Deborah Mayo recommended that I consider coming up with a new name for the statistical methods that I used, given that the term “Bayesian” has all sorts of associations that I dislike (as discussed, for example, in section 1 of this article).
I replied that I agree on Bayesian, I never liked the term and always wanted something better, but I couldn’t think of any convenient alternative. Also, I was finding that Bayesians (even the Bayesians I disagreed with) were reading my research articles, while non-Bayesians were simply ignoring them. So I thought it was best to identify with, and communicate with, those people who were willing to engage with me.
More formally, I’m happy defining “Bayesian” as “using inference from the posterior distribution, p(theta|y)”. This says nothing about where the probability distributions come from (thus, no requirement to be “subjective” or “objective”) and it says nothing about the models (thus, no requirement to use the discrete models that have been favored by the Bayesian model selection crew). Based on my minimal definition, I’m as Bayesian as anyone else.