NUTS-mul and NUTS-BPS show nearly identical qualitative ergodicity behavior depending on target tails, with both mixing in O(d^{1/4}) time for Gaussians but smaller constants for NUTS-BPS.
hub Mixed citations
A Conceptual Introduction to Hamiltonian Monte Carlo
Mixed citation behavior. Most common role is method (50%).
36
Pith papers citing it
Method
50% of classified citations
abstract
Hamiltonian Monte Carlo has proven a remarkable empirical success, but only recently have we begun to develop a rigorous understanding of why it performs so well on difficult problems and how it is best applied in practice. Unfortunately, that understanding is confined within the mathematics of differential geometry which has limited its dissemination, especially to the applied communities for which it is particularly important. In this review I provide a comprehensive conceptual account of these theoretical foundations, focusing on developing a principled intuition behind the method and its optimal implementations rather of any exhaustive rigor. Whether a practitioner or a statistician, the dedicated reader will acquire a solid grasp of how Hamiltonian Monte Carlo works, when it succeeds, and, perhaps most importantly, when it fails.
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representative citing papers
Mortality forecasting is recast as integrating a flow field through the low-dimensional Tucker decomposition score space of the Human Mortality Database, yielding lower bias and error than Lee-Carter, Hyndman-Ullah, or UN models in cross-validation.
AMIGO is an end-to-end differentiable forward model of JWST AMI that corrects detector systematics to recover high-precision astrometry and detect close high-contrast companions.
MSFAST extends the FAST FPCA method to multivariate sparse data via Bayesian modeling with orthonormal splines, standardization, Procrustes alignment, and efficient computation, yielding valid inferences especially in low signal-to-noise settings.
A homotopy-plus-MCMC data-generation pipeline trains a mass-conditioned diffusion model that yields 40% more feasible initial costates and a better Pareto front for multiobjective indirect low-thrust transfers than adjoint-control-transformation baselines.
A fully Bayesian pixel-based Doppler imaging framework uses Gaussian Process priors and Hamiltonian Monte Carlo to simultaneously infer surface maps and geometric parameters from spectral data.
AM-SGHMC combines adaptive neural networks with SGHMC to produce a reusable MCMC sampler for Bayesian updating of similar structural dynamic models without per-task retraining.
An adaptive hierarchical RMHMC sampler with closed-form leapfrog integrator and automatic mass matrix tuning for efficient MCMC in high-dimensional Bayesian problems.
Template-Adapted Mixture Model uses many biased simulations for data-driven estimates of signal and background distributions, yielding unbiased signal fraction estimates with well-calibrated uncertainties.
Bayesian joint model infers infectious virus shedding trajectories and derived infectiousness metrics from PCR and other proxies in SARS-CoV-2 using data from five cohorts of roughly 2000 infections.
The GW-galaxy cross-correlation method, unified with spectral sirens in a harmonic framework, can measure H0 to 1% and Omega_m to 5% precision with 2 years of data from next-generation detectors like Einstein Telescope and Cosmic Explorer.
TGR performs manifold-informed latent foresight search to boost trajectory coverage in long-context reasoning tasks by up to 13 AUC points with minimal overhead.
Combined five-PTA dataset yields posterior on SGWB power-law amplitude and index consistent with nonzero signal but below 5-sigma significance, with reconstructed angular correlations matching the Hellings-Downs prediction.
RefineStat improves small language model performance on probabilistic program synthesis by adding semantic constraint enforcement and diagnostic-aware refinement, producing syntactically and statistically reliable code that often matches larger models.
Comparative evaluation of Bayesian Neural Network surrogates versus Gaussian Processes in Bayesian Optimization applied to Carbon Capture and Storage operations, presented as the first such application in reservoir engineering.
Introduces statistically efficient estimators for Renyi-α, Tsallis-α, reverse and forward KL divergences with REINFORCE and score-matching control variates for faster GFlowNet training.
dynesty is an open-source Python package for dynamic nested sampling that improves efficiency in Bayesian posterior and evidence estimation compared to MCMC on certain problems.
An amortized variational framework jointly targets the posterior and posterior-predictive distributions via a KL upper bound and moment regularization, yielding more accurate predictions at lower online cost than two-stage variational inference.
Bayesian X-Learner delivers calibrated posterior inference for CATE by combining cross-fitted doubly robust pseudo-outcomes with a Welsch redescending pseudo-likelihood and MCMC sampling.
Tempered sequential Monte Carlo samples from a Boltzmann-tilted distribution over controllers to optimize trajectories and policies under differentiable dynamics.
A hybrid method models squared losses from Bayesian CNV posteriors with a Gamma distribution on validation samples to produce tolerance intervals with valid frequentist coverage, achieving single-digit mean absolute coverage error on targeted amplicon panels.
Jeffreys Flow distills Parallel Tempering trajectories via Jeffreys divergence to produce robust Boltzmann generators that suppress mode collapse and correct sampling inaccuracies for rare event sampling.
