Bayesion statistics and God's existence

[lucaspa]

I know, the thread got closed. However, I noticed no one talked about the Bayesian statistics themselves.

 

Bayesian statistics were very popular in the 1980s and 1990s. So popular that a number of clinical medical journals, such as Archives of Internal Medicine, required all clinical studies to use Bayesian statistics to give a probability of the efficacy and safety of a drug.

 

Bayes formula is P(H/E) = [P(E/H) x P (H)]/P(E), where:

 

H = hypothesis

E = evidence

P(H/E) = the probability of the hypothesis being true given the current evidence

P(E/H) = the probability of the evidence being present if the hypothesis is true

P(H) = the prior probability of the hypothesis

P(E) = probability of the evidence being found

 

P(H) and P(E) are related such that P(E) cannot be less than P(H)

Let's try this with an example, Einstein's theory of relativity and the bending of light experiment by Eddington in 1919.

 

It is reasonable to start off a new hypothesis with a prior probability of 0.5 (50/50). So P(H) = 0.5 After all, no current evidence contradicted relativity in 1919.

 

P(E/H) would be high, so let's have it = 0.9

At the time, it was not thought that there was a good probability of finding light bending, so P(E) will be set jsut a bit higher than P(H). So P(E) = 0.6

P(H/E) = (0.9 x 0.5)/0.6 = 0.75.

 

In this case, the probability of Relativity being true increased from 0.5 before the experiment to 0.75 after it. An increase of 0.25

 

Now, you could argue that Relativity was so weird that it's P(H) should have been lower. In that case, the P(E) would have been higher and you would have gotten a bigger bump.

 

For instance: P(H) = 0.1 and P(E) = 0.2

 

P(H/E) = (0.9 x 0.1)/0.2 = .45 Now the probability increased by 0.35 instead of 0.25. If you change P(H/E) to 0.99, the new P(H/E) = .495

 

If you also change P(E) to 0.11, then P(H/E) = 0.9. This is more like what we intuitively feel that the Eddington experiment did for General Relativity.

 

Now, there are several places where you can validly argue the accuracy of assigning numbers in Bayes Theorem in general and in this particular case.

 

However, notice that if you set the probability of God lower, then you are likely to increase the power of Bayes theorem. That is, if you set the P(H) of God at 0.1 instead of 0.5, it is likely you would have seen a greater increase in probability than if you start with P(H) = 0.5.

 

What we are not given in the news article are the different weights of the P(E). P(E) can be unpacked as a sum of P(E)1 + P(E)2 + P(E)3 ... with some of the P's having a negative number. In science you can sometimes make a good estimate of the different P(E), but this was not given for this case, and it can be argued that choosing the P(E) is arbitrary. Also, we don't have the P(E/H) given, altho I suspect it was 0.99 or close.

 

All in all, my opinion is that the Bayesian calculation for the existence of God is GIGO, but there are valid and invalid reasons for thinking so. Also, I tend to think of all Bayesian statistics as GIGO.