Levy walks, solar flares, and warming

However, now this topic was discuss long enough.
I will stop now.
thank you to all of you. !

I am not letting Nicola have the final word:
Nicola Scafetta (17:07:19) :
“Your methodology has removed a known solar signature on climate which is associated to the Gleissberg (50-80 years) and Suess (160-260
years) solar variability. Moreover, if the record were twice as long what kind of fit would you use? A 4th, 5th or 6th order polynomial?”
As explained earlier our methodology removes things that may be of solar origin. But everything of solar origin does not have to derive f rom Levy-walk statistics. On of the great problems with your methodology, and this permeates everything you do in climatology, is your uncritical mixing of categories.
We have also explained earlier how we determine the order of the fitting polynomial. It is by increasing the order till the value for H converges, combined with an a posteriori test that the polynomial varies slowly over the largest time scale T for which we find memory (the SDA-curve has a linear slope H up to to a certain time T, after which is becomes flat). But other detrending procedures are equally adequate; smoothing by a running mean is fine, as long as the length of the smoothing window is selected from the same criteria. If the signal is reasonably stationary an increase in the record length should not change the length of the smoothing window. The polynomial order may increase to provide the same level of smoothing.
Nicola Scafetta (17:07:19) :
“Levy-walk noises may present very long trending properties because of their fat temporal tail distributions”.
This statement is too vague. Our attempts to produce the trends observed in the GTA by using the prescription for generating a LW-noise time series in your 2003 and 2004 work have failed. We have asked you several times for a prescription for how you generate realizations for LW time series that can be compared to the measured GTA signal, but we get no answer. Instead you keep repeating the mantra:
“In any case, the real problem with your work is that you mistake the increments with the time structure. We talk about waiting time distribution, you are talking about increment distributions. The scaling is in the time structure, not in the increments.”
In all my later messages I have been talking about time structure and waiting time distributions, and this is perfectly relevant for certain types of solar records. But climate data like the GTA are given as time series of increments sampled at regular intervals. If you remove the information about the increments, there is no information left. In your SDA and DEA analysis of the GTA (which is the only analysis you do on these data) you use of course the increments, because this is all you have. As long as you do not give a clear prescription for how you go from an assumed underlying time structure of waiting times to an observable time series of increments, there is no way your hypothesis can be tested. I think I know why you avoid that. It is because you are afraid that more detailed statistical tests on such a synthetic time series will reveal that it is profoundly different from the observed GTA signal.
Nicola Scafetta (17:07:19) :
“In science the logic is: A implies B, observe B is true, then A is possible.”
I agree with the first statement. But in a Bayesian framework it can be made more precise. It is not only interesting to know that A is possible but rather how probable it is that A is true, and how more probable this has become after we have observed B to be true. If we denote the prior probability of A and B as p(A), and p(B), and the conditional probability of B, given A, as p(B|A), the Bayes’ theorem states that the probability of A, give that we have observed B to be true , is
p(A|B)=p(B|A)p(A)/p(B).
From this expression we see that the confidence in A is changed by the factor p(B|A)/p(B) by observing that B is true. Assume that A is the hypothesis that LW noise is hidden in the GTA signal, and B is the observation of exponents from DAE and SDA analysis with D different from H, but both close to unity. The question is now what values we assign to p(B|A) and p(B). Let us assume that we agree that if if A is true we will observe B, we will have that p(B|A)=1, so our change in belief is really given by 1/p(B).
Here we are coming to the point where our paths diverge. From a glance at the GTA signal I would be certain that B is true, without performing any analysis at all, hence I would assign a prior probability p(B)=1, and hence the analysis would not change my belief. This can be formulated in a less subjective way by showing that there exist a set of mutually exclusive alternative hypotheses H_i that all give the result B and whose probability sum up to nearly 1, i.e. that p(B)=\sum_i p(B|H_j)p(H_j)~1.
You, Nicola, do not realize that there are so many other probable explanations of your observation B, so you will assign a very small value to the prior probability of B, i.e. you would assume p(B)<<1. But that assumption is objectively wrong.
Another (and more subjective) element that determines the a posteriori belief p(A|B) is the prior belief in the hypothesis A. I find it very improbable, and would set p(A)<<1. Your analysis should only change into a believer if the product p(A)/p(B) is close to unity. But since I don't consider p(B) to be much less than unity, I still should not believe in your hypothesis.

Nicola Scafetta (05:44:10) :
“The Bayesian framework does not have any physical meaning because in physics one deals also with the unknown.
If we were living in 1600 you would use it to support Aristotle against Galileo.”
Interesting. Could you elaborate on that? How systematic testing of hypotheses against observations within a Bayesian framework would end up supporting Aristotle, who never bothered doing experiment or observation.
Should I understand your statement that you reject Bayesian hypothesis testing as a scientific method?