pymc-fundamentalslisted

# PyMC Fundamentals ## When to Use This Skill - Writing new PyMC models in Python - Understanding PyMC syntax and API - Converting models from Stan/JAGS to PyMC - Diagnosing sampling issues with ArviZ ## Model Structure ```python import pymc as pm import numpy as np import arviz as az with pm.Model() as model: # 1. Priors mu = pm.Normal("mu", mu=0, sigma=10) sigma = pm.HalfNormal("sigma", sigma=1) # 2. Likelihood y_obs = pm.Normal("y_obs", mu=mu, sigma=sigma, observed=y_data) # 3. Sample trace = pm.sample(1000, tune=1000, return_inferencedata=True) # 4. Diagnostics az.summary(trace) ``` ## CRITICAL: SD Parameterization **PyMC uses SD (like Stan), NOT precision (like BUGS):** ```python # PyMC (SD) pm.Normal("x", mu=0, sigma=1) # sigma is SD # BUGS equivalent would be tau = 1/sigma² = 1 ``` ## Distribution Quick Reference ### Continuous ```python pm.Normal("x", mu=0, sigma=1) # Normal pm.HalfNormal("x", sigma=1) # Half-normal (>0) pm.HalfCauchy("x", beta=2.5) # Half-Cauchy (>0) pm.Exponential("x", lam=1) # Exponential pm.Uniform("x", lower=0, upper=1) # Uniform pm.Beta("x", alpha=1, beta=1) # Beta pm.Gamma("x", alpha=2, beta=1) # Gamma pm.StudentT("x", nu=3, mu=0, sigma=1) # Student-t pm.LogNormal("x", mu=0, sigma=1) # Log-normal pm.TruncatedNormal("x", mu=0, sigma=1, lower=0) # Truncated ``` ### Discrete ```python pm.Bernoulli("x", p=0.5)