Meet Reverend Thomas Bayes. He was a Presbyterian minister who lived in London and had a keen interest in mathematics.
He died in 1764, but a formula he developed 300 years ago continues to rock the world ... from search engines to medical diagnosis to spam filters to Christian apologetics. If you use Google, like most of us do, you are using a Bayesian search engine. Your spam filters, most likely, are based on a Bayesian approach.
I first heard of Bayes Theorem in grad school at Duke. Turns out Duke has a lot of Bayesians. Go here and search for the word "Duke" and you will see what I mean.
Why the interest in Bayes, you say?
Aside from the incredible success of Bayesian applications in today's world, I have begun to see Bayesian inferences popping up in the field of apologetics. If you read the transcript to the Craig - Ehrman debate, you read an application of probability calculus regarding the probability of the resurrection hypothesis being true in light of the evidence of the resurrection -- and in light of the paucity of evidence for naturalistic alternatives.
Bayesian thinking has also played a role in the intelligent design discussion. I have seen ID'ers use Bayesian thinking to argue for an inference to the best explanation. I have seen anti-ID'ers use Bayesian statistics to argue against the anthropic principle.
The reason is because Bayes Theorem is used to adjust our beliefs in something in light of observable evidence supporting that belief. Bayes is about modifying degrees or strength of belief.
Here is another way to think about it.
Bayes Theorem, unlike Karl Popper's falsification approach, assists us in dealing with positive evidence. Popper's philosophy tells us to set up conditions to falsify or disconfirm a theory. We test for that condition, and if it happens, the theory is falsified. The underlying philosophy is that theories can never be absolutely confirmed, but they can be decisively disconfirmed if predictions turn out to be false.
Bayes is different. Bayes modifies our belief in something in light of supportive evidence. Get the difference?
Incidentally, Bayes does not trump Popper or anything like that. If evidence turns up which disconfirms a hypothesis, then a Bayesian will reach the same conclusion as a Popperian. In Bayesian terms, if evidence disconfirms a hypothesis, then confidence in the hypothesis goes to zero.
So how does Bayes Theorem work?
I will explain that in my next post on Reverend Bayes and his elegant little formula.
MY brain...it hurts...make it stop. A googling I go to get ready for your next post. I have a long standing rule to introduce myself to a new theory or concept every week, agree with it or not. Here I go with Bayes..
Posted by: Carl Holmes | June 25, 2006 at 20:42
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We use Baysean algorithms in engineering to decide when we have enough data to make a decision. i.e., based on the degree of prior confidence in our approach, how much additional testing and development do we need to have confidence that we have a quality design? I can see the same approach being useful in apologetics where human nature guarantees that doubt will always be present to some degree. How much evidence do we need to be convinced? Unfortunately, Americans tend to think in black and white and it's difficult to sell this way of thinking.
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Of course a Calvinist might say the entire line of thought is irrelevent.
Posted by: John M. | June 26, 2006 at 11:12
Many digital communications receivers (from radios to cell phones to wi-fi) are based on Bayes theorem. The problem in communications is - given that our receiver has received some signal S, what is the probability that the signal X was sent at the transmitter? In a digital system, X can be only 1 of a finite number of values so all we have to do is find the X with the highest probability and that is the signal that was sent.
Anyway, Popperian philosophy of science and Bayesian philosophy of science are really just two of the newest ways of arguing about the proper way of doing science. Popper says we should make conjectures and hypotheses and then used tests to deductively refute those hypotheses. Bayesians say we should gather evidence and then based on the evidence, use induction to find the theory that best fits the data.
Posted by: macht | June 26, 2006 at 11:49
Bayesian thinking is hot -- thanks in large part to the success of Google.
Bayesian methodology can point to some tremendous success stories in technical applications. That gets people's attention and earns the right to be heard.
My interest is in the philosophical end of things. The Bayesian approach lends itself well to interpreting evidence -- which, of course, makes it a natural fit for apologetics (at least evidential apologetics).
A presuppositionalist will, of course, discount the subjective nature of Bayes and argue that worldviews will cloud probabilities. That is, the noetic effect of the Fall will render Bayes useless in apologetics. That is why John's comment "Of course a Calvinist might say the entire line of thought is irrelevent" is spot on (since most Calvinists tend to be presuppositional in their approach to apologetics).
Macht, your point about induction is exactly why Bayesian statistics will soon emerge in the intelligent design debate (if it has not already). The premise of the design inference is an inductive argument at its core. If Bayes philosophy triumphs over Popper, then ID benefits.
The irony is that Bayes lends strength to subjective epistemology -- degrees of belief etc. That makes it kind of postmodernish whereas Popper has more of a clear right and wrong kind of feel.
That is what makes the study of the acceptance of Bayes Theorem so fascinating. It has implications on multiple fronts.
Posted by: Mr. Dawntreader | June 26, 2006 at 12:07
You may be aware of this already, but Dembski thinks that a Bayesian approach to design inferences is "problematic."
People like Elliot Sober have already used a Bayesian approach to critique ID.
I suppose I could also point out that Plantinga uses Bayes theorem in his famous evolutionary argument against naturalism.
Posted by: macht | June 26, 2006 at 17:44
You said:
"Bayes is different. Bayes modifies our belief in something in light of supportive evidence. Get the difference?"
I said:
"No, I don't get the difference."
Help me, help me, my mind is expanding!
Posted by: Lingamish | June 27, 2006 at 01:06
You may be aware of this already, but Dembski thinks that a Bayesian approach to design inferences is "problematic."
Yes. You stole my thunder :) I will address this in a future post. Dembski is a frequentist. He dedicates a chapter to it in The Design Revolution.
That is part of what makes Bayesian so much fun -- it twists and turns -- Plantinga and
Bill Craig use it, but Dembski eschews it.
I love the controversy.
Posted by: Mr. Dawntreader | June 27, 2006 at 16:35
Help me, help me, my mind is expanding!
It is good for you! :)
Hang around ... maybe it will make more sense after reading my example.
Posted by: Mr. Dawntreader | June 27, 2006 at 16:38