I had the pleasure of taking a great Bayesian stats class in college and these methods seem preferable.

Unfortunately, the requirement of priors (seemingly) precludes Bayesian stats from many A/B testing applications. For example, our site launches every article with 3 or 4 headline variations. A priori, we have no idea which headline will be most successful or even what the expected conversion rate is for that article.

Is there any way to use Bayesian methods in such a scenario?