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pymc
Probabilistic programming for Bayesian statistical modeling and inference. PyMC provides declarative model specification with MCMC (NUTS) and variational inference samplers; NumPyro offers JAX-accelerated equivalent for large-scale problems. Use when: quantifying uncertainty in parameter estimates, building hierarchical or mixed-effects models, Bayesian A/B testing or experimentation, posterior predictive checks, model comparison with WAIC or LOO-CV, scientific measurement with error propagation, any analysis requiring credible intervals, probability statements like P(effect > 0), or situations where understanding the full posterior distribution matters more than a single p-value. Also use when priors encode domain knowledge, sample sizes are small, or data is naturally nested.