Bayesian analysis of intelligent design (revised!)

This is a revision of my earlier post. In Jaynes' awesome statistical manifesto book (another link), I just saw for the second time the odds ratio form of Bayes' rule, which is a lot cleaner for this sort of static analysis. So anyway...

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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 Intelligent Design theory (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

I'll explain the interesting conditional hypotheses H|E and E|H and the prior H in a second. 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. I guess we could take a poll of how many organisms picked at random look intelligently designed, but that confuses me greatly with what the events are and such.

Instead, let's eliminate the P(E). The standard way to do this is to expand it into a sum. But then it's hard to see how increaes and decreases in different variables affect the overall outcome. Instead, we use here the odds-ratio form of Bayes' rule.

P(H|E)   =  P(E|H)  P(H)  / P(E)  and of course  
P(~H|E)  =  P(E|~H) P(~H) / P(E)

so then divide...

P( H|E)     P(E| H)   P( H)
-------  =  ------- * -----
P(~H|E)     P(E|~H)   P(~H)

Let O(A) mean the "odds" of A. O(A) = P(A) / P(~A). If you want to roll a 6 on a die , your probability is 1/6 ("one out of six"), and your odds are 1:5 ("one to five against.") Note that P(A) > P(B) implies O(A) > O(B), so you can use your up and down intuitions about likeliness just fine with odds ratios. This notation makes Bayes' rule look really clean:

           P(E| H)
O(H|E)  =  -------- * O(H)
           P(E|~H)

It's easy to see: The "looks designed => was desgned" reasoning of ID is supported by high P(H), high P(E|H), and low P(E|~H).

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

H: prior belief organism was designed
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.

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 all that not up for 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|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. I don't think this question is mentioned that much in creationism/evolution debates.

P(E|~H) is a big point of controversy. 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.

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

Conclusions: (1) lots hinges on a hard-to-debate prior P(H). This implies that ID can be quite rational given a strong prior belief in a creator, or quite irrational given a strong prior disbelief in a creator. One of ID's aims is to rationally disprove evolution by arguing about E|~H and E a lot. But I don't think argument over H is going to get you anywhere; if your prior beliefs in God are very different, it may be difficult to reconcile your beliefs in evolution versus intelligent design.

(2) Don't forget the neglected E|H: if an organism was intelligently designed, the plausibility it looks that way to us.

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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?

ID advocates are trying to establish a scientific/rational argument for intelligent design:

The theory of intelligent design (ID) holds that certain features of the universe and of living things are best explained by an intelligent cause rather than an undirected process such as natural selection. ID is thus a scientific disagreement with the core claim of evolutionary theory that the apparent design of living systems is an illusion.

In a broader sense, Intelligent Design is simply the science of design detection -- how to recognize patterns arranged by an intelligent cause for a purpose. Design detection is used in a number of scientific fields, including anthropology, forensic sciences that seek to explain the cause of events such as a death or fire, cryptanalysis and the search for extraterrestrial intelligence (SETI). An inference that certain biological information may be the product of an intelligent cause can be tested or evaluated in the same manner as scientists daily test for design in other sciences.

I'll put SETI in a similar category with ID, but those other quite fine fields mentioned all have reasonable and agreed-upon priors, like whether you suspect humans lived on a certain island, wanted to commit arson, etc. It seems reasonable to use prior hypotheses about the existence and intentions of human beings. In a given scientific community, there's probably decent consensus on the priors. A bunch of arson analysts might agree on H, that of all fires a given percentage of them are arsons. But given the evidence surrounding a specific fire, they can investigate and argue about H|E, whether it was an arson, by examining whether or not an arson is a likely explanation for the facts of the case: E|~H and E|H.

But of aliens and God, well, the H is a matter of faith. In evolution theory, E|~H is super controversial, and E|H is ignored. ID'ers and evolutionists just don't have enough common ground for there to be a good debate.