pymc-bayesian-modeling

Bayesian modeling is performed using PyMC to define hierarchical structures, priors, and likelihoods. You construct the model graph, fit it to your dataset using MCMC sampling, and validate the results with ArviZ diagnostics.

Variational Inference is supported through the ADVI method alongside MCMC NUTS sampling. This allows you to fit probabilistic programming models faster when full MCMC sampling is computationally prohibitive, still providing posterior approximations for uncertainty quantification.

Bayesian inference validation is handled by ArviZ, which assesses model convergence, fit, and reliability. You use it to compute diagnostics and visualize posterior distributions, ensuring your MCMC or ADVI results are statistically robust before interpretation.

Time series regression and custom probabilistic distributions are fully supported. You can define custom distribution structures and likelihoods using PyMC, enabling flexible probabilistic programming for complex time-dependent statistical models.

Bayesian statistical modeling requires Python dependencies including PyMC, ArviZ, pandas, scipy, scikit-learn, matplotlib, and statsmodels. These provide the environment for probabilistic programming, data manipulation, scientific computing, and model visualization.

Bayesian regression provides explicit uncertainty quantification through posterior distributions rather than point estimates. This approach allows you to incorporate prior knowledge and probabilistically validate hierarchical model structures, which frequentist statistics cannot easily do.