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?