A parallel evolutionary multiple-try metropolis Markov chain Monte Carlo algorithm for sampling spatial partitions

Cho, Wendy Tam; Liu, Yan Y.

doi:10.1007/s11222-020-09977-z

A parallel evolutionary multiple-try metropolis Markov chain Monte Carlo algorithm for sampling spatial partitions

Journal Article · Tue Jan 12 00:00:00 EST 2021 · Statistics and Computing

DOI:https://doi.org/10.1007/s11222-020-09977-z· OSTI ID:1777811

^[1]; Liu, Yan Y. ^[1]

Univ. of Illinois at Urbana-Champaign, IL (United States); Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

We develop an Evolutionary Markov Chain Monte Carlo (EMCMC) algorithm for sampling spatial partitions that lie within a large, complex, and constrained spatial state space. Our algorithm combines the advantages of evolutionary algorithms (EAs) as optimization heuristics for state space traversal and the theoretical convergence properties of Markov Chain Monte Carlo algorithms for sampling from unknown distributions. Local optimality information that is identified via a directed search by our optimization heuristic is used to adaptively update a Markov chain in a promising direction within the framework of a Multiple-Try Metropolis Markov Chain model that incorporates a generalized Metropolis-Hastings ratio. We further expand the reach of our EMCMC algorithm by harnessing the computational power afforded by massively parallel computing architecture through the integration of a parallel EA framework that guides Markov chains running in parallel.

View Accepted Manuscript (DOE)

Research Organization:: Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: AC05-00OR22725

OSTI ID:: 1777811

Journal Information:: Statistics and Computing, Journal Name: Statistics and Computing Journal Issue: 1 Vol. 31; ISSN 0960-3174

Publisher:: SpringerCopyright Statement

Country of Publication:: United States

Language:: English

References (30)

