Note: this is the fifth and final installment of our review of the paper “Bayesian reasoning in science” by Colin Howson and Peter Urbach.

We now come to the “main event”: the problem of priors.

That is, where are you supposed to get your Bayesian priors from? (To return to the coin-toss experiment we discussed in our previous post, for example, what prior should the experimenter assign to the probability of the coin being fair?) Aren’t all persons’ priors ultimately subjective and thus non-scientific, for as Howson and Urbach acknowledge on p. 374 of their paper: “at some point … prior probabilities will have to be used which merely reflect [subjective] opinion.”

In the last part of their paper, Howson and Urbach describe several valiant attempts to generate “explicit, ‘objective’ rules for calculating priors” yet end up conceding that “there seems to be no way of ‘objectively’ defining prior probabilities.” So, what is to be done, then? How do Howson and Urbach, in particular, deal with the problem of priors?

In brief, the authors argue that subjectivity is good, that subjectivity is universal, and that subjectivity is irrelevant.

First, they argue that the subjective nature of Bayesian priors is a strength, not a weakness: “… our argument has all along been that this is really no weakness: it allows expert opinion due weight …” [Time out #1: what if the “experts” themselves disagree with each other? Whose prior wins out?]

Next, they take a direct swipe at Fisher and his sundry disciples, arguing that all science is inherently subjective [time out #2: really?] and that Bayesian methods are at least open and honest about their subjectivity. In the pull-no-punches words of Howson and Urbach:

[A subjective prior] is a candid admission of the personal element which is there in all scientific work. The inventors of ‘objective’ methodologies [ i.e. Fisher and his ilk] … merely sweep the personal element under the carpet.

Lastly, they argue that the subjective nature of Bayesian priors is irrelevant, since persons with different prior beliefs should converge in their posterior beliefs as data and evidence accumulate (assuming those persons are good Bayesians, of course). [Time out #3: so why do we see so little convergence in so many different domains, such as politics, economics, and philosophy?]

Are you persuaded by any of these arguments? Are they consistent with each other? Let us know what you think …

Keep calm and update your priors.