(This article was originally published at Statistical Modeling, Causal Inference, and Social Science, and syndicated at StatsBlogs.)

Xian and I respond to the four discussants of our paper, “Not only defended but also applied”: The perceived absurdity of Bayesian inference.” Here’s the abstract of our rejoinder:

Over the years we have often felt frustration, both at smug Bayesians—in particular, those who object to checking of the fit of model to data, either because all Bayesian models are held to be subjective and thus unquestioned (an odd combination indeed, but that is the subject of another article)—and angry anti-Bayesians who, as we wrote in our article, strain on the gnat of the prior distribution while swallowing the camel that is the likelihood. The present article arose from our memory of a particularly intemperate anti-Bayesian statement that appeared in Feller’s beautiful and classic book on probability theory. We felt that it was worth exploring the very extremeness of Feller’s words, along with similar anti-Bayesian remarks by others, in order to better understand the background underlying controversies that still exist regarding the foundations of statistics. We thank the four discussants of our article for their contributions to our understanding of these controversies as they have existed in the past and persist today.

Why was Feller both so stridently anti-Bayesian and so confident that non-Bayesian methods could solve all statistical problems? We locate Feller’s attitude within a post-WW2 “anti-Bayesian moment” in which Bayesian inference was perceived as a threat to the dominance of non-Bayesian methods, which were mature enough to have solved problems yet new enough to still appear to have limitless promise.

Our article that started off the discussion is here.

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