Monte Carlo sampling methods using Markov chains and their applications

1970/04/01 by W. K. Hastings, W. Keith Hastings · 15,264 citations
Computer Science · Mathematics · Physics and Astronomy · #Algorithm #Applied mathematics #Bayesian Methods and Mixture Models #Computer science #Exposition (narrative) #Generalization #Hybrid Monte Carlo #Markov Chains and Monte Carlo Methods #Markov chain #Markov chain Monte Carlo #Mathematical analysis #Mathematics #Monte Carlo integration #Monte Carlo method #Quasi-Monte Carlo method #Rejection sampling #Sampling (signal processing) #Scientific Research and Discoveries #Slice sampling #Statistical physics #Statistics

paper · doi:10.1093/biomet/57.1.97

published in Biometrika 57(1), 97-109 (Oxford University Press)

openalex publication_date 1970/04/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

A generalization of the sampling method introduced by Metropolis et al. (1953) is presented along with an exposition of the relevant theory, techniques of application and methods and difficulties of assessing the error in Monte Carlo estimates. Examples of the methods, including the generation of random orthogonal matrices and potential applications of the methods to numerical problems arising in statistics, are discussed.

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• Introduction to the variational and diffusion Monte Carlo methods
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• Bayesian Active Learning of (small) Quantile Sets through Expected Estimator Modification
• Quantum-Enhanced Simulated Annealing Using Rydberg Atoms
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• A Tutorial on Reversible Jump MCMC with a View toward Applications in QTL‐mapping
• Quantum Circuits for the Metropolis-Hastings Algorithm
• Hubble's Multi-Year Search for Exospheres in the TRAPPIST-1 System Reveals Frequent Microflares
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• GRIP: Generative Robust Inference and Perception for Semantic Robot Manipulation in Adversarial Environments
• A Bayesian Multisource Fusion Model for Spatiotemporal PM2.5 in an Urban Setting
• Course Project Report: Comparing MCMC and Variational Inference for Bayesian Probabilistic Matrix Factorization on the MovieLens Dataset
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• Results from the T2K experiment on neutrino mixing including a new far detector μ-like sample
• Constrained Sampling for Language Models Should Be Easy: An MCMC Perspective
• Performing Bayesian Risk Aggregation using Discrete Approximation Algorithms with Graph Factorization
• Analysis of Langevin Monte Carlo via convex optimization
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• Lipschitz stability for Bayesian inference in porous medium tissue growth models
• Progressive Tempering Sampler with Diffusion
• Efficient Gibbs Sampling in Cox Regression Models Using Composite Partial Likelihood and Pólya-Gamma Augmentation
• Bayesian Causality Test for Integer-Valued Time Series Models with Applications to Climate and Crime Data
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• The utility of a Bayesian analysis of complex models and the study of archeological ¹⁴C data
• Adaptive Markov Chain Monte Carlo for Auxiliary Variable Method and Its Application to Parallel Tempering
• Dense Uncertainty Estimation
• Bayesian semi-parametric forecasting of ultrafine particle number concentration with penalised splines and autoregressive errors
• Efficient posterior sampling for high-dimensional imbalanced logistic regression
• Spatial methods and their applications to environmental and climate data
• Understanding Past Population Dynamics: Bayesian Coalescent-Based Modeling with Covariates
• A Bayesian statistical analysis of stochastic phenotypic plasticity model of cancer cells
• Aggregated Gradient Langevin Dynamics
• Stein variational reduced basis Bayesian inversion
• Flexible mean field variational inference using mixtures of non-overlapping exponential families
• Bayesian Estimation of Species Divergence Times Under a Molecular Clock Using Multiple Fossil Calibrations with Soft Bounds
• Bayesian Inference Forgetting
• Latent Guided Sampling for Combinatorial Optimization
• Beyond the Coverage of Information Spreading: Analytical and Empirical Evidence of Re-exposure in Large-scale Online Social Networks
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• Psi-Sampler: Initial Particle Sampling for SMC-Based Inference-Time Reward Alignment in Score Models
• A Semiparametric Stochastic Volatility Model with Dependent Errors
• Distributed Averaging via Lifted Markov Chains
• Bayesian full waveform inversion with sequential surrogate model refinement
• AIDE: An algorithm for measuring the accuracy of probabilistic inference algorithms
• Random Coordinate Langevin Monte Carlo
• A Repelling-Attracting Metropolis Algorithm for Multimodality
• Joint Modeling of Longitudinal Imaging and Survival Data
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• A localized consensus-based sampling algorithm
• Test Scene Design for Physically Based Rendering
• Population counts along elliptical habitat contours: hierarchical modelling using Poisson-lognormal mixtures with nonstationary spatial structure
