From: Iain Strachan (iain.strachan.asa@ntlworld.com)
Date: Fri Aug 29 2003 - 15:49:53 EDT
Steve Bishop:
> Hi all,
>
> I have recently noticed how Swinburne and others have been using Bayes
> theory to "prove" Christianity. Using Bayes' theorem maintains that the
> ressurection of Jesus is 97% probable.
I find this hard to believe. Bayesian inference relates to using Bayes theorem to change the uncertainty about a random variable given data measurements. The so called "Prior distribution" (sometimes know as the "a priori" distribution) represents our state of knowledge (or ignorance) about an event before any empirical measurement (or event). When an event occurs, or measurements are made, Bayesian theory can then be used to infer the "posterior distribution" (or "a posteriori" distribution). We expect that the measurements (or event) will reduce our uncertainty about the variable; the posterior distribution will be more sharply peaked than the prior.
A problem for the theory is how to choose an appropriate prior distribution.
Here's a simple example. Suppose I told you that a person is 6ft 2in tall. Is it a man or a woman? Most people will probably say "male" on the grounds that 6ft 2 is above average for a man, but much further above average for a woman, & thus a 6ft 2in woman is less likely than a 6ft 2in man, given a normal distribution. However, there is an implicit assumption in this deduction, namely that the prior probability of a person being male is 0.5. If I told you I was thinking of a 6ft 2in nurse, then your prior probability of male probably drops to 0.05 to 0.1 (there are male nurses, but still mostly female). Then if I told you it was a 6ft 2in midwife who qualifited in 1953, then your prior probability of it being a man drops to around zero. Hence the prior probability influences your decision. In the case of the 6ft 2in person, we say probably male. The 6ft 2in nurse, we're not so sure; the 6ft 2in midwife from 1953 we are pretty certain it is a woman (probably more than 99% certain).
Now the problem I have with saying that Bayes shows that resurrection is 97% probable is this. How on earth do you assign a prior probability to someone rising from the dead? Is it zero, 1e-6, 1e-12, 1e-100? It's like picking a number out of thin air. And what are the events; the extra bits of information, that swing the posterior probability to .97? How can you be sure of those facts? How many examples are there of someone rising from the dead, to even find causes that would change the prior probability?
>
> Thomas Bayes (1702-1761) - the founder of Bayesian statistics
I don't think this is really true. Bayes formed a theorem of probability (which I read somewhere he didn't think of as terribly significant). It is only in recent times that a branch of statistics and probabilistic inference has arisen that exploits Bayes' theorem.
Practical uses for Bayesian techniques in, for example expert systems have only been possible with the advent of high powered computers. The theory used is called "Bayesian Belief Networks", which have been extensively studied. Unfortunately it is only possible to form inferences exactly for a very limited number of simple topologies (networks of causes), because the computational cost rises exponentially, though there are reasonably effective approximation techniques exist; but again, these are only feasible on a modern high powered computer. A good introduction to this is Kevin Murphy's paper:
A Brief Introduction to Graphical Models and Bayesian Networks
which can be found at: http://www.ai.mit.edu/~murphyk/Bayes/bayes.html
> Has any work been done on the connection between his beliefs and his
> mathematics?
>
As I said earlier, if I recall correctly, Bayes didn't regard his theorem as particularly significant. It seems his paper that sets out Bayes' theorem was published posthumously.
Iain.
This archive was generated by hypermail 2.1.4 : Fri Aug 29 2003 - 15:52:55 EDT