred to by Rasmus. He relied on the assertion that the "historical climate has been fairly stable", citing here , which, in turn, showed the MBH98-99 hockeystick as "proof". Such tangled webs.
Here’s Demetris comment in full as all of it is worth considering:
1. "Statistical questions demand, essentially, statistical answers". (Here I have quoted Karl Poppers’ second thesis on quantum physics interpretation – from his book "Quantum Theory and the Schism in Physics"). The question whether "The GCMs […] give a good description of our climate’s main features" (quoted from the rasmus’s response) or not is, in my opinion, a statistical question as it implies comparisons of real data with model simulations. A lot of similar questions (e.g., Which of GCMs perform better? Are GCMs future predictions good enough? Do GCM simulations reproduce important natural behaviours?) are all statistical questions. Most of all, the "attribution" questions (to quote again rasmus, "how much of the trend is natural and how much is anthropogenic" and "to which degree are the variations ‘natural’") are statistical questions as they imply statistical testing. And undoubtedly, questions related to the uncertainty of future climate are clearly statistical questions. Even if one believes that the climate system is perfectly understood (which I do not believe, thus not concurring with rasmus), its complex dynamics entail uncertainty (this has been well documented nowadays). Thus, I doubt if one can avoid statistics in climatic research.
2. Correct statistical answers demand correct statistics, appropriate for the statistical behaviours exhibited in the phenomena under study. So, if it is "well known" that there is long term persistence (I was really happy to read this in rasmus’s response) then the classical statistical methods, which are essentially based on an Independent Identically Distributed (IID) paradigm are not appropriate. This I regard as a very simple, almost obvious, truth and I wonder why climatic studies are still based on the IID statistical methods. This query as well as my own answer, which is very similar to Cohn and Lins’ one, I have expressed publicly three years ago (Koutsoyiannis, D., Climate change, the Hurst phenomenon, and hydrological statistics, Hydrological Sciences Journal, 48(1), 3-24, 2003 – http://www.extenza-eps.com/IAHS/doi/abs/10.1623/hysj.22.214.171.124481). In this respect, I am happy for the discussion of Cohn and Lins work hoping that this discussion will lead to more correct statistical methods and more consistent statistical thinking.
3. Consequently, to incorporate the scaling behaviour in the null hypothesis is not a matter of "circular reasoning". Simply, it is a matter of doing correct statistics. But if one worries too much about "circular reasoning" there is a very simple technique to avoid it, proposed ten years ago in this very important paper: H. von Storch, Misuses of statistical analysis in climate research. In H. von Storch and A. Navarra (eds.): Analysis of Climate Variability Applications of Statistical Techniques. Springer Verlag, 11-26, 1995 (http://w3g.gkss.de/staff/storch/pdf/misuses.pdf). This technique is to split the available record into two parts and formulate the null hypothesis based on the first part.
4. Using probabilistic and statistical methods should not be confused with admitting that things "happen spontaneously and randomly" or "without a cause" (again I quoted here rasmus’s response). Rather, it is an efficient way to describe uncertainty and even to make good predictions under uncertainty. Take the simple example of the movement of a die and eventually its outcome. We use probabilistic laws (in this case the Principle of Insufficient Reason or equivalently The Principle of Maximum Entropy) to produce that the probability of a certain outcome is 1/6 because we cannot arrive at a better prediction using a deterministic (causative) model. This is not a denial of causal mechanisms. If we had perfectly measured the position and momentum of the die at a certain moment and the problem at hand was to predict the position one millisecond after, then the causal mechanisms would undoubtedly help us to derive a good prediction. But if the lead time of one millisecond needs to be a few seconds (i.e. if we are interested about the eventual outcome), then the causal mechanisms do not help and the probabilistic answers become better. May I add here my opinion that the climate system is perhaps more complex than the movement of a die. And may I endorse this thesis saying that statistical thermophysics, which is based on probabilistic considerations, is not at all a denial of causative mechanisms. Here, I must admit that I am ignorant of the detailed structure of GCMs but I cannot imagine that they are not based on statistical thermophysics.
5. I have difficulties to understand rasmus’s point "A change in the global mean temperature is different to, say the flow of the Nile, since the former implies a vast shift in heat (energy), and there has to be physical explanations for this." Is it meant that there should not be physical explanations for the flow of the Nile river? Or is it meant that the changes in this flow do not reflect changes in rainfall or temperature? I used the example of Nile for three reasons. Firstly, because its basin is huge and its flow manifests an integration of climate over an even more extended area. Secondly, because it is the only case in history that we have an instrumental record of a length of so many centuries (note that the measurements are taken in a solid construction known as the Nilometer), and the record is also validated by historical evidence, which for example witness that there were long periods with consecutive (or very frequent) droughts and others with much higher water levels. And thirdly, because this record clearly manifests a natural behaviour (it is totally free of anthropogenic influences because it covers a period starting at the 6th century AD).
6. I hope that my above points should not be given a "political" interpretation. The problem I try to address is not related to the political debate about the reduction of CO2 emissions. Simply I believe that scientific views have to be as correct and sincere as possible; I also believe that the more correct and sincere these views are the more powerful and influencing will be.
This is very clearly put and I would barely disagree on the location of a comma. Happily, Gavin has let Rasmus off the bench to respond. It’s fun seeing Rasmus run amok. You’ll enjoy his reply as well. Among other things, Rasmus tells us: "I am not an ‘anti-statistics’ guy. Statistics is a fascinating field. In fact, most of my current work is heavily embracing statistics." There are a few pearls that are worth incorporating into the The Sayings of Rasmus.
Koutsoyannis’ post was followed up by one from Isaac Held, a very eminent climate scientist, who twitted Rasmus for his statistics. I’ll try to post some excerpts from Koutsoyannis’ articles on another occasion.