Generative Bayesian Computation

Quantile Neural Networks for Inference and Surrogates
1. Auflage 2027
ISBN: 978-1-041-45078-8
Verlag: Taylor & Francis Ltd

Buch, Englisch, 512 Seiten, Format (B × H): 178 mm x 254 mm

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 fails

- Replace 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 variances

- Complete 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 issues

- Conformal 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 down

- Seamless extension from static posterior computation to generative prediction, maximum expected utility decision-making, causal inference, and sequential filtering in state-space models

- Every method available through the GBC Python package with minimal boilerplate, enabling readers to move from theory to running code in minutes, with benchmark comparisons throughout

This 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.

Zielgruppe

Academic, Postgraduate, and Professional Reference

Autoren/Hrsg.

Polson, Nicholas G.

Sokolov, Vadim

Fachgebiete

• Mathematik | Informatik Mathematik Stochastik

Inhaltsverzeichnis

Part I Foundations. 1. Why Generative Bayesian Computation? 2. Motivating Datasets 3 Quantile Functions and the Pinball Loss. 4. The Noise Outsourcing Theorem. 5. Implicit Quantile Networks. Part II From RL to Surrogates. 6. Distributional Reinforcement Learning. 7. GBC Surrogates for Computer Experiments. 8.Boundary Augmentation for Jump Processes. 9. Sequential Design and Active Learning. Part III Inference and Applications. 10. Bayesian Inference Without MCMC. 11. Generative Bayesian Prediction. 12. Maximum Expected Utility. 13. Causal Inference via GBC. 14. When IQN Fails: Calibration and Remedies. Part IV Frontiers. 15. Sequential GBC for State-Space Models.

Über Autor(innen)

Nicholas G. Polson is the Robert Law, Jr. Professor of Econometrics and Statistics at the University of Chicago Booth School of Business. His research spans Bayesian statistics, machine learning, and mathematical probability, with particular emphasis on scalable methods for high-dimensional inference. He is a co-developer of the horseshoe prior for sparse regression and of the Pólya-Gamma data augmentation scheme for Bayesian logistic and negative binomial models, both of which are now in wide use across applied statistics. His current work develops generative approaches to Bayesian computation that replace traditional posterior simulation with deep learning surrogates. He teaches Bayesian statistics, machine learning, and business statistics at Booth, and is the co-author of AIQ: How People and Machines Are Smarter Together.

Vadim Sokolov is a faculty member in the Department of Systems Engineering and Operations Research at George Mason University. His research combines Bayesian statistics, deep learning, and large-scale simulation, with applications in transportation systems, urban modeling, and engineering design. Before joining George Mason, he was a computational scientist at Argonne National Laboratory, where he worked on agent-based models of metropolitan transportation networks and on high-performance computing for statistical inference. He has published widely on deep learning for prediction, Bayesian computation, and the use of neural surrogates in place of conventional Monte Carlo methods, and he is a long-standing collaborator with the first author on the generative Bayesian computation framework developed in this book.