Districting Modeling with Exact Contiguity Constraints Shirabe, Takeshi Environment and Planning B: Planning and Design, Vol. 36, Issue 6 https://doi.org/10.1068/b34104	journal	January 2009
Real-Parameter Evolutionary Monte Carlo With Applications to Bayesian Mixture Models Liang, Faming; Wong, Wing Hung Journal of the American Statistical Association, Vol. 96, Issue 454 https://doi.org/10.1198/016214501753168325	journal	June 2001
An efficient, multiple range random walk algorithm to calculate the density of states Wang, Fugao; Landau, D. P. arXiv https://doi.org/10.48550/arxiv.cond-mat/0011174	text	January 2000
Convergence of Adaptive Direction Sampling Roberts, G. O.; Gilks, W. R. Journal of Multivariate Analysis, Vol. 49, Issue 2 https://doi.org/10.1006/jmva.1994.1028	journal	May 1994
Genetic algorithms and scatter search: unsuspected potentials Glover, Fred Statistics and Computing, Vol. 4, Issue 2 https://doi.org/10.1007/BF00175357	journal	June 1994
An iterative Monte Carlo method for nonconjugate Bayesian analysis Carlin, Bradley P.; Gelfand, Alan E. Statistics and Computing, Vol. 1, Issue 2 https://doi.org/10.1007/BF01889986	journal	December 1991
Acceleration of the Multiple-Try Metropolis algorithm using antithetic and stratified sampling Craiu, Radu V.; Lemieux, Christiane Statistics and Computing, Vol. 17, Issue 2 https://doi.org/10.1007/s11222-006-9009-4	journal	January 2007
Interacting multiple try algorithms with different proposal distributions Casarin, Roberto; Craiu, Radu; Leisen, Fabrizio Statistics and Computing, Vol. 23, Issue 2 https://doi.org/10.1007/s11222-011-9301-9	journal	December 2011
Multicanonical algorithms for first order phase transitions Berg, Bernd A.; Neuhaus, Thomas Physics Letters B, Vol. 267, Issue 2 https://doi.org/10.1016/0370-2693(91)91256-U	journal	September 1991
The hub network design problem O'Kelly, Morton E.; Miller, Harvey J. Journal of Transport Geography, Vol. 2, Issue 1 https://doi.org/10.1016/0966-6923(94)90032-9	journal	March 1994
A spatially explicit evolutionary algorithm for the spatial partitioning problem Liu, Yan Y.; Cho, Wendy K. Tam Applied Soft Computing, Vol. 90 https://doi.org/10.1016/j.asoc.2020.106129	journal	May 2020
Sampling from complicated and unknown distributions Cho, Wendy K. Tam; Liu, Yan Y. Physica A: Statistical Mechanics and its Applications, Vol. 506 https://doi.org/10.1016/j.physa.2018.03.096	journal	September 2018
PEAR: a massively parallel evolutionary computation approach for political redistricting optimization and analysis Liu, Yan Y.; Cho, Wendy K. Tam; Wang, Shaowen Swarm and Evolutionary Computation, Vol. 30 https://doi.org/10.1016/j.swevo.2016.04.004	journal	October 2016
Equation of State Calculations by Fast Computing Machines Metropolis, Nicholas; Rosenbluth, Arianna W.; Rosenbluth, Marshall N. The Journal of Chemical Physics, Vol. 21, Issue 6 https://doi.org/10.1063/1.1699114	journal	June 1953
A cavity-biased ( T, V, μ ) Monte Carlo method for the computer simulation of fluids Mezei, Mihaly Molecular Physics, Vol. 40, Issue 4 https://doi.org/10.1080/00268978000101971	journal	July 1980
Facilitating the Gibbs Sampler: The Gibbs Stopper and the Griddy-Gibbs Sampler Ritter, Christian; Tanner, Martin A. Journal of the American Statistical Association, Vol. 87, Issue 419 https://doi.org/10.1080/01621459.1992.10475289	journal	September 1992
The Multiple-Try Method and Local Optimization in Metropolis Sampling Liu, Jun S.; Liang, Faming; Wong, Wing Hung Journal of the American Statistical Association, Vol. 95, Issue 449 https://doi.org/10.1080/01621459.2000.10473908	journal	March 2000
Automated Redistricting Simulation Using Markov Chain Monte Carlo Fifield, Benjamin; Higgins, , Michael; Imai, Kosuke Journal of Computational and Graphical Statistics, Vol. 29, Issue 4 https://doi.org/10.1080/10618600.2020.1739532	journal	May 2020
The Essential Role of Empirical Validation in Legislative Redistricting Simulation Fifield, Benjamin; Imai, Kosuke; Kawahara, Jun Statistics and Public Policy, Vol. 7, Issue 1 https://doi.org/10.1080/2330443X.2020.1791773	journal	January 2020
Quantifying Gerrymandering in North Carolina Herschlag, Gregory; Kang, Han Sung; Luo, Justin Statistics and Public Policy, Vol. 7, Issue 1 https://doi.org/10.1080/2330443X.2020.1796400	journal	January 2020
Monte Carlo sampling methods using Markov chains and their applications Hastings, W. K. Biometrika, Vol. 57, Issue 1 https://doi.org/10.1093/biomet/57.1.97	journal	April 1970
Nonuniversal critical dynamics in Monte Carlo simulations Swendsen, Robert H.; Wang, Jian-Sheng Physical Review Letters, Vol. 58, Issue 2 https://doi.org/10.1103/PhysRevLett.58.86	journal	January 1987
Efficient, Multiple-Range Random Walk Algorithm to Calculate the Density of States Wang, Fugao; Landau, D. P. Physical Review Letters, Vol. 86, Issue 10 https://doi.org/10.1103/PhysRevLett.86.2050	journal	March 2001
Parallel Hybrid Metaheuristics with Distributed Intensification and Diversification for Large-scale Optimization in Big Data Statistical Analysis Cho, Wendy K. Tam; Liu, Yan Y. 2019 IEEE International Conference on Big Data (Big Data) https://doi.org/10.1109/BigData47090.2019.9006045	conference	December 2019
The p -Regions Problem. p-区域问题: The p -Regions Problem Duque, Juan C.; Church, Richard L.; Middleton, Richard S. Geographical Analysis, Vol. 43, Issue 1 https://doi.org/10.1111/j.1538-4632.2010.00810.x	journal	January 2011
Stochastic Approximation in Monte Carlo Computation Liang, Faming; Liu, Chuanhai; Carroll, Raymond J. Journal of the American Statistical Association, Vol. 102, Issue 477 https://doi.org/10.1198/016214506000001202	journal	March 2007
Equi-energy sampler with applications in statistical inference and statistical mechanics Kou, S. C.; Zhou, Qing; Wong, Wing Hung The Annals of Statistics, Vol. 34, Issue 4 https://doi.org/10.1214/009053606000000515	journal	August 2006
Inference from Iterative Simulation Using Multiple Sequences Gelman, Andrew; Rubin, Donald B. Statistical Science, Vol. 7, Issue 4 https://doi.org/10.1214/ss/1177011136	journal	November 1992
Hit-and-Run Algorithms for Generating Multivariate Distributions Bélisle, Claude J. P.; Romeijn, H. Edwin; Smith, Robert L. Mathematics of Operations Research, Vol. 18, Issue 2 https://doi.org/10.1287/moor.18.2.255	journal	May 1993
Adaptive Direction Sampling Gilks, W. R.; Roberts, G. O.; George, E. I. The Statistician, Vol. 43, Issue 1 https://doi.org/10.2307/2348942	journal	January 1994

Similar Records

A spatially explicit evolutionary algorithm for the spatial partitioning problem

Journal Article · Fri May 01 00:00:00 EDT 2020 · Applied Soft Computing · OSTI ID:1606958

Metis: A Pure Metropolis Markov Chain Monte Carlo Bayesian Inference Library

Technical Report · Mon Jan 08 23:00:00 EST 2018 · OSTI ID:1417145

Accelerating Markov Chain Monte Carlo sampling with diffusion models

Journal Article · Tue Dec 12 19:00:00 EST 2023 · Computer Physics Communications · OSTI ID:2281802

Related Subjects

97 MATHEMATICS AND COMPUTING
Evolutionary Algorithms
Markov Chain Monte Carlo
Spatial Partitioning

A parallel evolutionary multiple-try metropolis Markov chain Monte Carlo algorithm for sampling spatial partitions

Citation Formats

References (30)

Similar Records

Related Subjects