That's not obvious. You'd need to study many specific cases, and see if starting from different priors reliably predicts the final posteriors. There might be no way to "get there from here" for some priors.
When we speak of the values that an organism has, which are analogous to the priors an organism starts with, it's routine to speak of the role of the initial values as locking in a value system. Why do we treat these cases differently?
There might be no way to "get there from here" for some priors.
That's obviously true for priors that initially assign probability zero somewhere. But as Cosma Shalizi loves pointing out, Diaconis and Freedman have shown it can happen for more reasonable priors too, where the prior is "maladapted to the data generating process".
This is of course one of those questionable cases with a lot of infinities being thrown around, and we know that applying Bayesian reasoning with infinities is not on fully solid footing. And much of the dis...
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