Overview
Bayesian analysis is not just a different way to compute p-values. It is a fundamentally different question: instead of "what is the probability of observing this data if the null hypothesis is true?", it asks "what is the probability that the hypothesis is true, given this data?" The answer is a probability distribution over the parameter of interest — not a binary reject/fail-to-reject decision.
The practical advantage of Bayesian inference is that it produces exactly what decision-makers want: the probability that a treatment is better than control, the probability that a parameter exceeds a threshold, and the expected value of a decision given uncertainty. These are direct answers to business questions. Frequentist p-values are not.
The Bayesian Analysis & Inference Prompt generates a complete Bayesian modeling framework: prior specification with justification, likelihood selection, posterior computation, credible interval interpretation, and a decision framework that uses the posterior distribution to make expected-value-optimal decisions.
What you get: - Prior specification with sensitivity analysis - Likelihood selection by data type - Posterior computation with PyMC or Stan - Credible interval interpretation vs. confidence intervals - Decision framework using posterior probabilities
Built for: data scientists and analysts who need to answer probabilistic business questions that frequentist methods answer poorly — or not at all.