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.

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• PPL Bench: Evaluation Framework For Probabilistic Programming Languages
• 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
• Sparse Bayesian mass-mapping using trans-dimensional MCMC
• Metropolis-Hastings Algorithms for Estimating Betweenness Centrality in Large Networks
• Posterior-based proposals for speeding up Markov chain Monte Carlo
• Binary sampling from discrete distributions
• A Menu-Driven Software Package of Bayesian Nonparametric (and Parametric) Mixed Models for Regression Analysis and Density Estimation
• Scalable hybrid quantum Monte Carlo simulation of U(1) gauge field coupled to fermions on GPU
• Analyzing MCMC Output
• A Probabilistic Calibration Procedure for the CORSAIR Polarimeter
• Precision annealing Monte Carlo methods for statistical data assimilation and machine learning
• 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
• Bayesian monotonic errors-in-variables models with applications to pathogen susceptibility testing
• A fast asynchronous MCMC sampler for sparse Bayesian inference
• The Dynamic Splitting Method with an application to portfolio credit risk
• Strong-coupling results for $\mathcal{N}=2$ superconformal quivers and holography
• A Mathematical Walkthrough and Discussion of the Free Energy Principle
• Convergence Rate of Multiple-try Metropolis Independent sampler
• 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
• 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
• MCMC for a hyperbolic Bayesian inverse problem in traffic flow modelling
• Quantifying Observed Prior Impact
• Discrete Sampling using Semigradient-based Product Mixtures
• Active embedding search via noisy paired comparisons
• Variational Langevin Hamiltonian Monte Carlo for Distant Multi-modal Sampling
• Bayesian Reasoning for Physics Informed Neural Networks
• Adaptive MCMC via Combining Local Samplers
• Inferring properties of the local white dwarf population in astrometric and photometric surveys
• Bayesian inference methodology to characterize the dust emissivity at far-infrared and submillimeter frequencies
• A probabilistic framework for approximating functions in active subspaces
• 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
• R-VGAL: A Sequential Variational Bayes Algorithm for Generalised Linear Mixed Models
• Spatial Bayesian Latent Factor Regression Modeling of Coordinate-based Meta-analysis Data
• Improved annealing for sampling from multimodal distributions via landscape modification
• Parallel tempering as a mechanism for facilitating inference in hierarchical hidden Markov models
• Stochastic Approximate Gradient Descent via the Langevin Algorithm
• Convergence Analysis of Schr{ö}dinger-F{ö}llmer Sampler without Convexity
• On Numerical Considerations for Riemannian Manifold Hamiltonian Monte Carlo
• System identification using Bayesian neural networks with nonparametric noise models
• A Pólya-Gamma Sampler for a Generalized Logistic Regression
• Quantifying the Quark Gluon Plasma
• A Factor Stochastic Volatility Model with Markov-Switching Panic Regimes
• Tailored Bayes: a risk modelling framework under unequal misclassification costs
• A Bayesian approach for small area population estimates using multiple administrative records
• Relative Entropy Gradient Sampler for Unnormalized Distributions
• Combining Learned Representations for Combinatorial Optimization
• Quantized Variational Inference
• UV bright red-sequence galaxies: a comparative study between UV upturn and UV weak systems
• Sampling and statistical physics via symmetry
• 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
• String and Membrane Gaussian Processes
• Estimation of Constrained Mean-Covariance of Normal Distributions
• Bayesian Parameter Estimation for Latent Markov Random Fields and Social Networks
• Method for Chance Constrained Optimal Control Using Biased Kernel Density Estimators
• Statistical modeling of rates and trends in Holocene relative sea level
• Scalable couplings for the random walk Metropolis algorithm
• Inverse Gaussian Process regression for likelihood-free inference
• Prediction of tool-wear in turning of medical grade cobalt chromium molybdenum alloy (ASTM F75) using non-parametric Bayesian models
• Bayesian analysis of diffusion-driven multi-type epidemic models with application to COVID-19
• Modelling Numerical Systems with Two Distinct Labelled Output Classes
• Approximate Bayesian Computation by Subset Simulation
• Bayesian identification of discontinuous fields with an ensemble-based variable separation multiscale method
• RMCMC: A System for Updating Bayesian Models
• A Flexible Joint Longitudinal-Survival Modeling Framework for Incorporating Multiple Longitudinal Biomarkers
• An introduction to computational complexity in Markov Chain Monte Carlo methods
• A probabilistic reduced-order modeling framework for patient-specific cardio-mechanical analysis
• Bayesian inference using intermediate distribution based on coarse multiscale model for time fractional diffusion equation
• Simulation-Based Inference for Global Health Decisions
• A Warm Start Method for Solving Chance Constrained Optimal Control Problems
• Bayesian inference and uncertainty quantification for image reconstruction with Poisson data
• Ares: A Mars model retrieval framework for ExoMars Trace Gas Orbiter NOMAD solar occultation measurements
• Bring the noise: exact inference from noisy simulations in collider physics
• Efficient maximum likelihood parameterization of continuous-time Markov processes
• From the Fire: A Deeper Look at the Phoenix Stream
• Rare Events, Extremely Rare Events and Fluctuations in a Thermodynamic System
• Generative Particle Variational Inference via Estimation of Functional Gradients
• Resonances in reflective Hamiltonian Monte Carlo
• Probabilistic Zeeman-Doppler imaging of stellar magnetic fields: I. Analysis of tau Scorpii in the weak-field limit
• A Flexible Joint Longitudinal-Survival Model for Analysis of End-Stage Renal Disease Data
• Estimation of all parameters in the reflected Orntein-Uhlenbeck process from discrete observations
• Constrained Monte Carlo Markov Chains on Graphs
• 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
• Extracting the Italian output gap: a Bayesian approach
• 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
• Partition function approach to non-Gaussian likelihoods: macrocanonical partitions and replicating Markov-chains
• MCMC Confidence Intervals and Biases
• Structured Stochastic Gradient MCMC
• hIPPYlib-MUQ: A Bayesian Inference Software Framework for Integration of Data with Complex Predictive Models under Uncertainty
• Wasserstein distance estimates for the distributions of numerical approximations to ergodic stochastic differential equations
• A Theory of Non-Acyclic Generative Flow Networks
• Optimal observational scheduling framework for binary and multiple stellar systems
• Testing the mass of the graviton with Bayesian planetary numerical ephemerides B-INPOP
• Understanding Hormonal Crosstalk in Arabidopsis Root Development via Emulation and History Matching
• On Scalable Testing of Samplers
• RadioLensfit: an HPC Tool for Accurate Galaxy Shape Measurement with SKA