precisely. We’re all Bayesians now.

(Actually, to take posterior probabilities literally, our (collective) arse is grass)

Roger, I agree with your comment about how “there is no good reason to suppose any longer that high impact climate outcomes are low probability.” If we think of the IPCC AR4 version of the science as a “prior” distribution, and the latest science as a “posterior” distribution, then in my opinion the posterior distribution is in the dangerous tail of the prior distribution. This is what I would call a “Bayesian” way of thinking about the problem.

Paul Krugman has blogged about Weitzman’s paper here, and Joe Romm has a response here.

Peter W, thanks for the link. I think I actually googled and got the old one. Do you know whether it changed much?

Paul H, just wait and see.

Roger Jones, what a fascinating comment. Much to think about.

There is one reason why I do not combine the terms low probability with high impact. There is no good reason to suppose any longer that high impact climate outcomes are low probability.

And people have accused me of being alarmist.

Also I love the notion that at least part of reality doesn’t conform to Bell curves.

I’ll have to take a longer run at the linked papers, but on a quick squizz they look interesting.

Get a grip!

Paul H

i can haz rayzon deter… raisin debtor… purrpose?

Although anyone reading a paper on climate change won’t be expecting much by way of absolute temp readings.

Took the words right out of my mouth, FDB.

“for U.S. readers: 10C=18F and 20C=36F”

I’m sure this guy Weitzman is very smart but on page 2 of his paper he says 10 degrees C = 18 degrees F and 20 degrees C = 36 degrees F.

When you’re talking about temperature changes, they are.

I’d like to encourage anyone brave enough to scan through a hundred pages o’ stuff to check out what we wrote in 2006 (first link below), using similar probabilistic approaches to Weissman.

There is one reason why I do not combine the terms low probability with high impact. There is no good reason to suppose any longer that high impact climate outcomes are low probability. Irreduceable probabilities is one reason why. Many of these outcomes have so-called “fat tails”, caused by feedbacks - they are not normally distributed, which assumption comes from looking at the world using bell curve frequentist statistics.

Some of our probabilistic work can be found here (pdf) and here although this whole issue is interesting (comes from an OECD study).

My view on value of statistical life (VSL) calculations is that they should not be used to value human lives but flow on impacts on the economy only.

In the second link Yohe and I say there better methods than cost benefit analysis to this issue, that point also agreed by Sheehan and one that we are pursuing.

One final point. The argument is often made that we would not accept a one in one million risk of an air crash, but people do (Aeroflot and even more adventurous airlines come to mind). It is also a frequentist risk, so we treat that differently to how we treat a one-off. How do people hedge single event uncertainties? We are not sure how, and people are not well equipped psychologically to do so.

It seems we are willing to place our long term survival as a global society, or even regional aspiringly comfortable society at much higher risk that one in one million. One in ten, two in three, fifty-fifty? This is a dead serious issue that is bound in human psychology and culture.

If we don’t want to gamble our place on Earth, we need to have a serious conversation about how society views large risks separately from the hysterical modus operandi of public debate in the media.

Weitzman’s approach is to recognise that climate change is a probabilistic problem and work with the probability distributions (PDFs) from the outset. The costs and impacts of climate change are associated with PDFs that have long tails - in other words the PDFs are functions that approach zero much more slowly than the Gaussian distribution (the bell curve). This is related to the fact that catastrophic impacts cannot be ruled out. Weitzman demonstrates that this implies that expected utility cost benefit analysis leads to infinite expected costs. So in order to bound (and better understand) these costs, Weitzman introduces a parameter that he describes as a VSL-like parameter (VSL is short for the value of statistical life). This parameter is supposed to roughly approximate the value of life or of civilisation as we known it. If we introduce this parameter, the expected costs of climate change become finite.

The more we study climate change (and experience it), the more tightly we can bound the costs of climate change, but the PDFs will still have long tails. Weitzman’s dismal theorem can be interpreted as stating that no matter how many times we update our probability distributions by obtaining more information, the expected cost of climate change will still approach infinity as the VSL-like parameter approaches infinity.