I'm very new to Bayesian statistics, but I've found myself in a situation where they might be able to help. I'll be running the same experiment repeatedly and analyzing the data every few months. The protocol is very simple and involves a comparison between the means of two samples. I'd like to use data from previous studies to inform future studies, but I'd like to clear up some uncertainties I have about Bayesian approaches before I get too far into the planning process.
If I'm running a sequence of experiments, what information is carried over from one experiment to another? Let's say experiment 1 has an uninformative prior, and the posterior from experiment 1 becomes the prior for experiment 2. What is the prior for experiment 3? The posterior for experiment 2? Is there a better way to handle priors in this situation?
I've read that Bayesian approaches aren't penalized for data peeking or interim analyses. Is there a danger in accumulating data continuously and analyzing it in the interim rather than breaking it up into discrete experiments (like i'm planning)?
When I played around with Bayesian approaches in the past, results were usually in close agreement to the frequentist approaches I'm more familiar with. Are there circumstances under which a Bayesian credible interval would diverge very significantly from a confidence interval?