Well, if it were that easy to prove it, anyone could.

(Besides, 67% doesn’t actually “prove” anything, or disprove it, either.)

cap: standard

If you apply a formula such as Unwin’s to alien life forms the probability that such life exists must approach somewhere around 90% or greater.  Yet, most Christians don’t believe life exists outside of this planet because they have seen no evidence of such life and there is no mention in the bible of such life.  It’s another ruse of pick and chose.

Not surprisingly Bayes’ theorem can work very well when it is properly applied to a physical problem. Here is an example from a 1968 paper by Edwin James of Washington University.

For example--a famous example that Laplace actually did solve--proposition A might be the statement that the unknown mass of Saturn Ms lies in a specfied interval, B the data from observations about the mutual perturbations of Jupiter and Saturn, C the common sense observation that Ms cannot be so small that Saturn would lose its rings; or so large that Saturn would disrupt the solar system. Laplace reported that the data up to the end of the 18th century, Bayes’ theorem estimates Ms to be (1/3512) of the solar mass, and gives a probability of .99991, or odds of 11,000:1, that Ms lies within 1% of that value. Another 150 years accumulation of data has raised the estimate 0.63 percent.

He also used Bayes’ theorem to decide which astronomy problems to work on.

Laplace also published (1812) a remarkable two--volume treatise on probability theory in which the analytical techniques for Bayseian calculations were developed to a level that is seldom surpassed today.

Unfortunately, there were some conceptual difficulties with the math that Laplace developed that he didn’t explain clearly enough, and Bayseian analysis languished until the middle of the last century.

Two other notably successful applications that I am aware of occurred in the 1960s when a Navy Scientist used Bayesian techniques to locate the H-Bomb that the Air Force carelessly dropped in the ocean and to locate the USS Scorpion.

I just finished this book. Unwin does do a good job of explaining Bayesian analysis (which, as VernR explained, works quite well for some problems), but fails to defend its use for a gauzy problem like the existence of God.

One huge problem I had with his analysis was his prior probability of 50%. I wouldn’t start at 50% for the existence of unicorns or dragons, so I started at 10% (to be generous), added the evidentiary area of “no direct sensory evidence exists for God’s existence,” worked through the steps, and came up with a probability of 0.01%.

Bottom line: this analysis will only reflect what you think already, which makes it worthless. I’m sure a devout Southern Baptist would end up with a probability of 99.9%.

This will probably seem long-winded, but I will finally get around to saying that both Les and KT are right.

Over the years I have tried to understand how to apply Baye’s theorem and have never succeeded very well—meaning that I can work simple textbook examples, if I don’t have to close the textbook. When I read through the original post and the SA article, two things threw me off of what was going on in this particular problem: the ‘modified’ form of the Bayes equation which I had never seen before I read Shermer’s article, and Unwin’s Divinity Scale which I didn’t immediately recognize as a scale of odds ratios (even though it was pretty clearly labeled as such).

The light-bulb flickered on earlier today when I realized that Unwin’s methodology was similar to a pedagogical exercise in sequential testing that Jaynes presented in one of his papers*. Jaynes was originally a EE so he re-expressed odds ratios on a decibel scale**. If you plot probability level (y axis) vs e, with e values from say -30 to + 30, you get a nice s-curve where y ranges values very nearly zero to y values very nearly one. At the y-axis crossing (e = 0) the p-level is one half.

In his analysis Unwin takes a reasonable Baysean position that, since he doesn’t know whether God exists or not, his prior assessment is that p = ½ (e = 0). Because of the transformation, what was a multiplicative (updating) process is now an additive process. Each piece of new evidence (D-value) results in a shift to the right or left along the e axis. Unwin’s D-values result in the following e value shifts

+10, -3, -10, +3, 0, +3.

This sequence nets to an overall shift in e to a final value of 3, which corresponds to an odds ratio of 2:1 (a final Pafter equal to 2/3).

Well, that is a nice numerical exercise, but statistics and probability theory were developed to predict outcomes of physical processes, to tell how precisely we know something after taking a series of measurements, or to use data to make ‘good’ decisions (about processes). Someone choosing a value on Unwin’s D-scale is in no sense making a measurement. That’s why Les was right—D-scale values are totally subjective personal assessments.

This next gets to KT’s point. In his writings, Jaynes indicated that if analysts have prior knowledge, they should use that knowledge as a starting point for their subsequent analyses. I say that in a so called Baysean discussion about the existence of God that true believers (David and others) would use an initial e value of + infinity and a true non-believers (nowiser and others) would use an initial e value of – infinity. No finite sequence of D-values would result in final assessments differing from initial assessments.

Shermer gets the final word.

Religious faith depends on a host of social, psychological and emotional factors that have little or nothing to do with probabilities evidence and logic. This is faith’s inescapable weakness. It is also, undeniably, its greatest power.

* My latest text book
** e = 10 log(odds ratio).

VernR commented that:

This next gets to KT’s point. In his writings, Jaynes indicated that if analysts have prior knowledge, they should use that knowledge as a starting point for their subsequent analyses. I say that in a so called Baysean discussion about the existence of God that true believers (David and others) would use an initial e value of + infinity and a true non-believers (nowiser and others) would use an initial e value of – infinity. No finite sequence of D-values would result in final assessments differing from initial assessments.

My comment: While this may be true, Bayesian analysis is not useful if the prior rules out any hypothesis (as +/- infinity would do). A more honest approach would put a very small or very large value of e (depending on who you are) and then let the evidence fall where it may. It appears to me (not having read Unwin) that he is playing fast and loose with how one folds the data into the likelihood. The criticisms of his work that address this aspect are right on target.