I respond to that by saying “ok I guess empirics aren’t super helpful for the big picture question let’s try to build mechanistic understanding of things grounded wherever possible in empirics, as well as priors about what types of distributions occur when various different generating mechanisms are at play”, whereas it sounds like you’re responding by saying something like “well as a prior we’ll just use the parts of the distribution we can actually measure, and assume that generalizes unless we get contradictory data”?
Yes, that would be my reply. Thanks for clarifying.
Yeah, so I basically think that that response feels “spiritually frequentist”, and is more likely to lead you to large errors than the approach I outlined (which feels more “spiritually Bayesian”), especially in cases like this where we’re trying to extrapolate significantly beyond the data we’ve been able to gather.
Yes, that would be my reply. Thanks for clarifying.
Yeah, so I basically think that that response feels “spiritually frequentist”, and is more likely to lead you to large errors than the approach I outlined (which feels more “spiritually Bayesian”), especially in cases like this where we’re trying to extrapolate significantly beyond the data we’ve been able to gather.