Bayes’ Theorem & Bayesian Reasoning

If you’re familiar with the recent revival in interest concerning the evidence for Gods existence, the evidence for the resurrection for Jesus, and the case for Jesus’ historicity, you probably (!) have heard of Bayes’ Theorem. So what’s all the fuss? Essentially, Bayes’ Theorem – as used in the Humanities – allows historians, philosophers, and Religious Studies scholars a simple and sure way of estimating and comparing the probabilities of various hypotheses. What makes it so special is that it factors in the relevant evidence, all the background knowledge, and all reasonable hypotheses (explanations). This means that people can’t just boast about how the evidence fits their theory so wonderfully. They also need to show that their theory is superior to other theories, and to show that its overall probability, with the prior (or inherent) probability factored in, is still impressive.

It is here where Bayes’ Theorem, or the less-quantitative (and thus less scary) version I call Bayesian Reasoning, really shines. The various hypotheses are compared to the relevant evidence. How well the theory explains the evidence gives us the consequent probability. Hopefully, it is high for our theory, and gives us a good ‘evidence differential’ too. i.e., it is somewhat exclusively high for our theory. That is only part of the probability calculation. Bayesians also factor in the prior probability, which is determined by the all-important background knowledge. The fellow that claims that aliens who are fascinated with bovine anuses has a pretty good theory, consequent probability wise, to explain the (graphic) evidence of his abused farm animals. Unfortunately for the perverted redneck, alien encounters being extremely rare means that we would apply a low prior probability to his not well thought out defense.

Can there really be a better way to approach probabilistic questions than by factoring in all the evidence and considering all the possible explanations? If there is, I’d like to hear it. Now part of the power behind Bayesian Reasoning is that its results give us probabilities rather than certainties, and the results can change as our collective knowledge increases. One implication is that the apologist cannot decry our love of Bayes simply because they feel that the use of prior probabilities disadvantages them – low priors can be overcome by the right evidence, in principle. Using Bayesian Reasoning to test religious claims is particularly exciting for atheists, making me wonder why sophisticated religious apologists use it too. But I suppose it’s not immune to the GIGO principle – garbage in, garbage out.

When using correctly sourced data, however, this logical and sound approach makes it incredibly easy to show how absurd religious claims often are. And now we have mathematical proof for our beloved skeptical maxim. Extraordinary claims really do require extraordinary evidence! —Raphael Lataster