Krdytkyu

Since the frequentist's p-values are uniformly distributed under the null hypothesis, it is a highly problematic practice to add more and more data to your sample until you find a significant result. Assuming the null hypothesis is true, my understanding is that this will almost assuredly lead to a Type I error. This is bad scientific practice.

However, I often hear that Bayesian statistics does not suffer the same fate. Is this true?

If little evidence for the alternative hypothesis exists for some given sample size, wouldn't only stopping once there is "sufficient" evidence for the alternative hypothesis also be problematic for the Bayesian?

It's not that the procedure you describe (keep collecting data until you like the results) does not inflate the type 1 error, if you naively conduct repeated Bayesian analyses, it's that the brand of Bayesian that considers that there is no issue in repeatedly looking at data simply considers type 1 errors an irrelevant concept - and would likely also not favor looking at whether a credible interval excludes 0 to make a decision.

An alternative way of looking at this is to write down the likelihood based on the whole experiment - e.g. if I can never see more heads than tails, because I will keep flipping coins until I see more tails than heads, then the final outcome of the experiment clearly does not follow a binomial distribution.

Another typical way tho handle multiplicity in a Bayesian setting is to use a hierarchical model, but I have never seen a clear description of how one would do that in this context.