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.
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A Conceptual Introduction to Hamiltonian Monte Carlo
Mixed citation behavior. Most common role is background (46%).
44
Pith papers citing it
Background
46% 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.
A Bayesian latent GP calibration framework for aerodynamic surrogates marginalizes input uncertainty and matches output uncertainty statistics, achieving 94.2-95.8% coverage of true 95% intervals.
Derives exact operating characteristic corrections and a numerical search over sample sizes to obtain optimal two-stage Bayes factor designs for two-arm binary-endpoint phase II trials that minimize expected sample size under the null.
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.
citing papers explorer
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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.
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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.