Comments on: Scale invariance for Dummies

By: Niche Modeling » CSIRO Data Policy: Go Pound Sand

Niche Modeling » CSIRO Data Policy: Go Pound Sand — Tue, 15 Jul 2008 12:42:33 +0000

[...] I’m not able to hand over the data from the 13 models, due to restrictions on Intellectual Property, but I can describe the methods used to determine statistical significance. Dewi Kirono says: Â· I have used a number of statistical tests (parametric and non-parametric) and found that most of them show agreement. I used the 5% significance level. One marginal case was the change in percentage area for exceptionally low rainfall in NSW, in which the T-test was insignificant at the 5% level while Kolmogorov-Smirnov test was significant 5% level. I feel the non-parametric test is more objective since it doesnâ€™t assume a Normal distribution. Â· For the percentage area (temp, rain), the 13-model-mean sample is the 108 yr time series for 1900-2007 and the 31 yr time series for 2010-2040. For percentage area (soil moisture), the sample is the 50 yr time series for 1957-2006 and the same 50 yr time series modified for a period centred on 2030 Â· For the frequency (temp and rain), the sample is the number of models (13) as each period (i.e. 1900-2007 and 2010-2040) only produces one return period value. Â· For soil moisture frequency, I cannot perform the test as we only have one value for the obs (1957-2006). Â· At the moment Iâ€™ve only applied the tests to the “mean” data not the “90th” and 10th” percentiles. This is because we cannot do that for soil moisture and because we deal with lots of zero values for the 10th percentile. Regards Kevin Hennessy I then asked for further clarification of how the statistical tests were performed, and asked again for the data. Further explanation of the statistical tests reveals that they consisted simply of comparison of the means for two time periods, where % area in individual years were the single data points. This simple test assumes the data points are independent, but due to autocorrelation is an unjustified assumption. Failing to account for autocorrelation grossly overestimates the power of the test to detect significant differences (see my post Scale Invariance for Dummies or Chapter 10 of my book). Also see the results of Breusch and Vahid 2008 from the Draft Garnaut Report (reviewed here), where t-test scores for rate of temperature increase dropped from more than 4 to less than 2 when autocorrelation was taken into account. I don’t know the exact autocorrelation, as I can’t get the data, but the temperature and rainfall variables that produce it have very high autocorrelation (or ‘bursty’) behaviour, and so these data must inherit that character. Dear David, [...]

By: Niche Modeling » Hurst Coefficient Software

Niche Modeling » Hurst Coefficient Software — Wed, 23 Apr 2008 08:20:19 +0000

[...] Long-range dependence is being identified many disciplines such as, networking, databases, economics, climate and biodiversity. LTP is competing with the sexy “long tail” for top spot as a theory of cultural consumption. Thus, the need for software offering complete long-range dependence analysis is crucial. While there are some steps towards this direction, none are yet completely satisfactory. For one, the Hurst exponent cannot be calculated in a definitive way, it can only be estimated. Second, there are several different methods to estimate the Hurst exponent, but they often produce conflicting estimates, and it is not clear which of the estimators are most accurate. A first step towards a systematic approach in estimating self-similarity and long-range dependence is the java tool called SELFIS, a java based tool that will automate the self-similarity analysis. In R there is the fracdiff package on CRAN for fitting frARIMA(p,d,q) models with fractional “d” and there’s a one-to-one relationship between ‘d’ and the Hurst parameter for these models: d = H – 1/2. These are better than the R/S method known to be far from optimal. A useful summary of the issues and reference to other resources is Estimating the Hurst Exponent. Demonstrating just how pervasive are these concepts in our daily life is the Physics of Fashion Fluctuations by R. Donangeloa, A. Hansenb,c, K. Sneppenb and S. R. Souzaa. Here a simple model for emergence of fashions â€” goods that become popular not due to any intrinsic value, but simply because â€œeverybody wants itâ€ â€” in markets where people trade goods shows spontaneous emergence of random products as money. The model supports collectively driven fluctuations characterized by a Hurst exponent of about 0.7. Scale Invariance for Dummies is an investigation of scale invariance or long term persistence (LTP) in time series including tree-ring proxies â€“ the recognition, quantification and implications for analysis â€“ drawn largely from Koutsoyiannis. [...]

