“A statistical model is usually taken to be summarized by a likelihood, or a likelihood and a prior distribution, but we go an extra step by noting that the parameters of a model are typically batched, and we take this batching as an essential part of the model.”
I read that as "botched", and it seemed much more insightful and possibly useful.
Perhaps "butched" too.
Batched is perhaps a botched term for this – discerning which parameters are common versus arbitrary by observations/groups in addition to which parameters are specified as being random draws from a common distribution (ala exchangeability formalisms) would arguably also be worthwhile.
For instance, for a multilevel model for repeated studies it would be a common start to have treatment group variances common within the studies, the variances arbitrarly different between studies and with random treatment effect parameters _drawn_ independently by study from a common distribution.
But then when I used that vocabulary in my thesis the examiners felt it worth while to point out that such nonstandard vocabulary would likely distract the interest of potential readers.
K?