Bayesian Inference

Examples demonstrating Bayesian parameter inference via MCMC sampling, variational inference, and model calibration workflows.

ex_mcmc_banana.py

MCMC sampling from a banana-shaped distribution.

Demonstrates different MCMC methods (AMCMC, HMC, MALA) for sampling from a challenging banana-shaped (Rosenbrock) posterior distribution.

ex_mcmc_fitline.py

MCMC-based Bayesian linear model calibration.

Uses Adaptive MCMC to calibrate a linear model to noisy data.

ex_mcmc_fitmodel.py

MCMC-based multivariate linear model calibration.

Uses Adaptive MCMC to infer parameters of a linear model with multiple features, including bias and weight parameters.

ex_mfvi.py

Mean-field variational inference.

Uses MFVI with different optimization methods (PSO, Scipy) to approximate posterior distributions for parameters in a simple model.

ex_minf.py

Model inference workflows.

Shows different approaches to Bayesian parameter inference including optimization-based and sampling-based methods for model calibration.

ex_minf_sketch.py (demo)

Comprehensive parameter inference sketch.

Detailed 1D parameter inference example using MCMC. Demonstrates configuring likelihood types, prior options, data variance treatment, and post-processing the calibration results.

ex_evidence.py

Model selection using Bayesian evidence.

Compares different polynomial chaos models using analytical linear regression (ANL) and computes evidence values to determine the best-fitting model order.