## Friday, November 04, 2011

### Reversing the null hypothesis

Eurekalert discusses three essays written by Kevin Trenberth, Judith Curry, and Myles Allen.

Trenberth says that the null hypothesis should be reversed: "the man-made climate apocalypse is coming" hypothesis should become the null hypothesis and you would have to provide a proof or evidence if you wanted to disprove it (very easy!). Curry correctly argues that Trenberth proposition is just a political doctrine meant to bully the climate skeptics but she unreasonably proposes that "hypothesis testing" should be abandoned in science (or at least in their discipline).

Myles Allen of Oxford, a mathematical physicist, correctly says that Trenberth's suggestion is misguided but Curry's suggestion is even more misguided. However, he incorrectly applies this correct appraisal to the climate science when he suggests that the hypotheses about a big human influence on various atmospheric phenomena haven't been excluded yet.

So what is the truth?

The truth is that the hypothesis testing is essential in any science. As long as climate science is expected to remain a science, it is needed in the climate science, too. A priori, before any evidence is accumulated, all qualitatively distinct hypotheses have to be given comparable prior probabilities. As evidence arrives, it modifies the posterior probabilities of different hypotheses. The hypotheses that are clearly incompatible with the evidence are being abandoned; the hypotheses that are consistent with the observations are being clarified, ramified, and new competing hypotheses evolved out of the old successful ones are competing in their ability to describe more detailed evidence.

In this evolution of the human knowledge, it's pretty much guaranteed that "simpler" hypotheses must be tested at the beginning, and only when they're excluded, more detailed, contrived, or "a priori arbitrary" hypotheses have to be tried. This obvious fact is also reflected in the language: the "null hypothesis" is the old and therefore simpler hypothesis we're testing. During the tests, it may happen that the quantity that was supposed to be zero according to the "null hypothesis" is measured to be greater than "5 standard deviations" – five times the typical "error margin". When this happens, it's a typical point where we may become sure that the "null hypothesis" is wrong because the thing that should have been zero isn't actually zero. We say that the null hypothesis is falsified (the number "5" is a matter of conventions but it should never be much lower than 5). When the null hypothesis is excluded, we are forced to consider more specific, more surprising, and potentially more "contrived" hypotheses where some new effects – previously set to zero – are no longer zero (sometimes they're equal to another non-zero number determined by other principles). The probabilities of all of our beliefs are being gradually adjusted according to various evidence that we're exposed to; if Judith Curry believes that this process may be abandoned – or that science may work without the fundamental process of the falsification of hypotheses – she's just wrong about a very basic point.

However, Kevin Trenberth is also wrong – when it comes to a more specific point that depends on what the hypotheses are. He says that the "man-made climate change" should become the new "null hypothesis" that must be universally believed unless you present evidence to the contrary. This proposal by Trenberth only has two problems: the "man-made climate change" claim cannot become a new "null hypothesis" because it is not "null" and because it is not a "hypothesis", either.

It's not null because for a claim to be "null", it must say that various a priori unknown effects have to be zero. The AGW doctrine says that they're not zero so it can't be null. The AGW doctrine is one of billions of different contrived hypotheses one could propose as alternatives to a null hypothesis – i.e. a random model of the (natural) climate change. Instead of CO2 from the fossil fuels, we could also propose that the thunderstorms are driven by the French perfumes or millions of other things. None of these things can be called "the null hypothesis" because it's obviously less null than the hypothesis that the human effect on important weather events is zero, i.e. null.

The second, related problem is that the AGW doctrine isn't really a hypothesis because it doesn't conjecture anything specific. It's not well-defined. The climate sensitivity isn't a well-known number. The same problem occurs with the hypothetical effects of CO2 on floods, hurricanes, snowstorms, or whatever the insane people have speculated over the years. If hardcore high-energy crackpots hadn't hijacked the phrase, I would quote Wolfgang Pauli who told David Bohm that his musings about (non-)quantum mechanics were not even wrong. A null hypothesis in the statistical approach to hypothesis testing must actually make some predictions. In typical cases, it says that the statistical distribution of certain quantities will be "unbiased" or "centered at zero": the mean value of a properly calculated things has to be zero according to a null hypothesis: that's why it has "null" in its name.

