Bayesian inference (and mathematical reasoning more generally) isn’t just about getting the answer; it’s also about clarifying the mapping from assumptions to inference to decision.

Palko writes:

I’m just an occasional Bayesian (and never an exo-biologist) so maybe I’m missing some subtleties here, but I believe educated estimates for the first probability vary widely with some close to 0 and some close to 1 with no good sense of the distribution. Is there any point in applying the theorem at that point? From this Wired article:

If or when scientists detect a putative biosignature gas on a distant planet, they can use a formula called Bayes’ theorem to calculate the chance of life existing there based on three probabilities. Two have to do with biology. The first is the probability of life emerging on that planet given everything else that’s known about it. The second is the probability that, if there is life, it would create the biosignature we observe. Both factors carry significant uncertainties, according to the astrobiologists Cole Mathis of Arizona State University and Harrison Smith of the Earth-Life Science Institute of the Tokyo Institute of Technology, who explored this kind of reasoning in a paper last fall.

My reply: I guess it’s fine to do the calculation, if only to make it clear how dependent it is on assumps. Bayesian inference isn’t just about getting the answer; it’s also about clarifying the mapping from assumptions to inference to decision.

Come to think about it, that last paragraph remains true if you replace “Bayesian inference” with “Mathematics.”