andrew_gelman_stats andrew_gelman_stats-2011 andrew_gelman_stats-2011-801 knowledge-graph by maker-knowledge-mining
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Introduction: Nick Polson and James Scott write : We generalize the half-Cauchy prior for a global scale parameter to the wider class of hypergeometric inverted-beta priors. We derive expressions for posterior moments and marginal densities when these priors are used for a top-level normal variance in a Bayesian hierarchical model. Finally, we prove a result that characterizes the frequentist risk of the Bayes estimators under all priors in the class. These arguments provide an alternative, classical justification for the use of the half-Cauchy prior in Bayesian hierarchical models, complementing the arguments in Gelman (2006). This makes me happy, of course. It’s great to be validated. The only think I didn’t catch is how they set the scale parameter for the half-Cauchy prior. In my 2006 paper I frame it as a weakly informative prior and recommend that the scale be set based on actual prior knowledge. But Polson and Scott are talking about a default choice. I used to think that such a
sentIndex sentText sentNum sentScore
1 Nick Polson and James Scott write : We generalize the half-Cauchy prior for a global scale parameter to the wider class of hypergeometric inverted-beta priors. [sent-1, score-0.997]
2 We derive expressions for posterior moments and marginal densities when these priors are used for a top-level normal variance in a Bayesian hierarchical model. [sent-2, score-1.187]
3 Finally, we prove a result that characterizes the frequentist risk of the Bayes estimators under all priors in the class. [sent-3, score-0.7]
4 These arguments provide an alternative, classical justification for the use of the half-Cauchy prior in Bayesian hierarchical models, complementing the arguments in Gelman (2006). [sent-4, score-0.897]
5 The only think I didn’t catch is how they set the scale parameter for the half-Cauchy prior. [sent-7, score-0.515]
6 In my 2006 paper I frame it as a weakly informative prior and recommend that the scale be set based on actual prior knowledge. [sent-8, score-0.988]
7 But Polson and Scott are talking about a default choice. [sent-9, score-0.245]
8 I used to think that such a default would not really be possible but given our recent success with automatic priors for regularized point estimates, now I’m thinking that a reasonable default might be possible in the full Bayes case too. [sent-10, score-1.296]
9 I found the above article while looking on Polson’s site for this excellent paper , which considers in a more theoretical way some of the themes that Jennifer, Masanao, and I are exploring in our research on hierarchical models and multiple comparisons. [sent-13, score-0.749]
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