December 25, 2005

Joe Carter & Bayes Theorem: A Train Wreck

My advice to those Creationists out there that do not understand probability theory is to simply leave it alone. Failure to head this advice could lead one to look perfectly ridiculous. Case in point, Joe Carter.

Joe wants to calculate the probability of the existence of God. To do this he has decided that Bayes Theorem is the way to go. Predictably the results are a complete train wreck of a post.

Well, lets check it out. First up is this comment,

The evolutionary history of man proceeds from the beginning of the universe (i.e., the Big Bang) to the pinnacle of human development (i.e., the creation of the human mind). Because the progression is linear, we can examine the evidence for each step and use Bayes' theorem to help us update or revise beliefs in light of new evidence.

Linear? No, the progression is sequential, not linear. So what are the events in question?

    E1. From the Big Bang to chemical evolution of non-living matter

    E2. Chemical evolution of non-living matter to single cell organism

    E3. Single cell organism to multicellular organism

    E4. Multicellular organism to Homo sapiens

    E5. Evolution of Homo sapient brain to modern human mind.

Joe then assigns relative probabilities to these events as follows:

  • E1. 0.5
  • E2. 0.1
  • E3. 10
  • E4. 2
  • E5. ??

For the last one, Joe says it is easy to assign a probability, but he apparently forgot to tell us the actual number.

Then based on all this Joe cranks out that the probability that God exists is 91%, implying a 9% chance that the world and universe are the result of natural processes.

So what is wrong with this? First, the God Hypothesis does not have to be mutually exclusive with some of the events that Joe mentions. That is E2 - E5 could have all been somehow "pre-programmed" into the universe prior to the big bang. After all, we are talking about a supernatural being who has powers we cannot understand. Thus, Joe's interpretations of the final probabilities is just not correct,

When I plug these rather generous numbers into the Bayes’ formula* I find that there is a 9% probability that the data supports the claim that human beings are the result of natural undirected causes and a 91% probability that it does not. To be clear, this is not saying that there is only a 9% likelihood that the theory is true, only that based on the data (or at least my interpretation of it) I would be foolish to think it is even remotely plausible that humans could be created by non-teleological processes.

Since the God Hypothesis is not mutually exclusive from many of his events Joe's conclusion does not follow.

The other problem is that Joe's probability assessments are completely and totally wrong. We are talking about God after all so the obvious probabilities are

E1 = E2 = E3 = E4 = E5 =1

That is God can do all of these things if he wills it. So even if we start with a low probability for the God Hypothesis, the mere fact that these events occurs will result in us favoring the God Hypothesis. Here is the proof:

Let G be the event God exists. Let A be one of the events in Joe's list. Now what we want to know is P(G|A), that is what is the probability that God exists given that A occurs (or we learn of A). Using Bayes Theorem we get

.

And dropping the denominator on the right hand side we can write,

And using similar reasoning we have the following for the Naturalist Hypothesis (i.e. there is no god),

Now, if we start with a non-informative prior probability (note this is Steve Unwin's default prior) The P(G) and P(~G) are equal and can be dropped. Now, with naturalism, it is probably going to be the case that P(A|~G) < 1. After all, isn't this what Creationists love to argue? The probability of the human brain evolving is miniscule via natural methods, therefore God. Therefore it follows that,

Even in the general case where the priors for God existing and God not existing being different wont save us so long as we have enough of these events. Eventually the God Hypothesis will win out. This is just another reason why the God Hypothesis is a science stopper. Including an omnipotent being into your scientific analysis destroys all other hypotheses. We can dispense with all other scientific theories and go with simply the God Hypothesis.

And the problems don't stop there. Joe Carter has whole heartedly embraced Dembski's explanatory filter in other of his arguments for why God exists and evolutionary theory is insufficient to explain the existence of even something as simple as a 100 protein amino acid. The problem here is that Dembski's explanatory filter is a classical or frequentist statistical concept...not a Bayesian one. Hence, Joe Carter literally doesn't know whether he is coming or going with regards to his statistical philosophy. He'll glomb onto anything that fits his world view, and to Hell with all the significant contradictions it implies about that world view.

Update: I thought I'd also note that I think that Joe's view/post is bad theology as well. Think of it this way, here we have a God that has to keep monkeying around with his creation. He can't "write really good code" and then run the "program". No, we have an idiot God that has to keep tweaking things. He has to make sure the right kind of life evolves, that amino acids form, create the flagellum, etc. This God is so dumb he has to leave his signature all over the place for us to find. Some God, he can't get it right after billions of years trying.

Posted by Steve at December 25, 2005 12:06 PM
Comments

I hate to point this out after you after you've already gone to so much trouble, but you've completely misread my post. And you're misunderstanding has lead you to knock down a strawman. For starters...