StanBKT provides a unified Bayesian inference framework for BKT models supporting HMC, variational inference, and hierarchical variants, evaluated on ASSISTments and intervention datasets.
SPICE is a scalable Bayesian MCMC engine for explanatory IRT calibration on sparsely linked persons and items in large assessment banks.
citing papers explorer
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A Theoretical Comparison of No-U-Turn Sampler Variants: Necessary and Sufficient Convergence Conditions and Mixing Time Analysis under Gaussian Targets
NUTS-mul and NUTS-BPS show nearly identical qualitative ergodicity behavior depending on target tails, with both mixing in O(d^{1/4}) time for Gaussians but smaller constants for NUTS-BPS.
-
Mortality Forecasting as a Flow Field in Tucker Decomposition Space
Mortality forecasting is recast as integrating a flow field through the low-dimensional Tucker decomposition score space of the Human Mortality Database, yielding lower bias and error than Lee-Carter, Hyndman-Ullah, or UN models in cross-validation.
-
AMIGO: a Data-Driven Calibration of the JWST Interferometer
AMIGO is an end-to-end differentiable forward model of JWST AMI that corrects detector systematics to recover high-precision astrometry and detect close high-contrast companions.
-
Bayesian Multivariate Sparse Functional Principal Components Analysis
MSFAST extends the FAST FPCA method to multivariate sparse data via Bayesian modeling with orthonormal splines, standardization, Procrustes alignment, and efficient computation, yielding valid inferences especially in low signal-to-noise settings.
-
Transfer Learning of Multiobjective Indirect Low-Thrust Trajectories Using Diffusion Models and Markov Chain Monte Carlo
A homotopy-plus-MCMC data-generation pipeline trains a mass-conditioned diffusion model that yields 40% more feasible initial costates and a better Pareto front for multiobjective indirect low-thrust transfers than adjoint-control-transformation baselines.
-
Bayesian Doppler Imaging: Simultaneous Inference of Surface Maps and Geometric Parameters
A fully Bayesian pixel-based Doppler imaging framework uses Gaussian Process priors and Hamiltonian Monte Carlo to simultaneously infer surface maps and geometric parameters from spectral data.
-
Adaptive Meta-Learning Stochastic Gradient Hamiltonian Monte Carlo Simulation for Bayesian Updating of Structural Dynamic Models
AM-SGHMC combines adaptive neural networks with SGHMC to produce a reusable MCMC sampler for Bayesian updating of similar structural dynamic models without per-task retraining.
-
Adaptive Riemannian Manifold Hamiltonian Monte Carlo with Hierarchical Metric
An adaptive hierarchical RMHMC sampler with closed-form leapfrog integrator and automatic mass matrix tuning for efficient MCMC in high-dimensional Bayesian problems.
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Many Wrongs Make a Right: Leveraging Biased Simulations Towards Unbiased Parameter Inference
Template-Adapted Mixture Model uses many biased simulations for data-driven estimates of signal and background distributions, yielding unbiased signal fraction estimates with well-calibrated uncertainties.
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Inferring infectiousness: a joint model of the within-host viral kinetics of SARS-CoV-2
Bayesian joint model infers infectious virus shedding trajectories and derived infectiousness metrics from PCR and other proxies in SARS-CoV-2 using data from five cohorts of roughly 2000 infections.
-
A unified harmonic framework for dark siren cosmology
The GW-galaxy cross-correlation method, unified with spectral sirens in a harmonic framework, can measure H0 to 1% and Omega_m to 5% precision with 2 years of data from next-generation detectors like Einstein Telescope and Cosmic Explorer.
-
The Geometric Reasoner: Manifold-Informed Latent Foresight Search for Long-Context Reasoning
TGR performs manifold-informed latent foresight search to boost trajectory coverage in long-context reasoning tasks by up to 13 AUC points with minimal overhead.
-
Stochastic gravitational-wave background search using data from five pulsar timing arrays
Combined five-PTA dataset yields posterior on SGWB power-law amplitude and index consistent with nonzero signal but below 5-sigma significance, with reconstructed angular correlations matching the Hellings-Downs prediction.
-
RefineStat: Efficient Exploration for Probabilistic Program Synthesis
RefineStat improves small language model performance on probabilistic program synthesis by adding semantic constraint enforcement and diagnostic-aware refinement, producing syntactically and statistically reliable code that often matches larger models.
-
Bayesian Neural Network Surrogates for Bayesian Optimization of Carbon Capture and Storage Operations
Comparative evaluation of Bayesian Neural Network surrogates versus Gaussian Processes in Bayesian Optimization applied to Carbon Capture and Storage operations, presented as the first such application in reservoir engineering.
-
On Divergence Measures for Training GFlowNets
Introduces statistically efficient estimators for Renyi-α, Tsallis-α, reverse and forward KL divergences with REINFORCE and score-matching control variates for faster GFlowNet training.
