I loved reading Nate Silver (he of the accurate 2012 election forecasts) new book ‘The Signal and the Noise: Why So Many Predictions Fail but Some Don’t.’ I especially liked his chapter on climate change: A Climate of Healthy Skepticism. In it he uses Bayes’ Theorem to address the probability of climate change being accurately predicted. His previous explanation, earlier in the book, of Bayes’ Theorem, which helps you adjust your belief rationally in the face of new evidence, is the first explanation of the theory I have fully grasped. Here is Nate applying it to the new evidence on climate change. The supporting detail is in the chapter of his book and the rest of his book too.
Uncertainty is an essential and nonnegotiable part of a forecast. As we have found, sometimes an honest and accurate expression of the uncertainty is what has the potential to save property and lives. In other cases, as when trading stock options or wagering on an NBA team, you may be able to place bets on your ability to forecast accurately.
However, there is another reason to quantify uncertainty carefully and explicitly. It is essential to scientific progress, especially under Bayes’Theorem.
Suppose that in 2001, you had started out with a strong prior belief in the hypothesis that industrial carbon emissions would continue to cause a temperature rise. (In my view, such a belief would have been appropriate because of our strong causal understanding of the greenhouse effect and the empirical evidence for it up to that point.) Say you had attributed the chance of the global warming hypothesis being true at 95%.
But then you observe some new evidence: over the next decade, from 2001 through 2011, global temperatures do not rise. In fact, they fall, although very slightly. Under Bayes’ Theorem, you should revise your estimate of the probability of global warming hypothesis downward: the question is by how much.
If you had come to a proper estimate of the uncertainty in the near-term temperature patterns, there is about a 15% chance that there will be no net warming over a decade even if the global warming hypothesis is true because of the variability of climate. Conversely, if temperature changes are purely random and unpredictable, the chance of a cooling decade would be 50% since and increase and a decrease in temperature are equally likely. Under Bayes’ Theorem, a no net warming decade would cause you to revise your estimate of the global warming hypothesis’s likelihood to 85% from 95%.
Here’s his math:
Initial estimate of how likely it is that global temperatures are increasing 95%: x
Probability of no net warming over 10 years if global warming hypothesis is correct: 15%: y
Probability of no net warming over 10 years if global warming hypothesis is false: 50%: z
Revised estimate of how likely it is that global warming is occurring, given no net temperature increase over 10 years:
Bayes’ Theorem gives us:
xy/xy +z(1-x) = 0.95.0.15/0.95.0.15 +.50(1-.95)= 85%
On the other hand, if you had asserted that there was just a 1% chance that temperatures would fail to increase over the decade, your theory is now in much worse shape because you are claiming that this was a more definitive test. Under Bayes’ Theorem, the probability you would attach to the global warming hypothesis has now dropped to just 28%.
When we advance more confident claims and they fail to come to fruition, this constitutes much more powerful evidence against our hypothesis.
He goes on to say some other interesting things, but my point here is not to contribute to the climate change debate, but simply to note that under Bayes’ Theorem, if your prior belief that climate change is not happening, that it is 0% probable, then no data will change your mind, as it is still 0% likely with the new data, and I guess if you are 100% certain it is happening then ditto as your standard for disproof will be higher and Bayes will predict it is still 100% whatever the new data. Personally, my own prior belief in 2 degree C warming per century was around 80% to begin with, so with the ten year hiatus, it drops to 54% in the light of the new data given Nate’s other assumptions.
So I guess my suggestion is that anyone who thinks global warming is either 0% likely or 100% likely is under Bayes’ Theorem not open to changing their prior conviction, or what I might call them, they are belief fundamentalists on this issue.
More on the Reverend Bayes (1701-1761) at: http://en.wikipedia.org/wiki/Thomas_Bayes