[archgoon]

Let's think about this.

Let's assume that when a river gets redirected, a scientist goes and investigates it (which seems reasonable), and is asked what is the chance that it happened by natural causes, or is due to global warming. Based on the analysis that @acover shared with us, we can see that out of a thousand such dispatches, 995 will be due to global warming and 5 will be due to natural variability. So it seems correct for that scientist to conclude "It's 99.5% due to global warming.". In fact, saying that it's .5% due to natural variability is equivalent.

You are probably thinking of the jelly bean situation, where a test is performed to detect something within a sample population. The test has a failure rate, and the population has a base rate of occurrence.

In this case (thanks @acover), they are directly calculating the base rate.

Now, you could also ask "How many times in a year will a scientist be dispatched and be wrong", which is a again a different question (and is closer to the scenario you described).

[acover]

I am out of my depths but I do not think you are correct.

The paper appears to create a model for a single glacier's retreat. Selects the parameters of this model by analyzing all glaciers. Then determines the retreat of this glacier is unlikely under this model.

The issue is that there is a sampling bias. This glacier is not like most glaciers [I assume]. It was not randomly sampled from all glaciers. It was selected because of a river diversion due to glacial retreat.

What did they do to compensate for this sampling bias? I don't see it.

[drt1245]

>Let's assume that when a river gets redirected, a scientist goes and investigates it

This is a faulty assumption and is what leads to the wrong conclusion. The probability of 0.5% is for a randomly selected river. That is, if you went and examined 200 randomly selected rivers, 1 of them (on average) would be redirected due to natural variability.

That does not imply that the remaining 199 were redirected due to global warming. It does not even imply that the remaining 199 were redirected at all!

What is needed is the percentage of rivers that have undergone this redirection. Here's a simplified example: If it's ~0.5%, you conclude it's just natural variation. If it's >0.5%, you conclude that something (possibly global warming) is increasing the number of rivers that are being redirected. If it's <0.5%, you conclude that something is decreasing the number of rivers that are being redirected.

[acover]

From the paper:

"shows our estimate that there is only a 0.5% chance that the observed retreat of Kaskawulsh Glacier happened in the absence of a climate trend"

The 0.5% has nothing to do with the river. It is their confidence that the retreat of the glacier could occur in the absence of a climate trend based on their model.

[archgoon]

Can you clarify why it is incorrect to reverse that into the statement "We estimate that there is a 99.5 percent chance that the observed retreat did not happen in the absence of a climate trend."? I confess to a fair amount of confusion at this point :) I'm sure there is something subtle (or perhaps obvious, and my brain is failing) that I'm missing.

What is the properly worded complement?

[archgoon]

This seems similar, but not identical, to the statement:

If there is not a climate trend, we would expect this to happen with a .05 chance.

If they meant the latter, my confusion is resolved.

[acover]

This is the blind leading the blind.

Fundamental truth: bayes theorem.

P(evidence | null hypothesis) = P(null hypothesis | evidence) * P (evidence) / P (null hypothesis)

The P-value test determines:

P(evidence | null hypothesis) = 0.5%

= there is a 0.5% chance of the observed evidence given the null hypothesis

The statement "We estimate that there is a 99.5 percent chance that the observed retreat did not happen in the absence of a climate trend."

translates to P(!null hypothesis | evidence) = 99.5%

By Bayes theorem:

P(!null hypothesis | evidence) = P(evidence | !null hypothesis) * P (!null hypothesis) / P (evidence)

We know almost none of these terms. The answer is not as simple as 99.5.

[archgoon]

Oh I thought we were having an interesting discussion about the linguistic mapping between probability and regular English. Sorry for wasting your time. :(

[archgoon]

> The probability of 0.5% is for a randomly selected river

Sorry, what is the probability .5% for exactly? The probability a river is redirected under global warming conditions? I didn't think that's what they computed. If it is, then my bad. :) I thought they had computed given that the river was redirected, what is the likelihood it happened due to global warming. Ah well, like I said, the details are the hard part. :)