The Economist: Statistics and climatology: Gambling on Tomorrow
Modelling the Earth's climate mathematically is hard already. Now a new difficulty is emerging.
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Pascal's way of looking at the world was that of the gambler: each throw of the dice is independent of the previous one. Bayes's allows for the accumulation of experience, and its incorporation into a statistical model in the form of prior assumptions that can vary with circumstances. A good prior assumption about tomorrow's weather, for example, is that it will be similar to today's. Assumptions about the weather the day after tomorrow, though, will be modified by what actually happens tomorrow.
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Climate models have lots of parameters that are represented by numbers—for example, how quickly snow crystals fall from clouds, or for how long they reside within those clouds. Actually, these are two different ways of measuring the same thing, so whether a model uses one or the other should make no difference to its predictions. And, on a single run, it does not. But models are not given single runs. Since the future is uncertain, they are run thousands of times, with different values for the parameters, to produce a range of possible outcomes. The outcomes are assumed to cluster around the most probable version of the future.
The particular range of values chosen for a parameter is an example of a Bayesian prior assumption, since it is derived from actual experience of how the climate behaves—and may thus be modified in the light of experience. But the way you pick the individual values to plug into the model can cause trouble.
They might, for example, be assumed to be evenly spaced, say 1,2,3,4. But in the example of snow retention, evenly spacing both rate-of-fall and rate-of-residence-in-the-clouds values will give different distributions of result. That is because the second parameter is actually the reciprocal of the first. To make the two match, value for value, you would need, in the second case, to count 1, ½, ⅓, ¼—which is not evenly spaced. If you use evenly spaced values instead, the two models' outcomes will cluster differently.
Climate models have hundreds of parameters that might somehow be related in this sort of way. To be sure you are seeing valid results rather than artefacts of the models, you need to take account of all the ways that can happen.
That logistical nightmare is only now being addressed, and its practical consequences have yet to be worked out. But because of their philosophical training in the rigours of Pascal's method, the Bayesian bolt-on does not come easily to scientists. As the old saw has it, garbage in, garbage out. The difficulty comes when you do not know what garbage looks like.
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