Hi I recently ran several Bayesian independent samples t tests using the informed prior vs the default prior. I understand why the same analyses using the informed prior gives a bigger Bayes factor compared to the default, but I didn’t expect the effect sizes to all be smaller (and credible intervals narrower) when using the informed prior. Does anybody know why this might be?
It's hard to address your specific problem without seeing your analysis, but I would guess that the informed prior added information making the posterior estimation more certain in the parameter estimate (and thus credible intervals narrower). When the prior is non-informative, the posterior is much more similar to likelihood (because the posterior is a compromise between the prior and the likelihood). It's possible that the informed prior centered on a smaller effect size, causing the posterior effect size to be smaller compared to the analysis with a non-informed prior.
This was so helpful! thank you so much Karyssa
Great! elucidate
Thank you!
Hi
I recently ran several Bayesian independent samples t tests using the informed prior vs the default prior. I understand why the same analyses using the informed prior gives a bigger Bayes factor compared to the default, but I didn’t expect the effect sizes to all be smaller (and credible intervals narrower) when using the informed prior. Does anybody know why this might be?
It's hard to address your specific problem without seeing your analysis, but I would guess that the informed prior added information making the posterior estimation more certain in the parameter estimate (and thus credible intervals narrower). When the prior is non-informative, the posterior is much more similar to likelihood (because the posterior is a compromise between the prior and the likelihood). It's possible that the informed prior centered on a smaller effect size, causing the posterior effect size to be smaller compared to the analysis with a non-informed prior.