A theoretical argument in favor of the Cauchy prior distribution for logistic regression coefficients

In the “weakly informative priors” article, we propose a Cauchy (0, 2.5) default prior distribution for logistic regression coefficients, motivating it from applied concerns and also as a regularizer.

Recently, Gregor Gorjanc pointed me to an article by Jairo Fuquen, John Cook, and Luis Pericchi, also recommending Cauchy prior distributions but this time using a robustness argument. Their article is a bit more mathematical than ours, and with a different focus, more concerned with improvements in specific applications than in the construction of a generic default prior distribution. But we have similar messages, and in that sense our papers are complementary.