Hierarchical Bayesian Modeling

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Hierarchical Bayesian modeling represents group-, subject-, or task-specific parameters as draws from shared population distributions, enabling partial pooling when individual datasets are sparse. Common approaches include multilevel regression and generalized linear mixed models, Gaussian-process and dynamical-system models, and inference using MCMC, variational methods, or amortized neural networks. These methods are used in settings such as longitudinal studies, multisite biomedical data, crowdsourced ratings, and reliability assessment, where both population trends and individual differences matter. A central challenge is balancing computational speed with accurate, calibrated uncertainty, while ensuring that pooling assumptions do not obscure real heterogeneity or cause negative transfer.

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36 papers3 papers in the last four weeks, level with the four weeks before. 0.0% of all new papers.

Theoretical and Practical Advances in Hierarchical Bayesian Deep Learning Methodology
Oct 13, 2026Neil K. Chada, Simon Cotter, Kody J. H. Law +1Bayesian Neural Networks Hierarchical Bayesian Modeling
Department of Mathematics, City University of Hong Kong, Hong Kong SAR. · School of Mathematics, University of Manchester, UK.
Uncovering and Fixing Collider Bias in Bayesian PINNs
Oct 8, 2026Michael Obermayr, Robert PeharzPhysics-Informed ML Bayesian Inverse Problems
TU Graz
Amortized Bayesian Inference on Multilevel Models of Arbitrary Structure
Sep 30, 2026Daniel Habermann, Andreas Bulling, Stefan T. Radev +1Amortized Inference Hierarchical Bayesian Modeling
Department of Statistics TU Dortmund University, Germany · Institute for Visualisation and Interactive Systems University of Stuttgart, Germany · Department of Cognitive Science Rensselaer Polytechnic Institute, USA
Prior-Amortized In-Context Bayesian Inference for Generalized Linear Mixed-Effects Models
Sep 21, 2026Alex Kipnis, Marcel Binz, Eric SchulzNeural Posterior Estimation Amortized Inference
Institute for Human-Centered AI, Helmholtz Munich, Germany
Diffusion Models and Concept Formation
Sep 11, 2026Zekun Wang, Karthik Singaravadivelan, Christopher J. MacLellanCognitive Modeling Hierarchical Representation Learning
College of Computing, Georgia Institute of Technology, Atlanta, GA 30332 USA
HB-PVI: A Hierarchical Bayesian Personalization and Value-of-Information Framework for Complex Activity Recognition
Sep 4, 2026Hammed A. OlayinkaCost-Aware Inference Human Activity Recognition
Department of Mathematical Sciences, Worcester Polytechnic Institute, Worcester, MA 01609 USA
Theoretical Study on the Evidential Learning-based Variational Autoencoder
Aug 19, 2026Ge WangQuery Identifiability Variational Autoencoders
Rensselaer Polytechnic Institute, Troy, New York, USA
Hierarchical Empirical-Bayes Naive Bayes: Minimax Smoothing and Calibration with AODE Extension
Aug 11, 2026Nguyen Thai Anh, Truong Viet Vu, Tran Thien Thanh +2Probability Calibration Empirical Bayes
Faculty of Information Technology, Van Lang School of Technology, Van Lang University, Ho Chi Minh City, 70000, Vietnam · Institute of Information Technology and Electrical-Electronics Engineering, Ho Chi Minh City University of Transport, Ho Chi Minh City, 700000, Vietnam
Hierarchical Solomonoff Induction: An Unbounded Machine Learning Model
Aug 2, 2026Nathan YoungHierarchical Bayesian Modeling Statistical Learning Theory
Strong AI Lab, University of Auckland
Recursive Gaussian Processes and the Bayesian Brain
Aug 1, 2026Moumita Das, Dipanjan Ray, Sourabh BhattacharyaComputational Cognitive Modeling Predictive Coding
1Indian Institute of Management, Udaipur, India · Department of Psychology and Cognitive Sciences, Ashoka University, Haryana, India · 3Koita Centre for Digital Health at Ashoka (KCDH-A), Haryana, India +1
Modeling Memory-Dependent Reliability of LLMs: A Hidden Markov Model
Jul 24, 2026Robab Aghazadeh Chakherlou, Siddartha Khastgir, Peter Popov +1LLM Evaluation Hierarchical Bayesian Modeling
WMG, University of Warwick, Coventry, United Kingdom · Centre for Software Reliability, City St George’s, University of London, London, United Kingdom
Transit Destination Inference from Tap-In-Only Bus Smart-Card Data: A Hierarchical Bayesian Approach
Jul 23, 2026Gefei Zhao, Jiahe Ling, Yuelong SuIntelligent Transportation Systems Traffic Flow Estimation
Department of Computer Science University of Wisconsin–Madison, Madison, WI, 53706 · Department of Industrial Engineering and Operations Research Columbia University, New York, NY, 10027 · State Key Laboratory of Intelligent GreenVehicle and Mobility Tsinghua University, Beijing, China, 100084
A Bayesian framework for the uncanny valley in humanoid robot design
Jul 7, 2026Shimon Honda, Rin Shibano, Hideyoshi YanagisawaHuman Preference Modeling Hierarchical Bayesian Modeling
