Parallel hierarchical sampling: a general-purpose interacting Markov chains Monte Carlo algorithm

DOI10.1016/j.csda.2011.11.020zbMath1246.65026OpenAlexW2046158133MaRDI QIDQ434903

J. Herrera, H. S. Yoon

Publication date: 16 July 2012

Published in: Computational Statistics and Data Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.csda.2011.11.020

zbMATH Keywords

convergencenumerical examplesparallel computationheavy tailsmulti-modalityGaussian mixturesMetropolis-HastingsBayesian model uncertaintyMarkov chain Monte Carlo algorithmsBayesian covariate selectioncancer patientsGaussian linear regression modelparallel hierarchical samplertreed survival models

Mathematics Subject Classification ID

Linear regression; mixed models (62J05) Applications of statistics to biology and medical sciences; meta analysis (62P10) Bayesian inference (62F15) Monte Carlo methods (65C05) Numerical analysis or methods applied to Markov chains (65C40) Statistical ranking and selection procedures (62F07) Cell movement (chemotaxis, etc.) (92C17)

Related Items

Weighted particle tempering, Integration based profile likelihood calculation for PDE constrained parameter estimation problems, High-dimensional Bayesian parameter estimation: case study for a model of JAK2/STAT5 signaling, Parameter uncertainty in biochemical models described by ordinary differential equations, Bayesian survival trees for clustered observations, applied to tooth prognosis, Constructing Sampling Schemes via Coupling: Markov Semigroups and Optimal Transport

Uses Software

• WinBUGS
• wavethresh
• MrBayes

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Bagging predictors
• Reversible jump Markov chain Monte Carlo computation and Bayesian model determination
• Adaptive proposal distribution for random walk Metropolis algorithm
• On Bayesian model and variable selection using MCMC
• Optimal scaling of random walk Metropolis algorithms with discontinuous target densities
• Monte Carlo errors with less errors
• On adaptive Markov chain Monte Carlo algorithms
• A new class of interacting Markov chain Monte Carlo methods
• Markov chain Monte Carlo: can we trust the third significant figure?
• Estimating Bayes factors via thermodynamic integration and population MCMC
• Distributed evolutionary Monte Carlo for Bayesian computing
• Limitations of Markov chain Monte Carlo algorithms for Bayesian inference of phylogeny
• Classification tree analysis using TARGET
• Interacting sequential Monte Carlo samplers for trans-dimensional simulation
• Conditions for rapid mixing of parallel and simulated tempering on multimodal distributions
• Nonparametric regression using Bayesian variable selection
• State-dependent criteria for convergence of Markov chains
• Exponential convergence of Langevin distributions and their discrete approximations
• Weak convergence and optimal scaling of random walk Metropolis algorithms
• Population Markov chain Monte Carlo
• Langevin diffusions and Metropolis-Hastings algorithms
• Slice sampling. (With discussions and rejoinder)
• Ordering and improving the performance of Monte Carlo Markov chains.
• Optimal scaling for various Metropolis-Hastings algorithms.
• Inference from iterative simulation using multiple sequences
• Model uncertainty
• A new strategy for speeding Markov chain Monte Carlo algorithms
• Bayesian analysis of mixture models with an unknown number of components\,--\,an alternative to reversible jump methods.
• Antithetic coupling of two Gibbs sampler chains.
• Polynomial convergence rates of Markov chains
• Optimal predictive model selection.
• Population theory for boosting ensembles.
• Markov chains for exploring posterior distributions. (With discussion)
• On the convergence of the Markov chain simulation method
• Rates of convergence of the Hastings and Metropolis algorithms
• Markov chain Monte Carlo and Rao-Blackwellization
• Multiprocess parallel antithetic coupling for backward and forward Markov chain Monte Carlo
• On swapping and simulated tempering algorithms.
• Nonparametric Bayesian survival analysis using mixtures of Weibull distributions
• Delayed rejection in reversible jump Metropolis-Hastings
• Learn From Thy Neighbor: Parallel-Chain and Regional Adaptive MCMC
• Optimum Monte-Carlo sampling using Markov chains
• Sequential Monte Carlo Samplers
• Population-Based Reversible Jump Markov Chain Monte Carlo
• Optimal scaling of Metropolis algorithms: Heading toward general target distributions
• The Calculation of Posterior Distributions by Data Augmentation
• Bayesian Variable Selection in Linear Regression
• Geometric convergence and central limit theorems for multidimensional Hastings and Metropolis algorithms
• A Bayesian CART algorithm
• Density and Hazard Rate Estimation for Right-Censored Data by Using Wavelet Methods
• Bayesian Model Averaging for Linear Regression Models
• Improving Convergence of the Hastings–Metropolis Algorithm with an Adaptive Proposal
• A Theory for Dynamic Weighting in Monte Carlo Computation
• Real-Parameter Evolutionary Monte Carlo With Applications to Bayesian Mixture Models
• On an adaptive version of the Metropolis–Hastings algorithm with independent proposal distribution
• The Multiple-Try Method and Local Optimization in Metropolis Sampling
• Computational and Inferential Difficulties with Mixture Posterior Distributions
• Markov Chain Monte Carlo: 10 Years and Still Running!
• Bayesian Phylogenetic Inference via Markov Chain Monte Carlo Methods
• Reversible Jump, Birth-and-Death and More General Continuous Time Markov Chain Monte Carlo Samplers
• Efficient Construction of Reversible Jump Markov Chain Monte Carlo Proposal Distributions
• A geometric approach to transdimensional markov chain monte carlo
• Annealing Markov Chain Monte Carlo with Applications to Ancestral Inference
• Equation of State Calculations by Fast Computing Machines
• Coupling and Ergodicity of Adaptive Markov Chain Monte Carlo Algorithms
• A Simplex Method for Function Minimization
• The Monte Carlo Method
• An adaptive Metropolis algorithm
• Monte Carlo strategies in scientific computing
• Random forests