Forget about water vapor ? Ignore natural variability ? Trust the climate models ? Climate forcing calculations are settled ?

Dr Norman Page, July 1, 2015 at 10:22 am

When dealing with time series ( surface temperature data ) selected from multiple quasi independent variables in complex systems such as climate, the knowledge , insight and understanding come before the statistical analysis. The researcher chooses the windows for analysis to best illustrate his hypotheses and theories. Whether they are ” true ” or not can only be judged by comparing forecast outcomes against future data. A calculation of statistical significance doesn’t actually add to our knowledge but might well produce an unwarranted confidence in our forecasts.

rgb at duke, July 5, 2015 at 8:33 pm

Sometimes things are just too hard, until they aren’t. Read Taleb’s “ The Black Swan ”. One of the most dangerous things in the world is to assume “ normal ( in the statistical sense ) behavior as a given in complex ( chaotic, non linear ) systems. IMO the whole point of Koutsoyiannis’ work is that we can’t make much statistical sense out of data without a sufficient understanding of the underlying process being measured.

This difficulty goes all the way down to basic probability theorem, where it is expressed as the difficulty of defending any given set of priors in a Bayesian computation of some joint / conditional probability distribution. One gets completely different answers depending on how one interprets a data set. My favorite ( and simplest ) example is how one best estimates the probability of pulling a black marble out of an urn given a set of data representing marbles pulled from the urn. The best answer depends on many, many assumptions, and in the end one has to recompute posterior probabilities for the assumptions in the event that one’s best answer turns out not to work as one continues to pull marbles from the urn. For example, we might assume a certain number of colors in the urn in the first place. We might assume that the urn is drawn from a set of urns uniformly populated with all possible probabilities. We might assume that there are just two colors ( or black and not-black ) and that they have equal a priori probability. Bayesian reasoning is quite marvelous in this regard.

Taleb illustrates this with his Joe the Cab driver example. Somebody with a strong prior belief in unbiased coins might stick to their guns in the face of a long string of coin flips that all turn up heads and conclude that the particular series observed is unlikely, but that is a mug’s game according to Joe’s common wisdom. It is sometimes amusing to count the mug’s game incidence in climate science by this criterion, but that’s another story.

It is also one of the things pointed out in Briggs’ lovely articles on the abuse of timeseries in climate science (

**really by both sides**). This is what Koutsoyiannis really makes clear. Analyzing a timeseries on an interval much smaller than the characteristic time(s) of important secular variations is a complete — and I do mean complete — waste of time. Unless and until the timescale of secular variations is known ( which basically means that you understand the problem ) you won’t even know how long a timeseries you need to be ABLE to analyze it to extract useful statistical information.

So often we make some assumptions, muddle along, and then make a discovery that invalidates our previous thinking. Developing our best statistical understanding is a process of self-consistent discovery. If you like, we think we do understand a system when our statistical analysis of the system ( consistently ) works. The understanding could still be wrong, but it is more likely to be right than one that leads to a statistical picture inconsistent with the data, and we conclude that it is wrong as inconsistency emerges.

How, exactly, do we “ know ” things ? How can we determine when a pattern is or isn’t random ( because even random things exhibit patterns, they just are randomly distributed patterns ! ) ?

https://www.edge.org/conversation/the-fourth-quadrant-a-map-of-the-limits-of-statistics

https://www.itia.ntua.gr/en/docinfo/673/

http://www.itia.ntua.gr/en/docinfo/1351/

http://onlinelibrary.wiley.com/doi/10.1029/2005GL024476/pdf

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