Department of Mechanical Engineering, Graduate School of Engineering, The University of Tokyo, Tokyo, Japan.
Integrating Neural Encoders in Bayesian Generalized Linear Mixed Models for Multimodal Data
Jul 6, 2026Yuankang Zhao, Youngsoo Baek, Felipe A. Medeiros +2Bayesian Inference Hierarchical Bayesian Modeling
Department of Biostatistics & Bioinformatics, Duke University · Department of Ophthalmology, University of Miami
Estimating Supply Incrementality in Two-sided Marketplaces: A Causal Machine Learning Approach
Jun 30, 2026Yufei Wu, Daniel Schmierer, Dan ZylberglejdCausal Effect Estimation Debiased ML
Airbnb, Inc. San Francisco, California, USA
Learning Dynamical Systems from Multiple Sparse Datasets: A Hierarchical Bayesian Modeling Approach
Jun 23, 2026Cristian Brugnara, Lea Multerer, Marco Forgione +1Irregular Time-Series Modeling Parameter Estimation
SUPSI, Dalle Molle Institute for Artificial Intelligence (IDSIA USI-SUPSI), Lugano, Switzerland
Multi-Task Bayesian In-Context Learning
Jun 18, 2026Qingyang Zhu, Eric Karl Oermann, Kyunghyun ChoAmortized Inference Bayesian Inference
New York University · NYU Langone Health
Credibility-Weighted Pricing of Autonomous Vehicle Liability Under Operational Design Domain Shift
Jun 16, 2026Doyeon JangBayesian Inference Autonomous Driving
Doyeon Jang
Nonlocal Bayesian Modeling of Continuous Spatio-Temporal Dynamics
Jun 12, 2026Jaeyeong Lee, Heeyoung KimIrregular Time-Series Modeling Bayesian Inference
Department of Industrial and Systems Engineering, Korea Advanced Institute of Science and Technology (KAIST), Daejeon, Republic of Korea
DTVEM-RE: A Hierarchical Random-Effects Extension of the Differential Time-Varying Effect Model for Person-Specific Multi-Lag Estimation in Intensive Longitudinal Data
Jun 12, 2026Amartya BhattacharyaIrregular Time-Series Modeling Hierarchical Bayesian Modeling
Geisel School of Medicine, Dartmouth College
Hierarchical Projection for Adaptive Knowledge Transfer
Jun 7, 2026Samhita Pal, Tian GuHierarchical Bayesian Modeling Cross-Domain Transfer Learning
Vanderbilt University Medical Center · Columbia University
Corrected Integrated Laplace Approximation for Bayesian Inference in Latent Gaussian Models
May 19, 2026Jinlin Lai, Charles C. Margossian, Daniel R. SheldonLatent Variable Models Importance Sampling
Manning College of Information and Computer Sciences University of Massachusetts Amherst · Department of Statistics University of British Columbia
Bayesian Nonparametric Mixed-Effect ODEs with Gaussian Processes
May 13, 2026Julien Martinelli, Maksim Sinelnikov, Harri Lähdesmäki +2Dynamical Systems Bayesian Inference
Inria SISTM team · Univ. Bordeaux, INSERM BPH, U1219, Inria SISTM team, VRI, France · Aalto University
Correcting Selection Bias in Sparse User Feedback for Large Language Model Quality Estimation: A Multi-Agent Hierarchical Bayesian Approach
May 12, 2026Andrea Morandi, Mahesh ViswanathanLLM Evaluation Bayesian Inference
Cisco Systems, Inc.
Two Ways to De-Bias an LLM-as-a-Judge: A Continuous-Score Comparison of Hierarchical Bayesian Calibration and Neural-ODE Score Transport
May 9, 2026Andrea MorandiPost-Hoc Calibration LLM-as-a-Judge
Cisco Systems, Inc.
Robust volatility updates for Hierarchical Gaussian Filtering
May 1, 2026Christoph Mathys, Nicolas Legrand, Peter Thestrup Waade +2Bayesian Filtering Hierarchical Bayesian Modeling
Interacting Minds Centre, Aarhus University, 8000 Aarhus C, Denmark · Centre for Humanities Computing, Aarhus University, 8000 Aarhus C, Denmark · Translational Neuromodeling Unit, University of Zurich & ETH Zurich, 8032 Zurich, Switzerland +1
Tokenised Flow Matching for Hierarchical Simulation Based Inference
Apr 22, 2026Giovanni Charles, Cosmo Santoni, Seth Flaxman +1Flow Matching Simulation-Based Inference
Imperial College London, London, United Kingdom · University of Oxford, Oxford, United Kingdom
Hierarchical Latent Structure Learning through Online Inference
Mar 19, 2026Ines Aitsahalia, Kiyohito IigayaHierarchical Representation Learning Latent Variable Models
Center for Theoretical Neuroscience and Zuckerman Institute, Columbia University, New York, NY 10027 · Department of Psychiatry, Columbia University Irving Medical Center, New York, NY 10032 · New York State Psychiatric Institute, New York, NY 10032 +1
Bayesian Inference of Psychometric Variables From Brain and Behavior in Implicit Association Tests
Mar 17, 2026Christian A. Kothe, Sean Mullen, Michael V. Bronstein +7Bayesian Inference Hierarchical Bayesian Modeling
Intheon, La Jolla, CA, USA · Department of Psychiatry and Behavioral Sciences, University of Minnesota, MN, USA · Institute for Health Informatics, University of Minnesota, MN, USA +2
Generalized Hierarchical Bayesian Segmentation with Irregular Designs, Multi-Sequence Hierarchies, and Grouped/Latent-Group Designs
Mar 16, 2026Omid Shams SolariChange-Point Detection Hierarchical Bayesian Modeling
sAIm Labs