• Bayesian Field Theory: Nonparametric Approaches to Density Estimation, Regression, Classification, and Inverse Quantum Problems
• The Thermodynamics of the Travelling Salesman Problem
• Modeling Item Response Theory with Stochastic Variational Inference
• Interpretable Scaling Behavior in Sparse Subnetwork Representations of Quantum States
• Sampling Algorithms, from Survey Sampling to Monte Carlo Methods: Tutorial and Literature Review
• Langer's nucleation rate reproduced on the lattice
• Calibration Concordance for Astronomical Instruments via Multiplicative Shrinkage
• An Additive Approximate Gaussian Process Model for Large Spatio-Temporal Data
• Teleparallel dark energy in a nonflat universe
• Efficient and Unbiased Sampling from Boltzmann Distributions via Variance-Tuned Diffusion Models
• An Adaptive Sequential Monte Carlo Sampler
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• Comparing Grid Model Fitting Methodologies for Low-Temperature Atmospheres: Markov Chain Monte Carlo versus Random Forest Retrieval
• Hierarchical Bayesian estimation for continual learning during model-informed precision dosing
• Energy-based generator matching: A neural sampler for general state space
• Generalizing Hamiltonian Monte Carlo with Neural Networks
• Couplings of the Random-Walk Metropolis algorithm
• Parameter estimation for land-surface models using Neural Physics
• Bayesian Mixture Models for Frequent Itemset Discovery
• Note on the computation of the Metropolis-Hastings ratio for Birth-or-Death moves in trans-dimensional MCMC algorithms for signal decomposition problems
• A likelihood-based Bayesian inference framework for the calibration of and selection between stochastic velocity-jump models
• A Simple Algorithm for Scalable Monte Carlo Inference
• LADA: Look-Ahead Data Acquisition via Augmentation for Active Learning
• Bayesian Parameter Identification for Jump Markov Linear Systems
• A Framework for Stochastic Differentiable Programming
• Temperature is All You Need for Generalization in Langevin Dynamics and other Markov Processes
• Discrete Equilibrium Sampling with Arbitrary Nonequilibrium Processes
• Delayed rejection schemes for efficient Markov-Chain Monte-Carlo sampling of multimodal distributions
• Beyond Equilibrium: Non-Equilibrium Foundations Should Underpin Generative Processes in Complex Dynamical Systems
• Lightweight Data Fusion with Conjugate Mappings
• Beyond Self-Repellent Kernels: History-Driven Target Towards Efficient Nonlinear MCMC on General Graphs
• Efficient computation of extreme excursion probabilities for dynamical systems
• In-situ learning harnessing intrinsic resistive memory variability through Markov Chain Monte Carlo Sampling
• Discrete Neural Flow Samplers with Locally Equivariant Transformer
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• Measuring Sample Quality in Algorithms for Intractable Normalizing Function Problems
• On Epidemic Spreading under Mobility on Networks
• Robust Distributed Estimation: Extending Gossip Algorithms to Ranking and Trimmed Means
• Estimation and uncertainty quantification for the output from quantum simulators
• A Bayesian Regression Approach for Predicting Seasonal Tropical Cyclone Activity over the Central North Pacific
• Exponential Convergence of CAVI for Bayesian PCA
• trnL-F and rpl16 Sequence Data and Dense Taxon Sampling Reveal Monophyly of Unilocular Anthered Gomphrenoideae (Amaranthaceae) and an Improved Picture of Their Internal Relationships
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• Bayesian empirical likelihood for quantile regression
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• An Introduction to MCMC for Machine Learning
• A Langevin sampling algorithm inspired by the Adam optimizer
• Analysis of Multiple-try Metropolis via Poincaré inequalities
• Estimation via Markov chain Monte Carlo
• Molecular evidence on plant divergence times
• The Multiple-Try Method and Local Optimization in Metropolis Sampling
• Bayesian coalescent inference of major human mitochondrial DNA haplogroup expansions in Africa
• Evidence for the disintegration of KIC 12557548 b
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• Solution to the galactic foreground problem for LISA
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• Monte Carlo sampling from the quantum state space. I
• Monte Carlo sampling from the quantum state space. II
• Continuous-time Monte Carlo methods for quantum impurity models
• EasyCritics – I. Efficient detection of strongly lensing galaxy groups and clusters in wide-field surveys
• Rotational evolution of slow-rotator sequence stars
• A Censored Bayesian Hierarchical Model For Precipitation
• The BUGS project: Evolution, critique and future directions
• Phase separation in confined systems
• CXOCY J220132.8−320144: An Edge‐on Spiral Gravitational Lens
• ExaBayes: Massively Parallel Bayesian Tree Inference for the Whole-Genome Era
• Sequential Monte Carlo Methods for System Identification**This work was supported by the projects Learning of complex dynamical systems (Contract number: 637-2014-466) and Probabilistic modeling of dynamical systems (Contract number: 621-2013-5524), both funded by the Swedish Research Council.
