Can Neural Networks Replace MCMC?

Today’s clip is from Episode 167 of Learning Bayesian Statistics, featuring Paul-Christian Bürkner and Steve Bronder, recorded live at StanCon 2026 in Uppsala, Sweden.

Paul Bürkner, creator of brms and a leading researcher behind BayesFlow, explains how neural networks can replace MCMC for Bayesian inference. Instead of evaluating likelihood and prior densities, the networks are trained on simulated data, so you can do simulation-based inference (SBI) even when the likelihood is intractable. Once trained, they give you amortized, real-time posteriors for new datasets, and they have made SBI…