Compare Bayesian and frequentist decisions

For a binary KPI with Beta(1,1) priors, you observe 10,000 users per arm and 515 vs. 500 conversions. a) Compute the posterior for each arm and the posterior probability that lift>0. b) Define a decision rule based on expected loss with asymmetric costs. c) Contrast the decision with a frequentist test under optional stopping and discuss operational implications (e.g., communicating posterior vs. p‑value, alpha spending). d) How would you set or elicit priors to avoid over‑optimism?