• Bayesian Inference of Phylogeny and Its Impact on Evolutionary Biology
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• Kondo effect and the fate of bistability in molecular quantum dots with strong electron-phonon coupling
• Use of phylogenetics in the molecular epidemiology and evolutionary studies of viral infections
• A Highly Magnified Star at Redshift 6.2
• Ultraviolet luminosity density of the universe during the epoch of reionization
• METHODS FOR BAYESIAN POWER SPECTRUM INFERENCE WITH GALAXY SURVEYS
• Hamiltonian Monte Carlo for (Physics) Dummies
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• Ultracold dipolar gases in optical lattices
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• Tunneling and Speedup in Quantum Optimization for Permutation-Symmetric Problems
• Real-time Approximate Bayesian Computation for Scene Understanding
• The initial conditions of observed star clusters – I. Method description and validation
• Accelerating Metropolis-within-Gibbs sampler with localized computations of differential equations
• General state space Markov chains and MCMC algorithms
• Transition Matrix Monte Carlo Method
• EMPIRICAL DELAY-TIME DISTRIBUTIONS OF TYPE Ia SUPERNOVAE FROM THE EXTENDED GOODS/HUBBLE SPACE TELESCOPESUPERNOVA SURVEY
• SELECTING QUASARS BY THEIR INTRINSIC VARIABILITY
• A Bayesian approach to parameter identification with an application to\n Turing systems
• A Bayesian Framework for Sparse Representation-Based 3-D Human Pose Estimation
• Inflationary cosmology with Chaplygin gas in Palatini formalism
• The Impact of Move Schemes on Simulated Annealing Performance
• Self-learning Monte Carlo method and cumulative update in fermion systems
• Photometric constraints on white dwarfs and the identification of extreme objects
• Tidal disruption of satellite galaxies in a semi-analytic model of galaxy formation
• Efficient sampling of fast and slow cosmological parameters
• Exact simulation of diffusions and improved algorithms for log-concave sampling
• NUCLEAR RADII OF UNSTABLE NUCLEI
• Estimating Parameters in Mathematical Model for Societal Booms through Bayesian Inference Approach
• Starobinsky cosmological model in Palatini formalism
• Bayesian parameter estimation of core collapse supernovae using gravitational wave simulations
• CONSTRAINING WHITE DWARF STRUCTURE AND NEUTRINO PHYSICS IN 47 TUCANAE
• Weak convergence of Metropolis algorithms for non-i.i.d. target distributions
• Coupled MCMC with a randomized acceptance probability
• Machine Learning Accelerates Parameter Optimization and Uncertainty Assessment of a Land Surface Model
• Bayesian approach to the detection problem in gravitational wave astronomy
• Asteroseismic detection of latitudinal differential rotation in 13 Sun-like stars
• Adaptive sampling-based quadrature rules for efficient Bayesian prediction
• Independent Doubly Adaptive Rejection Metropolis Sampling Within Gibbs Sampling
• Bayesian multiscale deep generative model for the solution of high-dimensional inverse problems
• Nonparametric Bayesian Volatility Estimation
• Weak Self-Interactions of Globular Proteins Studied by Small-Angle X-ray Scattering and Structure-Based Modeling
• Smoothing and Mean–Covariance Estimation of Functional Data with a Bayesian Hierarchical Model
• Measuring the sound horizon and absolute magnitude of SNIa by maximizing the consistency between low-redshift data sets
• On the uncertain nature of the core of α Cen A
• Pressure statistics from the path integral for Darcy flow through random porous media
• Bayesian monotonic errors‐in‐variables models with applications to pathogen susceptibility testing
• Random effects compound Poisson model to represent data with extra zeros
• Generalized Bouncy Particle Sampler
• Observational constraints and predictions of the interacting dark sector with field-fluid mapping
• The 1-1000 μm spectral energy distributions of far-infrared galaxies
• Bayesian nonstationary spatial modeling for very large datasets
• Bayesian analysis of multiple direct detection experiments
• Kernelized Hashcode Representations for Relation Extraction
• Bayesian neural networks for detecting epistasis in genetic association studies
• Markov Chain Monte Carlo-Based Machine Unlearning: Unlearning What Needs to be Forgotten