The AGW doctrine says that the mean value of these quantities (man-made influence on one atmospheric effect or another) is non-zero, so it is at most a non-null hypothesis, but it doesn't say what the number actually is so you can't subtract this predicted mean value to get a "null prediction". More precisely, it is not a hypothesis at all because it cannot be tested. It can't become a starting point of the scientific research because it is totally vacuous. The only invariant thing about the AGW doctrine is that the man is evil. But this pathological, politically emotional declaration can't be given any quantitative meaning in science, except for psychiatry. The whole doctrine isn't a hypothesis, it can't be tested, and it can't ever become a part of the scientific research. It will always remain a religious slogan of brainwashed political movements and any group of people that allows such political slogans to play a role becomes utterly unscientific.

Meanwhile, one may formulate more specific and genuinely scientific hypotheses that are "inspired" by the AGW doctrine. For example, one may conjecture that the number of hurricanes per year can't drop below the long-term average if the CO2 emissions exceed 25 billion tons a year or CO2 concentration exceeds 380 ppm. One may conjecture that above 2 ppm of the annual rise of the CO2 concentration, each 10-year period must experience a warming trend according to the linear regression applied to the satellite temperature data. Such specific conjectures are legitimate and accessible to the scientific method but every single non-vacuous scientific hypothesis inspired by the AGW doctrine has already been proved wrong. The proofs have been so consistent and the AGW-inspired hypotheses have been so consistently failing that we may also say that science (including rudimentary psychiatry) has also proved that whoever believes that man-made CO2 is an important and detrimental factor affecting the climate has been proved to be a psychopath, too.

This particular proposition is a good null hypothesis (in psychiatry) because it actually says that something is zero: the number of AGW crusaders who are not psychopaths at the same moment. However, their would-be "null hypotheses" are not null hypotheses because they can't make any analogous statement of the type that "something is zero".

1. What is thr difference between a hypothesis and a prior distribution?

2. It depends what Trenberth means, really. When it comes to the factual reality of AGW (i.e. that increasing atmospheric CO2 will increase global surface temperatures, even if the increase is undetectably, immeasurably small) then I think that most scientists would probably agree that that is a null hypothesis. But as for humans being the primary cause of the observed increase atmospheric CO2 and the primary cause on the increase in global temperatures, they still have a long way to go to prove that theory empirically. Right now it’s just the wish-fulfilment of ivory-dwelling climate modellers’ and has no basis in reality as far as I can see. It’s contradicted by a host of evidence and well-accepted, established physics, such as Henry’s law, isotope-measurements, and dozens of experiments of CO2’s emissivity. Trenberth has put so much into the AGW-theory, he can’t back out now to save face as the whole AGW-edifice crumbles rapidly around his feet, as much as he probably wants to.

3. Dear Richard, I am afraid you haven't understood what the "null hypothesis" is. The claim you mention doesn't make any quantitative statement - any statement that something is "null" or otherwise well-defined - so you can't test it (and/or exclude it in principle) in the way the null hypotheses are tested and excluded. That's why it's not a null hypothesis. I am not discussing whether the statement is right or wrong; I just say that it can't be classified as a null hypothesis in statistical tests, at least not in this form.

Harlow, a hypothesis is a particular statement such as "the daughters of Ms Horse and Mr Ass can't have any off-spring". A prior distribution is a collection of numbers interpreted as probabilities that are assigned to various possible answers to a question. For example, a biased coin yields "1" with 18% probability... and "6" with a 15% probability.

Hypotheses and prior (or other) distributions are related but I really don't understand in what sense you could confuse them. It's like confusing poems with electric trains. I really don't know how to help you if you confuse things that are this distant.

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5. Dear Lubos, your last metaphor was a bit dicey. :)