Monday, July 20, 2009

On possibility and necessity

Eli has come to understand that both frequentist (Tamino) and Bayesian (James Annan) statistical descriptions have serious problems when applied to climate from scientific and policy standpoints. The mixture of the two is quadratically difficult as anybunny entangled in discussions of future changes can tell. Local responses to global trends which are worse.

There is, however, another way of looking at things, loosely described as Possibility Theory. Possibility Theory grew from studies of fuzzy sets and is useful for analyzing situations where knowlege is incomplete and was first described by Lofti Zadeh. Wikipedia, of course, has a description.

Rather than assigning a distribution of probabilities, Possibility Theory differentiates between the possibility and the necessity of an outcome. Some are beginning to use possibility theory to describe climate related issues, for example stream flow, climate scenarios. Also take a look here


Hank Roberts said...


That's ... that's ... BEYOND PROBABILITY!

James Annan said...

Yes, I've been keeping an eye on this sort of thing but am not really convinced that the benefits are worth the effort. It's sort of like a "robust Bayes" analysis where you consider a range of priors, but you can't get something for nothing as you still have to decide how wide a range of priors to use.

One unwelcome consequence is that if you ask a bunch of experts for their opinions, there is a strong incentive for them all to exaggerate, because it is only the outliers that define the range of outcomes, all those in the middle might as well not have been there (and the experts know this!). Think opening the overton window so wide the house falls down.

Roger Jones said...

Hmmm, I've been doing this stuff for over a decade. It's really very simple but only one small hat tip from any of the three papers Eli linked to.

I know - I haven't been making it look scientific enough.

James, there is a very simple way to check outcomes versus priors and that is to find out how much a priori subjective assumptions affect potential decisions. I am amazed more people aren't doing this instead of investing in overly complex set-ups. Decision-makers just don't need that much precision.

Been saying this for a while now, testing and using it, but I guess no-one is going to take any notice until it is explained in mathematical notation obscure but impressive-looking jargon. The Shrdlu meta-gravy effect perhaps (if you've ever read Emile Mercier).

Anonymous said...

It's not clear to me why straightforward "expectation" (ie, overall expected cost) is not sufficient to figure out a sensible approach to investing in mitigation and adaptation.

After all, good poker players use this all the time whether and how much to bet based on their "expected return" -- taking into account the probability of various outcomes (getting certain hands) -- even though they have no idea what hand they will actually get or what hands others will get.

EliRabett said...

IEHO the real advantage of possibility theory is that it may fit better into the way policymakers think and act. That, and it divides ignorance from noise, something to be valued

EliRabett said...

Roger (or anyone else) if you want to put up a list of references with some comments the management would be pleased to move it to the top of the page. What was posted was a stub to get things going.

EliRabett said...

James, you might use a modified Delphi process to control enthusiasm, going back to the panel and asking them to rate the entire set of outcomes for a weighting

James Annan said...

find out how much a priori subjective assumptions affect potential decisions

Roger, I couldn't agree more and have argued for this myself.

Anonymous said...

Not sure, but I believe this easy to read on the bus book:
What's the Worst That Could Happen, by Greg Craven
...falls in this category.

Hank Roberts said...

I love the book review. The videos by the same guy who wrote the book have been really good for quite a while.

Can anyone (don't cheat) guess who the reviewer is, from this excerpt?

"... I learned something from it - an achievement I might have thought impossible ...."

(Clue, he's big on the blogosphere, especially the last week or two.)

jyyh said...

I've been thinking this but to find the various threshold values between different +- stable states in climate quickly becomes impossible as in the real world some changes are indeed gradual, but some are abrupt. Examples in the biological side of science are f.e. gradual shifts of preferred weather areas for a studied species or outbreaks of pests due unlucky cold spell that kills off parasites but not the pest. I know weather forecasters have expected weather patterns arising from some sort of typical conditions, say two thirds of low pressures go here but the one third does something else, maybe this could be expanded to climates also, or, as our host says is being done already. So much to read (and learn maths)... maybe that's a SEP...