It is an advantage that priors must be explicitly chosen.
There is always a prior. The question is how aware you are of it.
There is always a prior. The question is how aware you are of it.
An ideal Bayesian would employ the principle of maximum entropy for choosing priors [1], soon to discover the problem of underdetermination [2].
Such a person would suffer a death akin to Buridan's ass [3].
1. https://en.wikipedia.org/wiki/Principle_of_maximum_entropy
Very well said. Not to mention that being able to tune the prior shows how much you are depending on those assumptions.
One way to think about a prior is to make your prejudices transparent rather than unknown.
Recall as well that in the Bayesian approach the model itself is not subject to Bayesian updating: its part of your prior. Except that you never update it. So youre not merely choosing how to update parameters given data; you're also choosing what you're not going to update.
Example: I wear a bicycle helmet because it costs me next nothing and it possibly saves my life. I don't do any Bayesian analysis implicitly or explicitly, because on one side there is an outcome with value minus infinity, so it hardly matters what probability I multiply it with.
Now what if you needed a something like a $5k licence to wear the helmet. Would you feel like thinking harder and analysing further than you did? Most interesting decisions are more like this.
"Possibly saves my life" is your prior there, btw.