You are designing an A/B test for a major website change. Develop a detailed Bayesian analysis plan. Assume we have historical data suggesting a baseline conversion rate of 5%. Define appropriate prior distributions (e.g., Beta distribution) for both Control and Variant groups. Determine the sample size required to achieve 95% probability that the Variant outperforms the Control if the true lift is 2%. Explain how you would calculate the posterior distribution and the decision rule for stopping the test early.