Or in other words, How mature-I mean my statistical knowledge- should I be to start learning and doing Bayesian analysis?
Maturity is not really what is needed. Clarity of purpose is useful, though, and that clarity is often absent in statistics books and courses.
According to Richard Royall, there are three main types of question that are typically answered with the help of statistics, and I think that those questions are the prerequisite for learning all statistical approaches to a more than superficial level.
- What do the data say?
- What should I believe now that I have these data?
- What should I do or decide now that I have these data?
P-values interpreted as continuous indices of evidence and likelihood functions are well suited to answering the first question. Bayesian analyses are clearly well suited to answering question 2 and Frequentist approaches are well suited to answering question 3.
It is true that Bayesian analyses are often more involved than a simple recipe-based Frequentist hypothesis test approach, but that is inevitable given that considerations of information external to the data, sometimes in the form of opinion, come into the Bayesian analysis. However, a full understanding of the philosophy of the Frequentist approach requires more maturity on the part of students than is usually communicated by the test recipes.