I posted here about a data-processing mistake that I made recently (and luckily noticed). From a more general statistical perspective, the interesting thing is that I noticed the error because the mistaken case looked wrong. Checking funny-looking data points and correcting them if necessary can be viewed as a Bayesian procedure–but it’s well known (well, maybe not well enough known) that Bayesian point estimates can have systematic errors. This is a point made by Tom Louis in the context of estimating ensembles of parameters and by Phil Price and myself in our paper on why all maps of parameter estimates are misleading. Being Bayesian (or approximately Bayesian) is fine but it doesn’t solve all problems!

P.S. I’d like to use the term “bias” here but it has an inappropriate technical meaning in this context so I’m using the phrase “systematic error,” which hasn’t already been taken.

Can you comment more on the use of "Bias"?

The technical term bias seems to refer to many things in statistics. What you get from a biased sample is different than what you get from a biased estimator applied to an unbiased sample etc.

It seems to me that you're pointing out that sampling error is still a concern in Bayesian statistics. It would be interesting to hear an elaboration on this.

It seems like one of the claims of bayesian statistics is that it's a procedure for calculating the uncertainty associated with a parameter that describes a set of data, CONDITIONAL on the data and the assumptions of the model. When you use a point estimate you're inherently throwing away the bayesian uncertainty calculation…