• Higher order gravitational-wave modes with likelihood reweighting
• A Markov Chain Monte Carlo Method for Efficient Finite-Length LDPC Code Design
• Consistency check ofΛCDMphenomenology
• Fast Monte Carlo simulation for patient-specific CT/CBCT imaging dose calculation
• Canonical local algorithms for spin systems: heat bath and Hasting?s methods
• The search for multiple populations in Magellanic Cloud clusters – I. Two stellar populations in the Small Magellanic Cloud globular cluster NGC 121
• Nonlocal stochastic-partial-differential-equation limits of spatially correlated noise-driven spin systems derived to sample a canonical distribution
• New ATCA, ALMA and VISIR observations of the candidate LBV SK -67 266 (S61): the nebular mass from modelling 3D density distributions
• Allesfitter: Flexible Star and Exoplanet Inference From Photometry and Radial Velocity
• Bayesian Inference of Quasi‐Linear Radial Diffusion Parameters using Van Allen Probes
• THE FIRST BROWN DWARF/PLANETARY-MASS OBJECT IN THE 32 ORIONIS GROUP*
• Bayesian Hamiltonian Selection in X-ray Photoelectron Spectroscopy
• Quantum self-learning Monte Carlo and quantum-inspired Fourier transform sampler
• Parallelized inference for gravitational-wave astronomy
• Optimal weights for measuring redshift space distortions in multitracer galaxy catalogues
• Convergence Analysis of Schrödinger-Föllmer Sampler without Convexity
• Asteroseismology of solar-type stars
• Improved determination of the β−ν¯e angular correlation coefficient a in free neutron decay with the aSPECT spectrometer
• Inference of stochastic time series with missing data
• Lattice model of heavy-light three-body system
• Dark matter and lepton flavour phenomenology in a singlet-doublet scotogenic model
• Statistical inference of assortative community structures
• Engineering local optimality in quantum Monte Carlo algorithms
• Model-based asymptotically optimal dispersion measure correction for pulsar timing
• Is there another coincidence problem at the reionization epoch?
• Measuring the Higgs sector
• Metropolis-Hastings view on variational inference and adversarial training
• (MC)3—A Multi-Channel Markov Chain Monte Carlo algorithm for phase–space sampling
• A Common Derivation for Markov Chain Monte Carlo Algorithms with Tractable and Intractable Targets
• Anomalous paths in quantum mechanical path-integrals
• Pareto Optimality in Multilayer Network Growth
• Flow-based sampling for fermionic lattice field theories
• Diagrammatic Monte Carlo for the weak-coupling expansion of non-Abelian lattice field theories: Large-N U(N)×U(N) principal chiral model
• Boosting Generative Models by Leveraging Cascaded Meta-Models
• Bayesian inference of nuclear symmetry energy from measured and imagined neutron skin thickness in Sn<mml:mprescripts/><mml:none/>116,118,120,122,124,130,132, Pb<mml:mprescripts/><mml:none/>208, and Ca<mml:mprescripts/><mml:none/>48
• Directed-Loop Quantum Monte Carlo Method for Retarded Interactions
• Parameter estimation in modelling frequency response of coupled systems using a stepwise approach
• Scalable Approximate Inference and Some Applications
• Measurement of Spin Density Matrix Elements in Λ(1520) Photoproduction at 8.2-8.8 GeV
• Variance reduction for Random Coordinate Descent-Langevin Monte Carlo
• Bayesian inference of the incompressibility, skewness and kurtosis of nuclear matter from empirical pressures in relativistic heavy-ion collisions
• RoCUS: Robot Controller Understanding via Sampling
• Variational inference as an alternative to MCMC for parameter estimation and model selection
• Correspondence between neuroevolution and gradient descent
• Active Tuning of Synaptic Patterns Enhances Immune Discrimination
• Multiscale Shrinkage and Lévy Processes
• On the universality of MOG weak field approximation at galaxy cluster scale
• Texas Spectroscopic Search for Lyα Emission at the End of Reionization I. Constraining the Lyα Equivalent-width Distribution at 6.0 < z < 7.0
• Constraining the multiplicity statistics of the coolest brown dwarfs: binary fraction continues to decrease with spectral type
• State and parameter estimation using Monte Carlo evaluation of path integrals
