: You assign probability distributions to unknown parameters like the intercept ( ), slope ( ), and error ( ). Common choices include: pm.Normal for regression coefficients. pm.HalfNormal or pm.HalfCauchy for the standard deviation ( ) to ensure it remains positive.
: By default, PyMC uses the No-U-Turn Sampler (NUTS) , an efficient algorithm for complex Bayesian models.
: This connects the model to your observed data. For linear regression, the outcome variable is usually modeled as a Normal distribution: pm.Normal("y", mu=mu, sigma=sigma, observed=y) . 2. Inference and Sampling
PyMC provides a flexible framework for Bayesian linear regression, allowing you to model data by defining prior knowledge and likelihood functions. Unlike frequentist approaches that find a single "best" set of coefficients, PyMC generates a distribution of possible parameters (the posterior) using Markov Chain Monte Carlo (MCMC) sampling. 1. Model Definition
: This is the core formula, typically defined as mu = intercept + slope * x .
After sampling, you analyze the results to understand parameter uncertainty.
: Tools like ArviZ allow you to plot posterior distributions or trace plots to check for convergence.
: Unlike frequentist confidence intervals, Bayesian credible intervals (e.g., a 94% HDI) provide a direct probability that a parameter falls within a certain range. 4. Advanced Regression Types
