Priors, begginer questions and Titanic Data

Дата публикации: 31-07-2026 18:00:47

I think you want to jump up a level of abstraction and think about what the prior and likelihood are doing for you. You usually do not want to use the data to inform the prior other than loosely. You want to use prior knowledge of the problem.
You’re not going to be able to tell anything from just inspecting the posterior intervals. You can make them as small as you want with with tighter and tighter priors. Then you want to do posterior predictive checks to check calibration of within-data fits and cross-validation to test calibration on out-of-data prediction for quantities of interest. The goal is to measure whether the prior combined with the likelihood lead to well calibrated posteriors in the sense of having the correct coverage either at the parameter level or the posterior predictive level for new data.
When the combination of prior and likelihood don’t work well, you have the freedom to change either one. On the likelihood side, maybe you add more covariates, maybe you interact covariates, maybe you transform covariates in other ways (like logit transforming proportions) or swap in robust (Student-t) noise for normal noise in the regression, and so on.
You might find the Bayesian workflow paper (on arXiv) and now the book (Cambridge) useful. It’s the same authors as the ones who wrote the Stan prior choice wiki and they discuss all of this. Unfortunately it’s all using Stan in R, so not ideal. I suspect someone will translate the book to PyMC or NumPyro, so it’ll at least be in Python.

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