This is motivated by my desire to translate Bayesian conclusions such as I arrive at here into plainer language. If I find that the median of the posterior distribution over some parameter \theta is less than m, then I could say,
It is more likely than not that \theta < m.
But I would much rather make the plainer statement that:
\theta is probably less than m.
How do people feel about this?
This probably (sorry) doesn’t answer your question directly, but there has been some work done on the “perception of probability words”, with an interesting history. Here is one short summary I found with a quick search.
Personally I think your statement is reasonable, but it seems like respondents in these surveys tended to place a higher threshold on “probably” (and “probable”).
You might be able to find more applicable or modern results by following the links in the page above, or with a more thorough search than I did…
[edit: I just stumbled on this Wikipedia entry, which might have some further rabbit holes to follow - Words of estimative probability - Wikipedia ]
Thank you, Mark! This is very much the sort of thing I’d hoped for. It gives me a little ammunition in case reviewers object, but also serves as a caution, given that only a few people in that interactive graphic put ‘probably’ at 50–51%.
I get into this here where I suggest that the word “probably” is fine to use as long as it appears in language such as “the drug probably (0.54) causes a reduction in blood pressure” and 0.54 is the current posterior probability and the prior and data model are documented nearby.
This seems an excellent general practice to adopt. In my particular case here, the parentheses would have to read somewhat mysteriously (0.5+\epsilon); but a footnote could also serve the same purpose.