Generative Bayesian Computation

This book introduces Generative Bayesian Computation (GBC), a transformative framework that replaces traditional Markov chain Monte Carlo methods with deep quantile neural networks trained by stochastic gradient descent. At its core, GBC leverages the noise outsourcing theorem and implicit quantile networks to enable Bayesian inference, prediction, and decision-making directly from simulator outputs – no likelihood evaluation, no convergence diagnostics, no chains required. If you can simulate from your model, you can learn the posterior, predictive distribution, or optimal decision through a single training phase followed by fast forward passes. The book develops GBC from theoretical foundations through practical applications, spanning surrogate modeling for expensive computer experiments, likelihood-free Bayesian inference, treatment effect estimation, and sequential state-space filtering. It bridges three communities – Bayesian statistics, machine learning, and computational science – showing how distributional reinforcement learning tools become general-purpose Bayesian engines, how quantile functions provide exact representations of uncertainty, and how neural networks can replace Gaussian process emulators while scaling to high dimensions and handling jump discontinuities that defeat smooth approximations. Key Features:Learn posterior distributions directly from forward simulator runs, making GBC applicable to black-box models, agent-based simulations, and intractable likelihood scenarios where MCMC failsReplace O(n³) Gaussian process emulators with O(n) implicit quantile networks that handle high-dimensional inputs, jump discontinuities, and full predictive distributions rather than just means and variancesComplete development from quantile function theory and the noise outsourcing theorem through Wasserstein contraction arguments, with honest assessment of failure modes and moderate-deviation theory explaining tail calibration issuesConformal wrappers and recalibration methods that address the known failure mode on high signal-to-noise ratio data, with clear guidance on when and why approximations break downSeamless extension from static posterior computation to generative prediction, maximum expected utility decision-making, causal inference, and sequential filtering in state-space modelsEvery method available through the GBC Python package with minimal boilerplate, enabling readers to move from theory to running code in minutes, with benchmark comparisons throughoutThis book serves three overlapping communities: Bayesian statisticians seeking computational alternatives to MCMC and variational inference; machine learning researchers working in distributional RL, generative modeling, or uncertainty quantification who will discover the Bayesian foundations of their tools; and applied scientists and engineers running expensive simulators who need scalable uncertainty quantification. No prior knowledge across communities is assumed—the book provides multiple entry points depending on reader goals, from short courses on GBC surrogates, to simulation-based inference, to sequential models. Applied readers can skim proofs initially and focus on practical implementation, while theoretically oriented readers will find complete mathematical development including honest self-assessment, which documents known limitations and remedies essential for real-world deployment.