artigo interessante

[Francisco Cribari <cribari@de.ufpe.br>]

Fonte:
http://www.economist.com/science/displaystory.cfm?story_id=9645336


Statistics and climatology
Gambling on tomorrow

Aug 16th 2007
>From The Economist print edition

Modelling the Earth's climate mathematically is hard already. Now a new
difficulty is emerging

“SCIENCE” is a recently coined word. When the Royal Society, the world's
oldest academy of the discipline, was founded in London in 1660, the
subject was referred to as natural philosophy. In the 19th century,
though, nature and philosophy went their separate ways as the natural
philosophers grew in number, power and influence. 

Nevertheless, the link between the fields lingers on in the name of one
of the Royal Society's journals, Philosophical Transactions. And
appropriately, the latest edition of that publication, which is devoted
to the science of climate modelling, is in part a discussion of the
understanding and misunderstanding of the ideas of one particular
18th-century English philosopher, Thomas Bayes.

Bayes was one of two main influences on the early development of
probability theory and statistics. The other was Blaise Pascal, a
Frenchman. But, whereas Pascal's ideas are simple and widely understood,
Bayes's have always been harder to grasp. 

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. 

Psychologically, people tend to be Bayesian—to the extent of often
making false connections. And that risk of false connection is why
scientists like Pascal's version of the world. It appears to be
objective. But when models are built, it is almost impossible to avoid
including Bayesian-style prior assumptions in them. By failing to
acknowledge that, model builders risk making serious mistakes. 

Assume nothing

In one sense it is obvious that assumptions will affect outcomes—another
reason Bayes is not properly acknowledged. That obviousness, though,
buries deeper subtleties. In one of the papers in Philosophical
Transactions David Stainforth of Oxford University points out a
pertinent example. 

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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Francisco Cribari-Neto               voice: +55-81-21267425
Departamento de Estatistica          fax:   +55-81-21268422
Universidade Federal de Pernambuco   e-mail: cribari@de.ufpe.br
Recife/PE, 50740-540, Brazil         http://cribari.googlepages.com

    Bayes was a Bayesian, albeit a reluctant one. --Yudi Pawitan
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