• Information field theory for cosmological perturbation reconstruction and nonlinear signal analysis
• ESTIMATORS OF BINARY SPATIAL AUTOREGRESSIVE MODELS: A MONTE CARLO STUDY
• A more effective coordinate system for parameter estimation of precessing compact binaries from gravitational waves
• Adaptive Bayesian Radio Tomography
• Spectral gaps for a Metropolis–Hastings algorithm in infinite dimensions
• Joint deprojection of Sunyaev-Zeldovich and X-ray images of galaxy clusters
• KEPLER-432: A RED GIANT INTERACTING WITH ONE OF ITS TWO LONG-PERIOD GIANT PLANETS
• Time-inhomogeneous Quantum Walks with Decoherence on Discrete Infinite Spaces
• Simulation of weak polyelectrolytes: a comparison between the constant pH and the reaction ensemble method
• Accelerating uncertainty quantification of groundwater flow modelling using a deep neural network proxy
• Simulations of the galaxy population constrained by observations from z = 3 to the present day: implications for galactic winds and the fate of their ejecta
• Fractional quantum Hall edge: Effect of nonlinear dispersion and edge roton
• A large‐scale spatio‐temporal binomial regression model for estimating seroprevalence trends
• Adaptive Modeling of Correlated Noise in Space-Based Gravitational Wave Detectors
• Dynamics of the diffusive DM-DE interaction – Dynamical system approach
• Event-Chain Monte-Carlo Simulations of Dense Soft Matter Systems
• A generalized Bayesian approach to model calibration
• exofit: orbital parameters of extrasolar planets from radial velocities
• On the Convergence of Markov Chain Distribution within Quantum Walk Circuit Subspace
• Stoquasticity in circuit QED
• Particle Data Cloning for Complex Ordinary Differential Equations
• Unsupervised Classification of English Words Based on Phonological Information: Discovery of Germanic and Latinate Clusters
• SSSpaNG! Stellar Spectra as Sparse, data-driven, Non-Gaussian processes
• From Continuous Dynamics to Practical Gradient-Based Samplers
• Dual-space posterior sampling for Bayesian inference in constrained inverse problems
• Foreground effect on the J-factor estimation of classical dwarf spheroidal galaxies
• Decoding X-ray observations from centres of galaxy clusters using MCMC
• Extending canonical Monte Carlo methods
• Extending canonical Monte Carlo methods: II
• Improving the efficiency of Monte Carlo simulations of systems that undergo temperature-driven phase transitions
• Quality Control and Structural Reliability -- A Unified Framework for Integrating Conformity Assessment and Partial Safety Factors
• Patterns of Y-Chromosome Diversity Intersect with the Trans-New Guinea Hypothesis
• Annealed Mean Field Descent Is Highly Effective for Quadratic Unconstrained Binary Optimization
• Incorporating structured assumptions with probabilistic graphical models in fMRI data analysis
• Multilevel Monte Carlo algorithm for quantum mechanics on a lattice
• Monte Carlo method [wikipedia]
• Cluster analysis for DNA methylation profiles having a detection threshold. [europepmc]
• Inferring cellular networks--a review. [europepmc]
• BEAST: Bayesian evolutionary analysis by sampling trees. [europepmc]
• Dynamics of genome rearrangement in bacterial populations. [europepmc]
• Bayesian coalescent inference of major human mitochondrial DNA haplogroup expansions in Africa. [europepmc]
• Bayesian inference of population size history from multiple loci. [europepmc]
• Bayesian random local clocks, or one rate to rule them all. [europepmc]
• Modelling cholera epidemics: the role of waterways, human mobility and sanitation. [europepmc]
• A Bayesian framework to estimate diversification rates and their variation through time and space. [europepmc]
• Estimating ancestry and heterozygosity of hybrids using molecular markers. [europepmc]
• Simultaneous reconstruction of evolutionary history and epidemiological dynamics from viral sequences with the birth-death SIR model. [europepmc]
• Model selection on solid ground: Rigorous comparison of nine ways to evaluate Bayesian model evidence. [europepmc]
• PhyloWGS: reconstructing subclonal composition and evolution from whole-genome sequencing of tumors. [europepmc]
• Stochastic modelling, Bayesian inference, and new in vivo measurements elucidate the debated mtDNA bottleneck mechanism. [europepmc]