By: Niche Modeling » Example of Simple Linear Regression - global warming trends

Tue, 18 Mar 2008 20:43:31 +0000

[...] > pnorm(0.135,sd=0.155) [1] 0.8081141 Below is a table of data and results for all the four main global temperature indices. Source10yr_trend(t)SD0.2-tpIPCC Confidence UAH+0.0450.1350.1550.81Likely RSS+0.0090.1220.1910.94Very Likely CRU+0.0980.2160.1020.68Likely GISS+0.1730.1420.0270.58Medium Likelihood As of this month, the trend in temperatures for the last 10 years is so low, that an increase of 0.2C per decade could be rejected in 3 out of 4 indices with some level of confidence. In one case, using the IPCC terminology, these results suggest IPCC projection of global warming this century are very unlikely (1-10% chance) to be correct. This is a controversial result contradicting the IPCC ‘consensus’ position. To any controversial result there are objections. One is that ten years is too short a time to test climate trends. This is of course a statistical nonsense as a trend of any length in a time series can be tested providing appropriate uncertainty is used. With short trends the SD simply becomes much larger. For example, the SD for the 5 year trend is closer to 0.5C, so a trend deviation of more than twice as much would be needed to reject the null hypothesis at the same level as a 10 year trend. Another objection here is that a ten year trend is cherry picking. However, to cherry pick one needs options to pick from. Treating data from the present day 10 years back is not cherry picking as we are talking about temperatures now, and it is impossible to cherry pick the present, there is only one present. The choice of length of trend is the only free variable. Another objection is that increasing temperatures may being masked by factors such as volcanic eruptions, El NiÃ±os, sulphates, and trade winds. However, the masking effect was not part of the IPCC predictions of 0.2C per decade, and the results concern those predictions. Also, the masking argument tries to convince us that the modelsâ€™ magnitude of warming is certain, and explains failure by reference to uncertain factors. Such excuses for lack of predictive skill get tired very quickly. One could also argue that uncertainty limits may be wider than classical statistics and this finite empirical process for estimating SD suggest. Climatic processes exhibit a scaling invariant behavior, also known as long-range persistence (LTP) or the Hurst phenomenon which produces random long term trends. A combination of analytical and Monte Carlo methods such as described in Uncertainty assessment of future hydroclimatic predictions: A comparison of probabilistic and scenario-based approaches (2007) may extend uncertainty limits more and reduce the confidence in the judgements. I think it is a remarkable testament to the power of numbers, that one of the most complex and contentious issues of the time could potentially be brought down by such a simple statistical analysis. The IPCC model projections were only published in 2001 and are already looking very shaky. These projections are central to the IPCC mission. If the current stable temperature trend continues, put the AGW agenda on hold. [...]

By: Niche Modeling » Options for ACF in R

Niche Modeling » Options for ACF in R — Fri, 14 Jul 2006 18:57:31 +0000

[...] July 14th – Options for ACF in R [...]

By: Surf » Home

Surf » Home — Tue, 25 Apr 2006 05:35:19 +0000

[...] Scale invariance for dummies. [...]

By: davids

davids — Wed, 15 Mar 2006 21:03:04 +0000

Yes. Most natural series seem to have high LTP, including the reconstructions. The conclusion should be that the confidence intervals are greatly expanded by LTP â€”that excessive confidence is misplacedâ€”but the conclusions are not necessarily false. For more about falsification, see â€œA new climate reconstructionâ€?.

Yeah, I am just using the default theme. Supposedly the width is controlled by a couple of images. If I could only find out which ones and delete them.

By: davids

davids — Wed, 15 Mar 2006 21:03:00 +0000

Yes. Most natural series seem to have high LTP, including the reconstructions. The conclusion should be that the confidence intervals are greatly expanded by LTP —that excessive confidence is misplaced—but the conclusions are not necessarily false. For more about falsification, see “A new climate reconstruction”.

Yeah, I am just using the default theme. Supposedly the width is controlled by a couple of images. If I could only find out which ones and delete them.

By: John A

John A — Wed, 15 Mar 2006 21:02:47 +0000

Dave,

Letâ€™s see if I can work through this. What youâ€™re basically showing is that the statistical model (IID) used in multiproxy studies is fundamentally wrong, and leads to conclusions which are false or at the very least misleading. Is this correct?

[BTW, if possible Iâ€™d recommend you find a WordPress theme that spans the entire page, as this weblog is seriously hard on the eyes.]

By: Demetris Koutsoyiannis

Demetris Koutsoyiannis — Wed, 15 Mar 2006 21:02:22 +0000

This investigation by David Stockwell is extremely interesting and useful. Not only does it provide evidence that all available proxy series of temperature exhibit scaling behaviour. It also shows how inappropriate the classical (IID) statistical model is for them: in all cases the Hurst coefficient H is as high as 0.90Â±0.07, far from 0.5. The last part of the article correctly points out the significant implications. I have attempted, too, in several cases to emphasize these implications and expressed the opinion that statistical hydrology needs to be rectified in order to harmonize with this complex nature of physical processes. Now this investigation, with the large climatological data base it uses, points out that the same is true for climatology, given that climatology has been traditionally based on the classical (IID) statistical model, too.

However, probably the implications are even “worse” than described by David Stockwell. In fact, the formula SE[LTP]/SE[IID] = n^(H-0.5) he derives and the relevant plot indicate the increase of uncertainty under the SSS behaviour, if H is known a priori. Note that in the IID case there is no H (or H = 0.5 a priori) and, thus, no uncertainty about it. In the SSS case, H is typically estimated from the data, so there is more uncertainty due to statistical estimation error. This, however, is difficult (but not intractable) to quantify. And in the case of proxy data, there is additional uncertainty due to the proxy character of the data. This is even more difficult to quantify.

My conclusion is that the world is more uncertain and more indeterministic than modelled using classical statistics. In my opinion this is not bad; in contrast, this makes life more fascinating. Just think of the difference of watching, say, a football game in real time (live and thus indeterministic) or one day after (with known outcome and thus deterministic).

By: Demetris Koutsoyiannis

Demetris Koutsoyiannis — Wed, 15 Mar 2006 21:02:00 +0000

This investigation by David Stockwell is extremely interesting and useful. Not only does it provide evidence that all available proxy series of temperature exhibit scaling behaviour. It also shows how inappropriate the classical (IID) statistical model is for them: in all cases the Hurst coefficient H is as high as 0.90±0.07, far from 0.5. The last part of the article correctly points out the significant implications. I have attempted, too, in several cases to emphasize these implications and expressed the opinion that statistical hydrology needs to be rectified in order to harmonize with this complex nature of physical processes. Now this investigation, with the large climatological data base it uses, points out that the same is true for climatology, given that climatology has been traditionally based on the classical (IID) statistical model, too.