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Theoretical and Practical Advances in Hierarchical Bayesian Deep Learning Methodology

Neil K. Chada, Simon Cotter, Kody J. H. Law, Xinzhu Liang

Department of Mathematics, City University of Hong Kong, Hong Kong SAR. · School of Mathematics, University of Manchester, UK.

Bayesian Neural Networks Hierarchical Bayesian Modeling Markov Chain Monte Carlo

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Reliable uncertainty quantification remains an important challenge in AI. Hierarchical Bayesian methods provide a principled framework for this by representing unknown quantities through posterior distributions. Joint inference of neural-network parameters and prior hyperparameters is challenging for conventional Markov chain Monte Carlo (MCMC) methods due to strong dependencies. In this work, we introduce the multilevel particle marginal Metropolis-Hastings (MLPMMH) method, which combines pseudo-marginal inference for the hyperparameters with coupled sequential Monte Carlo (SMC) across hierarchy of network-width truncations for conditional parameter inference. The hierarchy is induced by a trace-class neural network (TNN) prior with width-dependent decay, motivated empirically by the compressible structure observed in trained neural-network parameters. Under standard multilevel coupling assumptions, we establish that MLPMMH achieves mean-square error (MSE)

\mathcal{O}(\varepsilon^2)

at expected computational cost

\mathcal{O}(\varepsilon^{-2})

, and verify the predicted rate on a Bayesian regression problem. To address larger-scale applications, we further introduce S-MLPMMH, a practical approximation that replaces the exact sampling components with a PCA-based hierarchy and scalable Bayesian Monte Carlo. Experiments on MNIST demonstrate competitive predictive performance and uncertainty quantification while exploiting the parallel structure of the approximation. Software has been made publicly available at https://github.com/submission-code-anon/mlpmmh-anon.