MCMC using Hamiltonian dynamics

Abstract

Hamiltonian dynamics can be used to produce distant proposals for the Metropolis algorithm, thereby avoiding the slow exploration of the state space that results from the diffusive behaviour of simple random-walk proposals. Though originating in physics, Hamiltonian dynamics can be applied to most problems with continuous state spaces by simply introducing fictitious "momentum" variables. A key to its usefulness is that Hamiltonian dynamics preserves volume, and its trajectories can thus be used to define complex mappings without the need to account for a hard-to-compute Jacobian factor - a property that can be exactly maintained even when the dynamics is approximated by discretizing time. In this review, I discuss theoretical and practical aspects of Hamiltonian Monte Carlo, and present some of its variations, including using windows of states for deciding on acceptance or rejection, computing trajectories using fast approximations, tempering during the course of a trajectory to handle isolated modes, and short-cut methods that prevent useless trajectories from taking much computation time.

References in corpus (5)

• Simulated Tempering: A New Monte Carlo Scheme
• Annealed Importance Sampling
• Riemannian Manifold Hamiltonian Monte Carlo
• A General Limitation on Monte Carlo Algorithms of Metropolis Type
• The Short-Cut Metropolis Method

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• Modeling the complexity of Elliptic Black Hole Solution In 4D Using Hamiltonian Monte Carlo with Stacked Neural Networks
• Hamiltonian Assisted Metropolis Sampling
• Efficient Probabilistic Inference in the Quest for Physics Beyond the Standard Model
• Subsampling MCMC - An introduction for the survey statistician
• RoCUS: Robot Controller Understanding via Sampling
• Structural complexity of snapshots of 2D Fermi-Hubbard systems
• A general framework for modelling zero inflation
• The Taxicab Sampler: MCMC for Discrete Spaces with Application to Tree Models
• Pseudo-extended Markov chain Monte Carlo
• Goal-Oriented Bayesian Optimal Experimental Design for Nonlinear Models using Markov Chain Monte Carlo
• On decision-theoretic model assessment for structural deterioration monitoring
• Minimal Autocorrelation in Hybrid Monte Carlo simulations using Exact Fourier Acceleration
• Markov-chain sampling for long-range systems without evaluating the energy
• The Dynamic Splitting Method with an application to portfolio credit risk
• A fast asynchronous MCMC sampler for sparse Bayesian inference
• Strong-coupling results for $\mathcal{N}=2$ superconformal quivers and holography
• A Mathematical Walkthrough and Discussion of the Free Energy Principle
• Variational Inference for Shrinkage Priors: The R package vir
• Sampling in Combinatorial Spaces with SurVAE Flow Augmented MCMC
• QROSS: QUBO Relaxation Parameter Optimisation via Learning Solver Surrogates
• Precision annealing Monte Carlo methods for statistical data assimilation and machine learning
• Nonstationary Multivariate Gaussian Processes for Electronic Health Records
• f-SAEM: A fast Stochastic Approximation of the EM algorithm for nonlinear mixed effects models
• Correlated functional models with derivative information for modeling MFS data on rock art paintings
• Gaussian process with derivative information for the analysis of the sunlight adverse effects on color of rock art paintings
• Quantifying Observed Prior Impact
• Analyzing MCMC Output
• Sparse Bayesian mass-mapping using trans-dimensional MCMC
• Active embedding search via noisy paired comparisons
• Variational Langevin Hamiltonian Monte Carlo for Distant Multi-modal Sampling
• Spatial Bayesian Latent Factor Regression Modeling of Coordinate-based Meta-analysis Data
• A Menu-Driven Software Package of Bayesian Nonparametric (and Parametric) Mixed Models for Regression Analysis and Density Estimation
• PPL Bench: Evaluation Framework For Probabilistic Programming Languages
• Posterior-based proposals for speeding up Markov chain Monte Carlo
• R-VGAL: A Sequential Variational Bayes Algorithm for Generalised Linear Mixed Models
• Bayesian Reasoning for Physics Informed Neural Networks
• A probabilistic framework for approximating functions in active subspaces
• Inferring properties of the local white dwarf population in astrometric and photometric surveys
• Discrete Sampling using Semigradient-based Product Mixtures
• Bayesian inference methodology to characterize the dust emissivity at far-infrared and submillimeter frequencies
• Adaptive MCMC via Combining Local Samplers
• Simultaneously unveiling the EBL and intrinsic spectral parameters of gamma-ray sources with Hamiltonian Monte Carlo
• Stress Resultant-Based Approach to Mass Assumption-Free Bayesian Model Updating of Frame Structures
• Reconstructing the Magnetic Field in an Arbitrary Domain via Data-driven Bayesian Methods and Numerical Simulations
• Sequential Kalman Tuning of the $t$-preconditioned Crank-Nicolson algorithm: efficient, adaptive and gradient-free inference for Bayesian inverse problems
• Approximate Bayesian inference for high-resolution spatial disaggregation using alternative data sources
• Metropolis-Hastings Algorithms for Estimating Betweenness Centrality in Large Networks
• Binary sampling from discrete distributions
• Bayesian monotonic errors-in-variables models with applications to pathogen susceptibility testing
• Scalable hybrid quantum Monte Carlo simulation of U(1) gauge field coupled to fermions on GPU
• Convergence Rate of Multiple-try Metropolis Independent sampler
• MCMC for a hyperbolic Bayesian inverse problem in traffic flow modelling
• A Probabilistic Calibration Procedure for the CORSAIR Polarimeter
