Assigning a Prior Distribution

As we saw in the murder mystery of the preceding chapter, there is no such thing as the prior probability distribution of a parameter or a set of models. A prior expresses uncertainty arising from incomplete knowledge, and whatever the subject is, people have different knowledge and expertise. So instead of speaking of ’the prior probability of x’, each of us should say ’my prior probability for x’. We assign a prior probability distribution; we do not identify it. This is even the case when we invite the opinion of experts on the likely values of our model’s parameters. There is an art and science to eliciting expert opinion in order to formulate a Bayesian prior (Mikkola et al., Bayesian Analy 1:1–33, 2023; O’Hagan, Environ Model Softw 36:35–48, 2012), but ultimately the responsibility for the prior lies with the modeller, not the expert panel.