• CoMEt: a statistical approach to identify combinations of mutually exclusive alterations in cancer. [europepmc]
• Emerging Computational Methods for the Rational Discovery of Allosteric Drugs. [europepmc]
• Inferential Structure Determination of Chromosomes from Single-Cell Hi-C Data. [europepmc]
• SiFit: inferring tumor trees from single-cell sequencing data under finite-sites models. [europepmc]
• outbreaker2: a modular platform for outbreak reconstruction. [europepmc]
• Epistatic mutations under divergent selection govern phenotypic variation in the crow hybrid zone. [europepmc]
• Simulation and inference algorithms for stochastic biochemical reaction networks: from basic concepts to state-of-the-art. [europepmc]
• Improved Specificity and False Discovery Rates for Multiplex Analysis of Changes in Strain-Specific Anti-Influenza IgG. [europepmc]
• Inferring who-infected-whom-where in the 2016 Zika outbreak in Singapore-a spatio-temporal model. [europepmc]
• Exact and efficient hybrid Monte Carlo algorithm for accelerated Bayesian inference of gene expression models from snapshots of single-cell transcripts. [europepmc]
• Optimal foraging and the information theory of gambling. [europepmc]
• Fermionic neural-network states for ab-initio electronic structure. [europepmc]
• The Bayesian superorganism: externalized memories facilitate distributed sampling. [europepmc]
• Evaluation of the Secondary Transmission Pattern and Epidemic Prediction of COVID-19 in the Four Metropolitan Areas of China. [europepmc]
• Incorporating the Q-Matrix Into Multidimensional Item Response Theory Models. [europepmc]
• Hamiltonian Monte Carlo sampling to estimate past population dynamics using the skygrid coalescent model in a Bayesian phylogenetics framework. [europepmc]
• Social bonds, social status and survival in wild baboons: a tale of two sexes. [europepmc]
• Identifiability analysis for stochastic differential equation models in systems biology. [europepmc]
• Adaptive dating and fast proposals: Revisiting the phylogenetic relaxed clock model. [europepmc]
• The Application of Bayesian Methods in Cancer Prognosis and Prediction. [europepmc]
• Metrics to relate COVID-19 wastewater data to clinical testing dynamics. [europepmc]
• Methodology-Centered Review of Molecular Modeling, Simulation, and Prediction of SARS-CoV-2. [europepmc]
• Bayesian rank-based hypothesis testing for the rank sum test, the signed rank test, and Spearman's ρ . [europepmc]
• Using empirical biological knowledge to infer regulatory networks from multi-omics data. [europepmc]
• Bayesian parameter estimation for dynamical models in systems biology. [europepmc]
• Primary and booster vaccination in reducing severe clinical outcomes associated with Omicron Naïve infection. [europepmc]
• A Bayesian Model for Spatial Partly Interval-Censored Data. [europepmc]
• Brain-wide representations of behavior spanning multiple timescales and states in C. elegans. [europepmc]
• PyMC: a modern, and comprehensive probabilistic programming framework in Python. [europepmc]
• Internal and external normalization of nascent RNA sequencing run-on experiments. [europepmc]
• A practical guide to adopting Bayesian analyses in clinical research. [europepmc]
• Collective predictive coding hypothesis: symbol emergence as decentralized Bayesian inference. [europepmc]
• Diffusion of proteins in crowded solutions studied by docking-based modeling. [europepmc]
• Calibration of stochastic, agent-based neuron growth models with approximate Bayesian computation. [europepmc]
• Data Generation for Machine Learning Interatomic Potentials and Beyond. [europepmc]
• Geometric variations in nucleosomal DNA dictate higher-order chromatin structure and enhancer-promoter communication. [europepmc]

Related

• Sampling Algorithms, from Survey Sampling to Monte Carlo Methods: Tutorial and Literature Review
• A Common Derivation for Markov Chain Monte Carlo Algorithms with Tractable and Intractable Targets
• A Conceptual Introduction to Markov Chain Monte Carlo Methods
• Stationarity and Convergence of the Metropolis-Hastings Algorithm: Insights into Theoretical Aspects
• The Convergence of Markov chain Monte Carlo Methods: From the Metropolis method to Hamiltonian Monte Carlo