As I taught my bayesian modeling class today again the issue came up of how can we make sure that priors are not biasing in undue ways our results. Which is a fair and well-grounded question and yet a bit annoying that it's always posed as "is it not like p-hacking"? 1/n
Why are they not and how can we build best practices around priors to make students confident in how to use them in sensible ways? (besides them reading @dan_p_simpson et al Bayesian Workflow). Some thoughts on how to present and use them: 2/n
1) Priors (+likelihood) formalize what we know of the data / experiment / phenomenon, not our wishes for a result. E.g. Is it arbitrary to assume performance below chance is not very likely? Or that perfect performance, and Cohen's d's of 10 are also very unlikely? 3/n
2) Priors are made explicit and explicitly motivated (to paraphrase @djnavarro, priors are *disclosed* researcher's degrees of freedom. 4/n
3) Accordingly priors can be tested (prior predictive checks), discussed, criticized and improved (critical cumulative science!). 5/n
4) You can/should be skeptical of your priors and run several checks on them: is the posterior updating from the prior? how robust are the inferential results to changes in the priors? 6/n
5) Often for complex models priors are a way to help the model actually perform reasonable inferences without getting stuck in weird unlikely regions of parameter values. "I don't care about the results, just please stop that invasion of divergences. Sob!" 7/n
I agree that these sound a lot like artisanal practices (known your information and with your data, test formalizations, check for obvious issues). But I can't see any other ways of tackling non-trivial modeling work. Am I forgetting something? ( @JCSkewesDK?)
Note that this also applies to informed priors (e.g. based on previous literature). They do nudge the results in certain directions and exactly for that they can help critically understanding e.g. whether our results really differ from previous and how they contribute
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