I haven't read the linked paper yet, but the blog post points a little to what's on my mind. To borrow a bit from a different paper and anonymous reviewer on o

I haven't read the linked paper yet, but the blog post points a little to what's on my mind. To borrow a bit from a different paper and anonymous reviewer on one of my papers, inference serves different aims or philosophies. Sometimes it serves more of an estimation function, to increase information about some quantity, or to improve the estimate of that quantity. But sometimes it serves an evaluative, competitive function, in the Popperian sense of affording risky tests of one or more theories or models. In this latter Popperian aim of inference, priors are to be minimized, which is in many ways the opposite scenario that is assumed with standard subjective Bayesian methods. And even with the former "estimation" inferential aims, there may be situations where you truly have no information or don't feel comfortable assuming it. What's nice about Bayesian statistics is it still provides a framework for this scenario, in the form of reference priors, in that if nothing else your design and model supporting the parameter(s) to be inferred about implies some kind of assumptions about what you're making inferences about. That in turn can be transformed into a "least informative" prior. So it allows an objective Bayesian framework. However, in that framework, in many cases you're still often left with uniform priors, which then reduce to frequentist statistics. And in a broader sense, frequentist methods are even further removed from making assumptions in that they completely eliminate the prior from inferential consideration. There's a tension then, in that in small samples your priors will bias your estimates. If you use least informative priors, you're often doing something akin to frequentist methods anyway. And in large samples the likelihood dominates the posterior so it matters still less. From a certain perspective, ultimately with Bayesian methods you're making a bet that your priors are accurate enough that the increased bias in estimates will be small enough to be offset by decreased variance due to use of a prior. It's a gamble though, the risks of which will probably vary depending on the costs and benefits of different types of error. It's nice to see a paper trying to be honest about the problems with Bayesian inference, as it's a bit overhyped at the moment imho.