All the probabilities in a Bayesian calculation are plausibilities. In this case the plausibility happens to be equal to a frequency: this is equivalent to using the principle of indifference about the identity of the particular person.

]]>I enjoyed your recent Bayesian lecture. I do wonder about the irony of your example involving the patient with a positive test result–Given the probability of false positives, what is the probability that this particular patient actually has the disease in question?

The irony of this example is that in order to use the Bayesian method effectively, we must have some means of finding the probability of false positives. How do we do this in practice? Well, we just count them; that is, we become “frequentists.” So on the right side of Bayes theorem we have a frequentist estimate yielding a Bayesian result for probability on the left side.

My suspicion is that this operation, although very useful, tends to give many users too much false confidence in Bayesian probabilities. I would favor calling the left side of Bayes theorem the “estimated probability,” to avoid the trap of sweeping our ignorance under some rug. In this case the actual probability would be an abstract idea as in the classical theory of stochastic systems.

]]>Yet here you explicitly agree with that statement.

]]>This is not the same as a “frequentist estimate”. There are probabilities that the Bayesian can calculate that the frequentist cannot even define, such as the probability of general relativity given our observations of the solar system. We can’t observe more than one universe, so we can’t count the number that obey general relativity.

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