Then based on all this Joe cranks out that the probability that God exists is 91%, implying a 9% chance that the world and universe are the result of natural processes.

Um, no. The post wasn't about the probability that God exist. In fact, I made it rather clear what it is about. Did you miss the line that read: "...I find that there is a 9% probability that the data supports the claim that human beings are the result of natural undirected causes and a 91% probability that it does not."

So what is wrong with this? First, the God Hypothesis does not have to be mutually exclusive with some of the events that Joe mentions.

You're right. And if you read the post again you'll notice that I never claimed it did.

Joe Carter has whole heartedly embraced Dembski's explanatory filter in other of his arguments for why God exists and evolutionary theory is insufficient to explain the existence of even something as simple as a 100 protein amino acid.

I have no idea what you are talking about. I don't recall embracing Dembski's explanatory filter "whole heartedly" much less doing so in a post arguing for the existence of God. Are you sure you have the right blogger? Perhaps you are confusing me with someone else.

The problem here is that Dembski's explanatory filter is a classical or frequentist statistical concept...not a Bayesian one. Hence, Joe Carter literally doesn't know whether he is coming or going with regards to his statistical philosophy.

Again, I don't know what you're talking about. I never mentioned Dembski or his explanatory filter in the post on Bayes. Where in the world did you get the idea that I was confusing the two?

Think of it this way, here we have a God that has to keep monkeying around with his creation. He can't "write really good code" and then run the "program". No, we have an idiot God that has to keep tweaking things.

Again, you're knocking down a strawman. I not only never said such a thing but it is the complete opposite of what I think. I think that there is likely a biotic law that is both both teleological and detectable by an inference from design. It's a false dichtomy to claim that either natural selection is the sole mecahnism for evolution or we must claim that "God is tweaking things."

I really can't believe you wasted so much time writing a rebuttal to things I've never written. Didn't you go back and check what I wrote while you were writing this post?

I suppose that since you couldn't defend the fact that there is a paucity of evidence for non-telological explanations you decided to knock down strawmen instead. Instead of working so hard to deny the evidence, why not just follow where it leads (as Anthony Flew did)?

Posted by: Joe Carter on December 26, 2005 01:14 AM
Um, no. The post wasn't about the probability that God exist. In fact, I made it rather clear what it is about. Did you miss the line that read: "...I find that there is a 9% probability that the data supports the claim that human beings are the result of natural undirected causes and a 91% probability that it does not."

Yes, but the problem still remains that neither is undirected. If God works in a way that totally appears to our limite view point as if man was created via natural means, it is still directed. If God is incompetent and leaves evidence all over the place of his existence/direction then it is still directed. Your conclusion is still incoherent.

I have no idea what you are talking about. I don't recall embracing Dembski's explanatory filter "whole heartedly" much less doing so in a post arguing for the existence of God. Are you sure you have the right blogger? Perhaps you are confusing me with someone else.

I know you don't Joe. There are philosophical differences as to how inferences should be made in a statistical sense. Broadly speaking there is the frequentist/classical and the conditional/Bayesian. The two are, generally speaking, not compatible as they take rather different views of things like probability and what exatly is being estimated.

And please stop playing word games here. The whole point of Dembski's filter is to detect the presence of design and hence imply the existence of a designer. It is also clear you think the designer is God. Therefore, it logically follows you see Dembski's filter as a method of proving the existence of God (as does Dembski).

The fact that you don't understand the differences between the Bayesian method and Dembski's method highlights that you are not being coherent in your view of statistical inference.

Again, I don't know what you're talking about. I never mentioned Dembski or his explanatory filter in the post on Bayes. Where in the world did you get the idea that I was confusing the two?

Statistics isn't just a great big grab bag of things you take that you like and reject when you don't like. If you are going to use the Bayesian method of inference it means you should have major methodoligical issues with Dembski's filter and otehr things he has written. And the problem is reversed if you accept Dembski's methods, but then want to use Bayesian methods. They. Are. Not. Compatible.

Again, you're knocking down a strawman. I not only never said such a thing but it is the complete opposite of what I think. I think that there is likely a biotic law that is both both teleological and detectable by an inference from design. It's a false dichtomy to claim that either natural selection is the sole mecahnism for evolution or we must claim that "God is tweaking things."

Oh please, this is the whole crux of the biological design hypothesis. That certain things cannot happen naturally (or even by what appears as a natural process) but has to be the result of direct intervention. That is basically "tweaking things". Your God is incompetent. This is why Intelligent Design is bad theology, IMO.

I really can't believe you wasted so much time writing a rebuttal to things I've never written. Didn't you go back and check what I wrote while you were writing this post?

Coming from somebody who doesn't understand the difference between Bayesian and Classical inference you'll have to pardon me if I consider this to also be incoherent.

