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Six Sigma Deviation for Antarctic Sea Ice

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Re: Six Sigma Deviation for Antarctic Sea Ice

#31
post #27

Earlier quoted context omitted.

> It boggles my mind that a warm blooded creature that needs arable land would be upset about icecaps melting. The earth is a large system with lots of inertia. When some aspect of it changes relatively quickly, it's natural to be uneasy. Particularly when the downstream consequences of that change are already becoming visible. To wit CO2 levels over the last 1my. https://www.epa.gov/climate-indicators/climate-change…

[flagged]

Do you have stake in the game? If you are wrong about this, will you take responsibility?

The wager is: we try to do the conservative thing by reducing emissions. The side effects are positive, anyway, since it will also reduce pollution.

The other side of this wager is, we do nothing: and the potential is catastrophic for everyone.

Doesn't it seem like a silly gamble?

Re: Six Sigma Deviation for Antarctic Sea Ice

#32
I want to make clear up front that I take global warming absolutely seriously, that it is undoubtedly human-caused, and that it is progressing faster than consensus models have predicted.

But the interpretations given to 34 years of highly-correlated time-series data are highly questionable and largely unwarranted.

Put briefly, we have very little long-term global remote-sensing data largely because remote sensing didn't exist until the 1960s, and largely came of age long after then. As with this data series which begins in 1989.

We *ABSOLUTELY DO* have many other long-term data series showing tremendous changes and associated climatic conditions: ice-core data going back 800,000 years, sea-level measurements going back a billion+ years (at which point plate tectonics are a major confounding factor), plant growth distributions and patterns dating back millions of years, and global temperature inferences also dating back on the order of a billion years or more.

And yes, assuming a normal distribution, a six-sigma event is extraordinarily rare. But to make accurate inferences of such extreme-outlier events based on 34 measurements is statistical malpractice.

Call this "unprecedented in the data record". Call it "extremely concerning". Find other data series with which this pattern can be correlated and from which stronger inferences might be drawn.

(Note that ice-field extant data before the age of satellite observation are very thin, though outlier events such as bergs being sited in temperate waters might well occur, and that shipping logs do tend to record numerous events of interest and date back about 500 years over a fairly wide area. Indigenous records from, say, Tierra del Fuego might also note sitings over a longer period.)

Sources: three years of stats courses at uni, work in stats and data reporting professionally and at an amateur level, though not an actual statistician.

Re: Six Sigma Deviation for Antarctic Sea Ice

#33
post #16
post #9

Earlier quoted context omitted.

Maybe you can make an argument that, in the absence of any information, your best bet is assuming a Gaussian distributon, but it definitely is not safe to assume so. Your data might not be symmetrically or even unimodally distributed and making these assumption can lead to completely wrong conclusions.

If you know that your data has a well-defined mean and standard deviation but you know nothing else about it then you start with a Gaussian distribution. This isn't an assumption. The Gaussian distribution has the highest entropy and hence encodes the least information possible about the data. Then as you learn more about your data, you would update this distribution using Bayes' theorem. This could give rise to skew…

I would consider a well-defined mean and standard deviation an assumption. The distribution of maximum entropy is determined by the constraints. Those constraints have to be assumed. If you constrain your problem to only have nonzero probabilities in a fixed interval, then a uniform distribution will have maximum entropy.

Re: Six Sigma Deviation for Antarctic Sea Ice

#34
post #11

Earlier quoted context omitted.

In this case, as each day is highly correlated to the previous one, it is safe to say that the distribution of daily sea ice variation is probably not Gaussian? (Though obviously, this is very bad...)

The comparison is between ice extent measurements at the same date, at differing years, so the day-to-day correlation is not the relevant metric here, but the year-to-year correlation, which should be very low.

There's still something funny about quoting tail probabilities converted to once in X years, though, isn't there? Maybe I'm thinking about this wrong...

Re: Six Sigma Deviation for Antarctic Sea Ice

#35
Well bite me for not chiming in with some rehash of the Earths-heating-be-very-afraid greenhouse dogma, but specifically

( https://www.nature.com/articles/s41598-022-05449-8 ) Persistent extreme ultraviolet irradiance in Antarctica despite the ozone recovery onset ?

That is an Earth change I could sink my teeth into because our measurements of ozone are first rate, the crisis continues and Antarctica is a known target of the phenomenon.

Re: Six Sigma Deviation for Antarctic Sea Ice

#36
post #33
post #16

Earlier quoted context omitted.

If you know that your data has a well-defined mean and standard deviation but you know nothing else about it then you start with a Gaussian distribution. This isn't an assumption. The Gaussian distribution has the highest entropy and hence encodes the least information possible about the data. Then as you learn more about your data, you would update this distribution using Bayes' theorem. This could give rise to skew…

I would consider a well-defined mean and standard deviation an assumption. The distribution of maximum entropy is determined by the constraints. Those constraints have to be assumed. If you constrain your problem to only have nonzero probabilities in a fixed interval, then a uniform distribution will have maximum entropy.

I agree that there is an assumption that the data are well described by a distribution on R instead of some interval [a,b]. I don't know how well justified this is. The assumption of well defined mean and stddev is weak and better supported each time you collect more data. If your stddev is ill defined then you'll find your sample stddev will diverge (increase) as you add more data points.
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