what is the bayes theorem can you apply bayes theorem with prior samples can you use bayes theorem only on a previous experiment can you apply bayes theorem without sampling can you apply bayes theorem to prior samples can you apply bayes' theorem with the prior what sample does the bayes theorem apply to? why apply bayes theorem with only samples can you use bayes theorem without analytical expression when can you use bayes theorem without an analytical expression can bayes theorem be applied to prior data can you apply bayes theorem without prior analysis what is the bayes theorem and how is it applied can you apply bayes theorem to only samples is a prior a bayes' theorem? how to apply bayes theorem to sample can a prior use bayes' theorem how would you apply the bayes theorem can bayes theorem be applied to only samples can you apply bayes theorem to a prior