Posted by: Steve on December 26, 2005 10:09 AM

I know you don't Joe. There are philosophical differences as to how inferences should be made in a statistical sense. Broadly speaking there is the frequentist/classical and the conditional/Bayesian. The two are, generally speaking, not compatible as they take rather different views of things like probability and what exatly is being estimated.

Since I responded to this at my own blog, I won’t rehash it here. It appears that you seem to think that using probability frameworks is an either/or position, similar to being a Democrat or a Republican, and that you must choose one or the other for every case. I’m not sure where you got this idea but it appears to be the core of your strawman.

Therefore, it logically follows you see Dembski's filter as a method of proving the existence of God (as does Dembski).

Your grasp of logic appears to be as weak as your grasp of statistical methods. No, detecting design does not prove the existence of God. In fact, as Dembski himself notes, detecting design does not even prove the existence of a designer.

The fact that you don't understand the differences between the Bayesian method and Dembski's method highlights that you are not being coherent in your view of statistical inference.

Since you keep making stuff up, perhaps its time I call you on it. Please point out for me where I have used the Bayesian method as an explanatory filter. This is about the third time you’ve made that assertion without a shred of evidence to back it up.

Statistics isn't just a great big grab bag of things you take that you like and reject when you don't like. If you are going to use the Bayesian method of inference it means you should have major methodoligical issues with Dembski's filter and otehr things he has written. And the problem is reversed if you accept Dembski's methods, but then want to use Bayesian methods. They. Are. Not. Compatible.

You don’t really understand the difference between when frequentist and Bayesian methods apply, do you? I think that is the crux of the problem and the reason you completely misunderstand this whole argument.

Oh please, this is the whole crux of the biological design hypothesis. That certain things cannot happen naturally (or even by what appears as a natural process) but has to be the result of direct intervention.

I’m not sure why I even bother arguing with you since you obviously have no idea what you are talking about. The crux of the biological design hypothesis is that design can potentially be detected in nature. If it happens in nature it is a natural process, therefore design would also be a natural process.

That is basically "tweaking things". Your God is incompetent. This is why Intelligent Design is bad theology, IMO.

Okay, Steve, you just keep knocking down the strawmen if it makes you feel better. I think my time would be better spent arguing with someone who has a basic understanding of the concepts involved.

Posted by: Joe Carter on December 26, 2005 11:54 AM
Since I responded to this at my own blog, I won’t rehash it here. It appears that you seem to think that using probability frameworks is an either/or position, similar to being a Democrat or a Republican, and that you must choose one or the other for every case. I’m not sure where you got this idea but it appears to be the core of your strawman.

Yes, it largely is an either or proposition. You either think that whatever you are trying to estimate has a probability distribution attached to it or you don't. Just because being Democrat/Republican doesn't entail either/or choices on all policy issues, doesn't mean the Bayesian/Frequentist issue isn't either/or.

Your grasp of logic appears to be as weak as your grasp of statistical methods. No, detecting design does not prove the existence of God. In fact, as Dembski himself notes, detecting design does not even prove the existence of a designer.

Dude, you don't even know what I'm talking about when it comes to statistics, and yet you think you can tell me about statistics?

As for Dembski and his filter, the whole point is that it rules out all other explanations save design. This implies a designer. Q.E.D.

Since you keep making stuff up, perhaps its time I call you on it. Please point out for me where I have used the Bayesian method as an explanatory filter. This is about the third time you’ve made that assertion without a shred of evidence to back it up.

I think it is well past time for you to stop lecturing me on reading comprehension and work on your own. I never, ever said you used the Bayesian method as an "explanatory filter". What I have argued is that you use both

1. The Bayesian/Conditional approach,
2. The Frequentist/Dembski approach.

These are diametrically opposed viewpoints. This is like saying you favor government ownership of the means of production and free markets.

You don’t really understand the difference between when frequentist and Bayesian methods apply, do you? I think that is the crux of the problem and the reason you completely misunderstand this whole argument.

This is amusing, I'm going to get a lecture on when to use Bayesian methods? It isn't a question of when to use them. Theoretically one can use Bayesian methods pretty much whenver one uses Frequentist methods. There are differences in how estimators are calculated, and there are other issues depending on the context, such as with nonparametric methods. The problem is philosophical. You can't mix-and-match the two philosophies as they are incompatible and when you do mix-and-match you get incoherent results.

The crux of the biological design hypothesis is that design can potentially be detected in nature. If it happens in nature it is a natural process, therefore design would also be a natural process.

Well, congratulations on moving the goal posts to such an extent to render the question completely moot. Congratulations, even if you lose, you win.

Posted by: Steve on December 26, 2005 03:56 PM
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