Saturday, July 09, 2005

a bayesian analysis of intelligent design

UPDATE: just wrote a revision of this.

Pick an organism. Two propositions, H and E, each may be either true or false about it.

H: the organism was designed by an intelligent creator.
E: the organism looks like it was designed by an intelligent creator.

Most of what I know about ID is from seeing a talk by Michael Behe (may 2005). He had to major lines of argument: (1) it is implausible that an evolutionary process could produce life that looks as if it was intelligently designed. (2) Since it looks like it was intelligently designed, it was. He really emphasized the E component of the argument.

Justifications for E: Lots of organisms look like they were intelligently designed. They have complex and intricate mechanisms involving coordination among many components. Sometimes they look like things humans would design: for example, bacteria locomotion devices sometimes bear uncanny resemblance to human-designed motors or propellers.

Behe was really into showing all these quotes from pro-evolution authors like Dawkins who note this fact: many forms of life appear to us as if they were designed. Consider one of those organisms where E is true. This organism looks as if it was designed.

However, does that mean it actually was designed? That's a different proposition, the difference between H and E. Since I distrust human intuition on matters of intention ascription (we do it too often), I'd rather look towards a rational framework.

What is the plausibility that this ID-looking orgnanism actually was designed? That's asking to evaluate P(H|E). Bayes rule tells us how to find P(H|E): the plausibility of a hypothesis H, given the truth of a proposition E (evidence).

Bayes rule derived:

P(H|E) P(E) = P(E|H) P(H)

P(H|E) = P(E|H) P(H) = likelihood * prior
----------- --------------------
P(E) marginal likelihood

P(H|E): if the organism looks like it was ID'd, the plausibility it actually was. (the core ID argument)
P(E|H): if the organism was ID'd, the plausibility it looks ID'd.

P(E|H) at first seems odd: certainly, if a creator intelligently designed an organism, doesn't that mean we'd be able to tell? Well, not necessarily: what if a designer makes decisions we cannot understand, or we can't divine the intelligence in the design of an organism? If that is likely to be the case, then P(E|H) decreases, and H|E becomes less likely.

P(H) is a pretty nasty prior: forgetting the evidence of whether it looks designed, what's the chance an organism was intelligently designed? That question seems to hinge on prior beliefs in the existence and activity of a creator. It's not up to debate. If you are already certain God exists, it may be reasonable to entertain the notion that organisms were intelligently designed. If you are less certain God exists, you may believe P(H) to be lower.

P(E) denotes the likelihood to find an organism that looks like it was intelligently designed. Though P(H|E) denotes the plausibility H is true given E is true, to evaluate it we have to look at the probability E could be true independently. The standard way to do this is to expand P(E).

P(H|E) = P(E|H) P(H)
P(E|H) P(H) + P(E|~H) P(~H)

E|~H: if the organism was not ID'd (e.g. it evolved), the plausibility it looks ID'd.

Some evolutionary theorists argue P(E|~H) can be quite high. e.g. Dawkins' "Blind Watchmaker": Nature can create impressively complex and purposeful looking life through random chance and natural selection. Behe's presentation seemed to unfairly argue down E|~H by only considering gradualist Darwinist explanations of evolution. It seems implausible that one-at-a-time tiny mutations could produce big complex systems like the eye or the immune system. That is, it's too hard to get out of local minima. However, to examine E|~H you need to look at all alternatives to ID. Complexity theory explanations might note that great complexity and order can emerge out of randomness; thus, the formation of complex systems through evolution is more plausible than our intuitions might tell us. Or exaptation: old adaptations might be put to new uses.

And of course, there's the hard-to-debate prior P(~H) again.

For reference, here are all the propositions again:
H: the organism was designed by an intelligent creator
E: the organism looks like it was designed by an intelligent creator
E|H: if the organism was ID'd, the plausibility it looks ID'd.
E|~H: if the organism was not ID'd (e.g. it evolved), the plausibility it looks ID'd.

So, here's how things line up for and against ID:

belief pro-ID belief reasons anti-ID belief reasons
E|H high ID'd organisms will look ID'd to us low we may not understand a designer's designs; they may not look familiar or intelligent to us

E|~H low gradualist adaptationism is unlikely to explain complex systems high blind watchmaker, complexity theory, exaptation... an evolutionary process could lead to outcomes that look as if they were designed.

H high prior belief in a creator and that creator's likelihood to design life low prior disbelief in a creator and that creator's likelihood to design life

Caveat: I'm confused how to analyze a given organism versus picking one at random. Does that make a difference?

Also, I'm wondering how to determine how much priors matter. When should argumentation over evidence for evolution force you to revise your beliefs about God? Is there a rational way to do this belief revision? If there isn't, are we all condemned to stick to our prior beliefs?


At 12:00 PM, Anonymous Jon Baron said...

You ask whether it matters if you pick an organism at random or
not. I think the answer depends on what you mean by (the
implicit) "or not." If you select one because it is particularly
well designed, then you must take into account the effect of your
choice itself on the quality of the evidence. You would want
something like p(E/H) and p(E/"~H and I picked this because it
looked good"). The latter would of course be higher than
p(E/~H), and p(E/H) would also be higher than for some organism
picked at random.

You also ask whether there is a rational way to revise beliefs.
Of course I think there is, although it is often essentially
impossible to apply the normative model in real cases. This
case, though, is reasonably simple. The normative model is
Bayesian theory. I sketch a justification of it in
my chapter in
the Blackwell Handbook of Judgment and Decision Making

Of course, people do not follow this model, which keeps people
like me - psychology researchers who study biases - in business.


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