-
dynesty: A Dynamic Nested Sampling Package for Estimating Bayesian Posteriors and Evidences
dynesty is an open-source Python package for dynamic nested sampling that improves efficiency in Bayesian posterior and evidence estimation compared to MCMC on certain problems.
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Amortized Variational Inference for Joint Posterior and Predictive Distributions in Bayesian Uncertainty Quantification
An amortized variational framework jointly targets the posterior and posterior-predictive distributions via a KL upper bound and moment regularization, yielding more accurate predictions at lower online cost than two-stage variational inference.
-
Bayesian X-Learner: Calibrated Posterior Inference for Heterogeneous Treatment Effects under Heavy-Tailed Outcomes
Bayesian X-Learner delivers calibrated posterior inference for CATE by combining cross-fitted doubly robust pseudo-outcomes with a Welsch redescending pseudo-likelihood and MCMC sampling.
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Tempered Sequential Monte Carlo for Trajectory and Policy Optimization with Differentiable Dynamics
Tempered sequential Monte Carlo samples from a Boltzmann-tilted distribution over controllers to optimize trajectories and policies under differentiable dynamics.
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Combining Bayesian and Frequentist Inference for Laboratory-Specific Performance Guarantees in Copy Number Variation Detection
A hybrid method models squared losses from Bayesian CNV posteriors with a Gamma distribution on validation samples to produce tolerance intervals with valid frequentist coverage, achieving single-digit mean absolute coverage error on targeted amplicon panels.
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Jeffreys Flow: Robust Boltzmann Generators for Rare Event Sampling via Parallel Tempering Distillation
Jeffreys Flow distills Parallel Tempering trajectories via Jeffreys divergence to produce robust Boltzmann generators that suppress mode collapse and correct sampling inaccuracies for rare event sampling.
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StanBKT: Rethinking Parameter Estimation in Bayesian Knowledge Tracing
StanBKT provides a unified Bayesian inference framework for BKT models supporting HMC, variational inference, and hierarchical variants, evaluated on ASSISTments and intervention datasets.
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A Scalable Parametric Item Calibration Engine (SPICE) for Explanatory IRT with Sparse Data
SPICE is a scalable Bayesian MCMC engine for explanatory IRT calibration on sparsely linked persons and items in large assessment banks.
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The impact of observation density on Bayesian inversion of latent dynamics in shock-dominated flows
A latent-space reduced-order model using autoencoders and learned dynamics enables Bayesian recovery of initial density and pressure in Sod shock tube simulations, with posterior uncertainty contracting substantially as observation density increases.
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A Cubing Strategy for Identifying Stable Hyperparameter Regions for Uncertainty Quantification in Spatial Deep Learning
A recursive cubing framework identifies stable hyperparameter regions for MC dropout uncertainty quantification in spatial deep learning and produces competitive or superior predictive intervals versus a statistical baseline on simulations and land-surface temperature data.
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Uncertainty-Aware Prediction of Lung Tumor Growth from Sparse Longitudinal CT Data via Bayesian Physics-Informed Neural Networks
Bayesian PINN integrates Gompertz dynamics and HMC sampling to predict tumor growth from sparse CT data, achieving log-space RMSE of 0.20 with well-calibrated 95% credible intervals on 30 NLST patients.
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LITMUS: Bayesian Lag Recovery in Reverberation Mapping with Fast Differentiable Models
LITMUS introduces a differentiable Bayesian lag recovery framework that outperforms JAVELIN on OzDES-like mock data by reducing false positives from seasonal aliasing.
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Temporal Point Process Modeling of Aggressive Behavior Onset in Psychiatric Inpatient Youths with Autism
Applies self-exciting temporal point processes to model clustered aggression onsets in inpatient autistic youth and reports better fit than Poisson baselines.
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Uncertainty Quantification for Cardiac Shape Reconstruction with Deep Signed Distance Functions via MCMC methods
Deep signed distance functions combined with MCMC sampling enable uncertainty-aware reconstruction of left and right ventricles from limited data.
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Singularity Formation: Synergy in Theoretical, Numerical and Machine Learning Approaches
The work introduces a modulation-based analytical method for singularity proofs in singular PDEs and refines ML techniques like PINNs and KANs to identify blowup solutions, with application to the open 3D Keller-Segel problem.
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Uncertainty in Physics and AI: Taxonomy, Quantification, and Validation
A unified taxonomy of uncertainty in ML for physics is introduced together with validation tools such as coverage, calibration, and proper scoring rules, illustrated on regression and classification tasks.
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Parameter Estimation and Uncertainty Quantification for Systems Biology Models
Review of gradient-based and gradient-free methods for parameter point estimation plus profile likelihood, bootstrapping, and Bayesian inference for uncertainty quantification in systems biology models.
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Bayesian Neural Networks: An Introduction and Survey
A survey introducing Bayesian Neural Networks and comparing approximate inference methods to enable uncertainty quantification in neural network predictions.
- Adaptive Generalized Elliptical Slice Sampling
- Self-Supervised Laplace Approximation for Bayesian Uncertainty Quantification