bayesian-stats

name	bayesian-stats
description	Use this Skill when the user needs to build Bayesian statistical models: prior selection, posterior sampling with MCMC (NUTS), convergence diagnostics, posterior predictive checks, LOO-CV model comparison, hierarchical models, and Bayesian A/B testing. Covers PyMC 5.x and ArviZ.
tags	["mathematics","bayesian-inference","mcmc","pymc","arviz","hierarchical-models","model-comparison"]
version	1.0.0
authors	[{"name":"awesome-rosetta-skills contributors","github":"@awesome-rosetta-skills"}]
license	MIT
platforms	["claude-code","codex","gemini-cli","cursor"]
dependencies	{"python":["pymc>=5.0.0","arviz>=0.17.0","numpy>=1.23.0","pandas>=1.5.0","matplotlib>=3.6.0","scipy>=1.10.0"]}
last_updated	2026-03-17

Bayesian Statistical Inference

TL;DR — Full Bayesian workflow with PyMC 5.x and ArviZ: prior selection, NUTS sampling, convergence diagnostics (R-hat, ESS), posterior predictive checks, LOO-CV model comparison, hierarchical models, and Bayesian A/B testing.

---

1. Overview

What Problem Does This Skill Solve?

Bayesian inference provides a principled framework for combining prior knowledge with observed data to produce full posterior distributions over parameters — rather than single point estimates. This Skill covers the complete modern Bayesian workflow:

1. Prior selection — weakly informative vs. informative priors; prior predictive checks
2. MCMC sampling — NUTS sampler with automatic tuning
3. Convergence diagnostics — R-hat ≤ 1.01, effective sample size ≥ 400
4. Posterior analysis — summary statistics, credible intervals, trace plots
5. Model comparison — Leave-One-Out Cross-Validation (LOO-CV) with ArviZ
6. Hierarchical models — partial pooling, non-centered parameterization
7. Bayesian A/B testing — direct probability statements, no p-values needed

When Bayesian vs. Frequentist?

Situation	Prefer Bayesian
Small sample, prior knowledge available	Yes
Need full uncertainty quantification	Yes
Hierarchical / multilevel structure	Yes
Need P(hypothesis	data) directly
Large n, no prior, fast turnaround needed	Frequentist is fine

---

2. Environment Setup

conda create -n bayes python=3.11 -y
conda activate bayes
pip install pymc arviz numpy pandas matplotlib scipy

# Verify (PyMC uses pytensor backend)
python -c "import pymc as pm; print(pm.__version__)"

Quick sanity check — sample from a trivial model:

import pymc as pm
import arviz as az

with pm.Model():
    mu = pm.Normal("mu", mu=, sigma=)
    idata = pm.sample(, tune=, chains=, progressbar=)

(az.summary(idata))