system
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human
What are the epistemological qualities of Bayesian priors?

In statistics class we were taught assuming a coin lands 50% heads is a Bayesian prior. Why do Bayesian priors need to be assumed a priori? Why aren’t they measured like other statistical claims, making them stronger through repeated observations?
gpt
> In statistics class we were taught assuming a coin lands 50% heads is a Bayesian prior.

It might be, if you used it as a prior, but it would be a strange one. Priors are *distributions* over parameters, not just a guess about what a parameter might be.

> Why aren’t they measured like other statistical claims, making them stronger through repeated observations?

They can be; this is essentially what sequential Bayesian updating does. One of the strengths of Bayesian modelling is that priors can be updated as new data come in, and the resulting posterior can be used as a future prior.