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Priors

Gelman, Stat Modeling, Priors, here.

Nick Firoozye writes:

While I am absolutely sympathetic to the Bayesian agenda I am often troubled by the requirement of having priors. We must have priors on the parameter of an infinite number of model we have never seen before and I find this troubling. There is a similarly troubling problem in economics of utility theory. Utility is on consumables. To be complete a consumer must assign utility to all sorts of things they never would have encountered. More recent versions of utility theory instead make consumption goods a portfolio of attributes. Cadillacs are x many units of luxury y of transport etc etc. And we can automatically have personal utilities to all these attributes.

I don’t ever see parameters. Some model have few and some have hundreds. Instead, I see data. So I don’t know how to have an opinion on parameters themselves. Rather I think it far more natural to have opinions on the behavior of models. The prior predictive density is a good and sensible notion. Also if we has conditional densities for VARs then the prior conditional density. You have opinions about how variables interact and the forecast of some subset conditioning on the remainder. That this may or may not give enough info to ascribe a proper prior in parameter space all the better. To the extent it does not we must arbitrarily pick one (eg reference prior or maxent prior subject to the data/model prior constraints). Without reference to actual data I do not see much point in trying to have any opinion at all.

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