You’re talking about posteriors. They’re talking about priors, presumably foundational priors that for some reason aren’t posteriors for any computations. An important question is whether such priors exist.
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 pointingout, Diaconis and Freedmanhave 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 discussion is about failure to satisfy Frequentist conditions that many may not care about (though they do have a section arguing we should care). But it is still a very good paper, showing that non-zero probability isn’t quite good enough for some continuous systems.
What makes you say that Bayesians are locked in? It’s not true. If they’re presented with evidence for or against their beliefs, they’ll change them.
You’re talking about posteriors. They’re talking about priors, presumably foundational priors that for some reason aren’t posteriors for any computations. An important question is whether such priors exist.
But your beliefs are your posteriors, not your priors. If the only thing that’s locked in is your priors, that’s not a locking-in at all.
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?
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 discussion is about failure to satisfy Frequentist conditions that many may not care about (though they do have a section arguing we should care). But it is still a very good paper, showing that non-zero probability isn’t quite good enough for some continuous systems.