Fuzzy dice

Source:  Climate Etc.  

by Judith Curry

Much is being made of Hansen’s ‘loaded dice’ as a metaphor for the changing climate.  I think we should be talking about ‘fuzzy dice.’

Hansen’s PNAS paper and the Washington Post have  received a huge play in the MSM and the blogosphere.  As an example of the media hype, see this article by Seth Borenstein (once again he solicited my comments, and didn’t use them).  “This is not some scientific theory. We are now experiencing scientific fact,” Hansen told The Associated Press in an interview.  The blogosphere is also rife with critiques of Hansen’s analysis; I had an earlier critical post at Climate Etc. [here].

Lets focus in on the ‘loaded dice’ metaphor used by Hansen.

‘Loaded’ dice

Here is how Hansen explains the ‘loaded dice’ in the op-ed:

Twenty-four years ago, I introduced the concept of “climate dice” to help distinguish the long-term trend of climate change from the natural variability of day-to-day weather. Some summers are hot, some cool. Some winters brutal, some mild. That’s natural variability.

But as the climate warms, natural variability is altered, too. In a normal climate without global warming, two sides of the die would represent cooler-than-normal weather, two sides would be normal weather, and two sides would be warmer-than-normal weather. Rolling the die again and again, or season after season, you would get an equal variation of weather over time.

But loading the die with a warming climate changes the odds. You end up with only one side cooler than normal, one side average, and four sides warmer than normal. Even with climate change, you will occasionally see cooler-than-normal summers or a typically cold winter. Don’t let that fool you.

When we plotted the world’s changing temperatures on a bell curve, the extremes of unusually cool and, even more, the extremes of unusually hot are being altered so they are becoming both more common and more severe.

The change is so dramatic that one face of the die must now represent extreme weather to illustrate the greater frequency of extremely hot weather events.

Rigging the dice

On the recent thread Loaded(?) dice, I argued that Hansen’s analysis of increasing probabilities of extreme heat events was ambiguous.  Apart from problems with the statistical methodology, there is an underlying assumption in Hansen’s analysis (as revealed in his op-ed) that any increase in heat waves must be due to anthropogenic global warming.  Hansen’s analysis failed to consider the 1930?s, when a very substantial number of heat wave records were set.

Cliff Mass has an interesting post entitled Climate Distortion.  Here is an excerpt:

Well, lets start with a little test.

The heat waves/droughts in the mid-section of the U.S. during past two years were caused by:

a.  90% natural variability and 10% human-induced global warming
b.  50% natural variability and 50% human-induced global warming
c.  10% natural variability and 90% human-induced global warming

Time is up!  Write down your answer.  As I will try to demonstrate, the correct answer is probably very close to (a).  90% of the temperature anomaly this and last summer is the result of natural variability with a minor assist from global warming.

Read the Mass’ post, see if you are convinced by his argument for (a).  Whether or not you are convinced by Mass’ argument for (a), I think that you will agree that there is no justification for a prima facie assumption of (c).

Kerry Emanuel has a great statement on this over at dotearth:

This is a collision between the fledgling application of the science of extremes and the inexperience we all have in conveying what we do know about this to the public. A complicating factor is the human psychological need to ascribe every unusual event to a cause. Our Puritan forebears ascribed them to sin, while in the 80’s is was fashionable to blame unusual weather on El Niño. Global warming is the latest whipping boy. But even conveying our level of ignorance is hard: Marty’s quotation of Harold Brooks makes it sound as though he is saying that the recent uptick in severe weather had nothing to do with climate change. The truth is that we do not know whether it did or did not; absence of evidence is not evidence of absence.

My summary point is that in order for Hansen to draw the conclusion he did from his analysis (even assuming that it was statistically robust), he needs to assume (c), that is, he has ‘rigged the dice’ with an unsupported assumption.  I.e. our old friend circular reasoning.

Fuzzy dice

I think the appropriate ‘dice’ metaphor is ‘fuzzy dice.’  The philosophical foundations for fuzzy dice are laid out in this paper by Joel Katzav (more on this paper next week).  Excerpt:

But philosophers of science, computer scientists and  others point out that probabilities fail to represent uncertainty when ignorance is deep  enough. Assigning a probability to a prediction involves, given standard probability frameworks, specifying the space of possible outcomes as well as the chances that the predicted outcomes will obtain. These, however, are things we may well be uncertain about given sufficient ignorance. For  example, we might be trying to assess the probability that a die will land on ’6? when  our information about the kind and bias of the die is limited. We might have the  information that it can exhibit the numerals ’1?, ’6? and ’8? as well as the symbol ‘*’, but  not have any information about what other symbols might be exhibited or, beyond the  information that ’6? has a greater chance of occurring than the other known symbols,  the chances of symbols being exhibited. The die need not be a six sided die. In such  circumstances, it appears that assigning a probability to the outcome ’6? will  misrepresent our uncertainty.

Assigning probability ranges and probabilities to ranges can face the same difficulties as assigning probabilities to single predictions. In the above example, uncertainty about the space of possibilities is such that it would be inappropriate to assign the outcome ’6? a range that is more informative than the unhelpful ‘somewhere between 0 and 1?. The same is true about assigning the range of outcomes ’1?, ’6? and  ’8? a probability.

One might suggest that, at least when the possible states of a system are  known, we should apply the principle of indifference. According to this principle, where knowledge does not suffice to decide between possibilities in an outcome space, they should be assigned equal probabilities. Some work in climate science acknowledges that this principle is problematic, but suggests that it can be applied  with suitable caution. Most philosophers argue that the principle  should be rejected. We cannot know that the principle of indifference will yield reliable predictions when properly applied. If, for example, we aim to represent complete ignorance of what value climate sensitivity has within the range 2 to 4.5 °C, it is natural to assign equal probabilities to values in this range. Yet whether doing so is reliable across scenarios in which greenhouse gasses double depends on what climate sensitivity actually tends to be across such scenarios and it is knowledge of this tendency that is, given the assumed ignorance, lacking. Further, we can only define a probability distribution given a description of an outcome space and there is no non-arbitrary way of describing such a space under ignorance. What probability should we assign to climate sensitivity’s being between 2 and 4 °C, given complete ignorance within the range 2 to 6 °C? 50 % is the answer, when the outcome space is taken to be the given climate sensitivity range and outcomes are treated as equiprobable. But other answers are correct if alternative outcome spaces are selected, say if the outcome space is  taken to be a function not just of climate sensitivity but also of feedbacks upon which climate sensitivity depends. And in the supposed state of ignorance about climate sensitivity, we will not have a principled way of selecting a single outcome space.

Although the case of the die is artificial, our knowledge in it does share some features with our knowledge of the climate system. We are, for example, uncertain about what possible states the climate system might exhibit, as already stated in the case of climate sensitivity. 

Quick summary:  The fuzzy dice metaphor implies that we may not be dealing with a six sided dice (representing our ignorance).  How should we reason about rolling fuzzy dice to infer something about future heat waves?  Stay tuned for my post next week on Katzav’s paper.

Be Sociable, Share!

Tags: , ,