I use Bayesian inference frequently and it comes up all the time when we are trying to interpret the results of test and measurements that we hear about. However, it’s incredibly difficult to develop an intuitive understanding of Bayes theorem. (This is something that Daniel Kahneman argues in “Thinking Fast and Slow” may never be intuitive.) Unfortunately most resources you’ll readily find (I’m looking at you Wikipedia) present an explanation that is rather obtuse. Eliezer S. Yudkowsky presents a good description [via Less Wrong] of how Bayesian inference works and provides nice examples to work through. This explanation is really quite good but it still doesn’t resolve the fundamental problem with any kind of statistical inference, namely that the user must really **think** about the problem. This is ultimately the step which seems to prevent people from making correct inferences. I use the word think here to mean that you have to work your brain, put aside other thoughts and focus. It’s easier to ignore the prior and take a frequentist approach. I wrote about this in an earlier post when I discussed how to interpret the DIBELS literacy test and how it might be misinterpreted.

This xkcd cartoon sums up the situation quite well:

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