When I was a grad student, a statistics postdoc confided to me that he was a “closet Bayesian.” This sounded absolutely bizarre. Why would someone be secretive about his preferred approach to statistics? I could not imagine someone whispering that although she’s doing her thesis in algebra, she’s secretively interested in differential equations.
I knew nothing about statistics at the time and was surprised to find that there was a bitter rivalry between two schools of statistics. The rivalry is still there, though it’s not as bitter as it once was.
I find it grating when someone asks “Are you a Bayesian?” It implies an inappropriate degree of commitment and exclusivity. Bayesian statistics is just a tool. Statistics itself is just tool, one way of understanding the world.
My car has a manual transmission. I prefer manual transmissions. But if someone asked whether I was a manual transmissionist, I’d look at them like they’re crazy. I don’t have any moral objections to automatic transmissions.
I evaluate a car by how well it works. And for most purposes, I prefer the way a manual transmission works. But when I’m teaching one of my kids to drive, we go out in my wife’s car with an automatic transmission. Similarly, I evaluate a mathematical model (statistical or otherwise) by how it works for a given purpose. Sometimes a Bayesian and a frequentist approach lead to the same conclusions, but the latter is easier to understand or implement. Sometimes a Bayesian method leads to a better result because it can use more information or is easier to interpret. Sometimes it’s a toss up and I use a Bayesian approach because its more familiar, just like my old car.