### Dr. James A. Lindsay's Bayesian Analysis of the Outsider Test for Faith

I find his analysis very helpful. He summarizes his post in the following words:
Bayes's theorem allows us to consider numerically what the effects of considering different pieces of information have on the likelihood (and thus acceptability) of a hypothesis we wish to put to the test. In the case of Loftus's Outsider's Test for Faith, we will approach the numbers that we put into Bayes's theorem far differently than we would without the OTF. In particular,
• The OTF has the goal of having someone consider their assumption of the prior probability that their religion is true more honestly against a broader perspective, greatly reducing the tendency of a biased believer inside a faith to overestimate the prior probability. The OTF will cause someone to lower their assumed prior probability to a more realistic value. (This is what I have called a here, usually labelled something like P(h|b) in math-speak.).
• The OTF has the goal of having someone consider how well the evidence (i.e. the universe) matches their religion's claims about it more honestly, greatly reducing the tendency of a biased believer inside a faith to overestimate the degree to which the assumption of truth of their religion predicts the evidence presented by the world. The OTF will cause someone to evaluate the failure of their religion to explain reality more seriously, lowering this consequent to a more realistic value. (This is what I have called t here, usually labelled something like P(e|h,b) in math-speak.)
• The OTF has the goal of having someone consider how well other explanations of the evidence would explain what is seen on the presumption that their religion is false. This number is hard to see honestly from within a religious framework and is likely to be underestimated by believers inside it, and the OTF will have the effect of reducing the tendency to underestimate this number. (This is what I have called n here, usually labeled something like P(e|~h,b) in math-speak.)

A few further notes on each:

• The overestimation of the prior probability from the insider's perspective is likely to be a wild exaggeration of reality that completely neglects the true diversity of incompatible religions and the viability of non-religious positions.
• The overestimation of how well the evidence matches what we should see under the assumption that the religion is true is likely to be the most incredibly wildly exaggerated number in the construction, often being relatively close to 1 for strong believers whereas an outsider is likely to see this number as so close to zero (or actually zero, if you believe me) as to literally destroy the entire basis for faith. Here is where the biggest struggle will take place for most believers who take the OTF--seeing that the world really would be a vastly different place if their religion was true. Only by truly stepping outside of it is there any hope of that, which is exactly what the OTF asks people to do.
• The underestimation of how well the evidence is explained by other explanations is likely to be severe as well. Even on the assumption that a religion must be the thing to explain it, with a complete rejection of naturalism, if someone admits that there are 20 religions attempting to do so, then this number has to be at least 19/20 (95%) from an outsider's perspective (instead of the 50-60% likely from believers--though some will go lower toward 0!). Even a cursory glance at science from the perspective of the outsider will point to hundreds if not thousands of ways that science has outperformed religion in explaining the world in even modestly educated folks, rendering this number very near 1 for anyone that takes the OTF honestly.