• Quantification of Predictive Uncertainty via Inference-Time Sampling
• Convergence Rates of Two-Component MCMC Samplers
• Efficient Multimodal Sampling via Tempered Distribution Flow
• Re-examining the Bayesian colour excess estimation for the local star-forming galaxies observed in the HETDEX Pilot Survey
• q-Paths: Generalizing the Geometric Annealing Path using Power Means
• Parallel tempering as a mechanism for facilitating inference in hierarchical hidden Markov models
• Generative Particle Variational Inference via Estimation of Functional Gradients
• Sampling and statistical physics via symmetry
• Wasserstein distance estimates for the distributions of numerical approximations to ergodic stochastic differential equations
• Tailored Bayes: a risk modelling framework under unequal misclassification costs
• System identification using Bayesian neural networks with nonparametric noise models
• Simulation-Based Inference for Global Health Decisions
• Structured Stochastic Gradient MCMC
• Method for Chance Constrained Optimal Control Using Biased Kernel Density Estimators
• From the Fire: A Deeper Look at the Phoenix Stream
• Estimation of Constrained Mean-Covariance of Normal Distributions
• On Numerical Considerations for Riemannian Manifold Hamiltonian Monte Carlo
• Improved annealing for sampling from multimodal distributions via landscape modification
• hIPPYlib-MUQ: A Bayesian Inference Software Framework for Integration of Data with Complex Predictive Models under Uncertainty
• Combining Learned Representations for Combinatorial Optimization
• A Pólya-Gamma Sampler for a Generalized Logistic Regression
• A Flexible Joint Longitudinal-Survival Model for Analysis of End-Stage Renal Disease Data
• Bayesian analysis of diffusion-driven multi-type epidemic models with application to COVID-19
• Scalable couplings for the random walk Metropolis algorithm
• Bayesian inference and uncertainty quantification for image reconstruction with Poisson data
• Modelling Numerical Systems with Two Distinct Labelled Output Classes
• On Scalable Testing of Samplers
• Statistical modeling of rates and trends in Holocene relative sea level
• Bayesian identification of discontinuous fields with an ensemble-based variable separation multiscale method
• A Flexible Joint Longitudinal-Survival Modeling Framework for Incorporating Multiple Longitudinal Biomarkers
• Partition function approach to non-Gaussian likelihoods: macrocanonical partitions and replicating Markov-chains
• Rare Events, Extremely Rare Events and Fluctuations in a Thermodynamic System
• A Theory of Non-Acyclic Generative Flow Networks
• Understanding Hormonal Crosstalk in Arabidopsis Root Development via Emulation and History Matching
• Bayesian inference using intermediate distribution based on coarse multiscale model for time fractional diffusion equation
• A probabilistic reduced-order modeling framework for patient-specific cardio-mechanical analysis
• Bring the noise: exact inference from noisy simulations in collider physics
• Resonances in reflective Hamiltonian Monte Carlo
• Probabilistic Zeeman-Doppler imaging of stellar magnetic fields: I. Analysis of tau Scorpii in the weak-field limit
• Efficient and simple Gibbs state preparation of the 2D toric code via duality to classical Ising chains
• Characterizing Binary Black Hole Subpopulations in GWTC-4 with Binned Gaussian Processes: On the Origins of the $35M_{\odot }$ Peak
• The Sequential Monte Carlo goes NUTS: Boosting Gravitational-Wave Inference
• A Salpeter IMF and an NFW halo: Disentangling the dark and stellar mass of an elliptical galaxy through precise lens modelling of a double-source-plane system
• Accelerating Bayesian inverse design in computational fluid dynamics using neural operators
• Optimal observational scheduling framework for binary and multiple stellar systems
• Testing the mass of the graviton with Bayesian planetary numerical ephemerides B-INPOP
• RadioLensfit: an HPC Tool for Accurate Galaxy Shape Measurement with SKA
• Convergence Analysis of Schr{ö}dinger-F{ö}llmer Sampler without Convexity
• Quantifying the Quark Gluon Plasma
• Relative Entropy Gradient Sampler for Unnormalized Distributions
• String and Membrane Gaussian Processes
• Quantized Variational Inference
• UV bright red-sequence galaxies: a comparative study between UV upturn and UV weak systems
• Uncertainty Estimation in Deep Neural Networks for Point Cloud Segmentation in Factory Planning
• FastAD: Expression Template-Based C++ Library for Fast and Memory-Efficient Automatic Differentiation
• Inverse Gaussian Process regression for likelihood-free inference
• An introduction to computational complexity in Markov Chain Monte Carlo methods
• A Warm Start Method for Solving Chance Constrained Optimal Control Problems
• Ares: A Mars model retrieval framework for ExoMars Trace Gas Orbiter NOMAD solar occultation measurements
• Estimation of all parameters in the reflected Orntein-Uhlenbeck process from discrete observations
• Stochastic Approximate Gradient Descent via the Langevin Algorithm
• A Factor Stochastic Volatility Model with Markov-Switching Panic Regimes
• A Bayesian approach for small area population estimates using multiple administrative records
• RMCMC: A System for Updating Bayesian Models
• Constrained Monte Carlo Markov Chains on Graphs
• Prediction of tool-wear in turning of medical grade cobalt chromium molybdenum alloy (ASTM F75) using non-parametric Bayesian models
• Approximate Bayesian Computation by Subset Simulation
• Efficient maximum likelihood parameterization of continuous-time Markov processes
• Extracting the Italian output gap: a Bayesian approach
• Bayesian Parameter Estimation for Latent Markov Random Fields and Social Networks
• MCMC Confidence Intervals and Biases