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I am generally curious what the term "principled" means.

It was used in the title of an unpublished manuscript, "Combining Computer Models in a Principled Bayesian Analysis". In addition, Zhang 2004 says "There are several advantages to a principled Bayesian analysis" here:

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Otherwise, I find relatively few google hits for the phrase. What does the term "principled" mean in this context?

Zhang, 2004 Causal Inference with Instrumental Variables. Ch. 8 in Gelman and Meng, Applied Bayesian Modeling and Causal Inference from Incomplete-Data Perspectives. Wiley.

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Too long for a comment:

Zhang starts the Bayesian analysis section with the phrase

More principled inferences come from Bayesian analysis.

and later says

There are several advantages of the principled Bayesian analysis.

I don't think "principled Bayesian analysis" is a thing. The word principled is just being used as an adjective to describe the Bayesian analysis, where "principled" means "following a set of principles". This is opposed to an ad-hoc approach based on something like the method of moments. For example, if you were doing a capture-recapture study of animal populations, the Lincoln-Peterson estimator of the true population is an ad-hoc estimate, and a Bayesian estimate would be a more principled approach. Here, Zhang is comparing the Bayesian analysis with some other kind of analysis done in the previous section, which seems to be more specific to this particular problem and therefore less based on general principles.

It is slightly odd to see a "the" there (shouldn't it be "a principled Bayesian analysis"?) but I think this is just because English articles are difficult. You can see that there is a "the" missing from the first sentence at the top of page 93, and there are a few other similar sentences here and there.

Of course, it's perfectly possible that "principled Bayesian analysis" really is a thing, and if that's the case then I would also be interested to know what it is!

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