The Dawn Treader

Bayes Bayes Bayes!

Evangelical Outpost has a great post feature which references one of my favorite topics: Bayes Theorem.

Bayesian thinking plays a role in the global warming debate.  How so?  Because the talking heads would have you believe that man is the main contributor to global warming.  But, is that true?

It is a non-falsifiable statement.  Therefore, the best approach is to assign probabilities and likelihoods, incorporate evidence, and adjust our beliefs in light of this evidence.  Now you have entered the realm of Bayes Theorem.  I spilled a fair amount of virtual ink last year on how to use Bayes Theorem.

The best post to start learning Bayes with is at the very bottom : Evidence, Probability and Belief : Introducing Reverend Bayes And His Remarkable Idea.

Dembski On Bayes

I would be remiss in my series on Bayes Theorem if I did not mention Dembski's view on using a Bayesian approach to infer design.

Bayesian Apologetics

Ok, so technology incorporating Bayes Theorem played a role in making him and him billionaires.    And Bayesian search technology played a key role in finding the USS Scorpion and the recovery of a lost H-bomb in the 1960s.  Bayes is clearly successful and has made some people look like absolute geniuses.

But does Bayes have any application in the field of apologetics?

Resolution To The Problem

Kudos to Tom for taking a swing at the Bayes problem.

Flexing Your New Bayesian Muscles

Now that you learned Bayes Theorem here, time to put it to use.

Here's a situation that doctors might encounter:

1% of women at age forty who participate in routine screening have breast cancer.  80% of women with breast cancer will get positive mammographies.  9.6% of women without breast cancer will also get positive mammographies.  A woman in this age group had a positive mammography in a routine screening.  What is the probability that she actually has breast cancer?

What do you think the answer is?

WARNING: Most doctors get the same wrong answer on this problem - usually, only around 15% of doctors get it right.  See Casscells, Schoenberger, and Grayboys 1978; Eddy 1982; Gigerenzer and Hoffrage 1995; and many other studies. 

If you get it right, you are smarter than 85 percent of the doctors in the United States!

Bayes Theorem For The Utterly Confused

Mention the word conditional probability and most people's eyes start to get a glazed look.  So, let's dispense with statistics-speak and splain Bayes Theorem in plain English.  In truth, you already know the gist of Bayes Theorem because it reflects the way we intuitively process observational evidence.

WARNING: this post contains mathematical concepts.

Evidence, Probability and Belief : Introducing Reverend Bayes And His Remarkable Idea

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.