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Aug 25 '19 at 9:18 answer pglpm timeline score: 0
Jul 9 '17 at 13:59 answer Ben Goodrich timeline score: 2
Jul 6 '17 at 2:20 comment added jbowman @whuber - I have to confess I sometimes think Bayesian statistics is what you should do when you want to update prior information and frequentist statistics what you should do when you don't want to include any prior information except for the minimum necessary to specify a likelihood function, parameter space, and perhaps a null hypothesis. I know there's a huge literature on noninformative priors, but the various methodologies generate inconsistent results and somehow don't seem as clean to me as "I'm going to do a Wilcoxon rank-sum test". Probably just lazy thinking on my part.
Jul 5 '17 at 22:17 comment added whuber It seems to me the two problems are the same. In the frequentist setting we have to study a range of plausible parameter values and examine the entire landscape of results, because we're not willing to stipulate a prior probability distribution. In the Bayesian setting you don't have to study a grid of parameter values, because you simply let your prior distribution choose them and average the results. To do Bayesian stats well, though, you need to evaluate the sensitivity to the prior, so maybe you should be exploring a grid of hyperparameters--and that's just like studying parameters.
Jul 5 '17 at 20:51 comment added Heisenberg @jbowman when you say make the prior match the GDP, does that mean that my prior should center on the true param values of the GDP? But my prior is a distribution and thus is characterized by more than just its center. How do you mean to "match the prior with the GDP"?
Jul 5 '17 at 19:42 comment added jbowman Unfortunately not. Consider a situation where the prior is far from the true value and the data is not strong enough to overwhelm it completely. In this case, the $\alpha$-credible interval won't have $\alpha$ coverage probability. This comes about because Bayesian statistics is about optimal updating of pre-existing information rather than about estimation without any pre-existing information being taken into account. If you make your prior match the DGP, though, you should be able to proceed as you suggest.
Jul 5 '17 at 19:40 answer AdamO timeline score: 1
Jul 5 '17 at 19:31 history asked Heisenberg CC BY-SA 3.0