Differential Evolution Markov Chain with snooker updater and fewer chains

By C. T. ter Braak, Jasper A. Vrugt. Statistics and computing, 2008

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Differential Evolution Markov Chain (DE-MC) is an adaptive MCMC algorithm, in which multiple chains are run in parallel. Standard DE-MC requires at least N=2d chains to be run in parallel, where d is the dimensionality of the posterior. This paper extends DE-MC with a snooker updater and shows by simulation and real examples that DE-MC can work for d up to 50–100 with fewer parallel chains (e.g.N=3) by exploiting information from their past by generating jumps from differences of pairs of past states. This approach extends the practical applicability of DE-MC and is shown to be about 5–26 times more efficient than the optimal Normal random walk Metropolis sampler for the 97.5% point of a variable from a 25–50 dimensional Student t3 distribution. In a nonlinear mixed effects model example the approach outperformed a block-updater geared to the specific features of the model.

Subfields: Mathematical Physics, Molecular Biology, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/608746634545c17109bbdf7153278629d053bc6a

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Citations in the corpus

Accelerating Markov Chain Monte Carlo Simulation by Differential Evolution with Self-Adaptive Randomized Subspace Sampling (2009, background): “Proof: The proof consists of three parts and follows [31,32].”
A SYSTEMATIC RETRIEVAL ANALYSIS OF SECONDARY ECLIPSE SPECTRA. I. A COMPARISON OF ATMOSPHERIC RETRIEVAL TECHNIQUES (2013, methodology): “Rather than standard MCMC approaches, we use an adaptive algorithm known as differential evolution Markov chain Monte Carlo (DEMC) (ter Braak 2006; ter Braak & Vrugt 2008).”
A formal likelihood function for parameter and predictive inference of hydrologic models with correlated, heteroscedastic, and non‐Gaussian errors (2010, methodology): “Finally, DREAM‐ZS contains a snooker update to generate jumps beyond parallel direction updates [ter Braak and Vrugt, 2008] and increase diversity of candidate points.”
Corruption of accuracy and efficiency of Markov chain Monte Carlo simulation by inaccurate numerical implementation of conceptual hydrologic models (2010, methodology): “A popular example is the method proposed by Strang [1968] , which, applied to equations (1) and (6), advances Sr,t0 to Sr,t in five consecutive steps:”
SPITZER PHASE CURVE CONSTRAINTS FOR WASP-43b AT 3.6 AND 4.5 μm (2016, methodology): “We estimate parameter uncertainties using a DifferentialEvolution Markov Chain algorithm (DEMC, ter Braak & Vrugt 2008).”
Inferring probabilistic stellar rotation periods using Gaussian processes (2017, background): “The other two proposals are a ‘differential evolution (DE) MCMC’ proposal (Ter Braak 2006; Nelson, Ford & Payne 2014) and the ‘snooker’ extension of DE (ter Braak & Vrugt 2008).”
Parameter Analysis and Estimates for the MODIS Evapotranspiration Algorithm and Multiscale Verification (2019, methodology): “Alternatively, the differential‐evolution Markov chain (DE‐MC) method (Ter Braak, 2006; Ter Braak & Vrugt, 2008) combines a genetic algorithm (Storn & Price, 1997) with the MCMC method.”
Confronting uncertainty in model-based geostatistics using Markov Chain Monte Carlo simulation (2011, methodology): “This scheme is an adaptation of the DE-MC (Differential Evolution Markov Chain, Ter Braak, 2006; Ter Braak and Vrugt, 2008) and SCEM-UA (Shuffled Complex Evolutionary Metropolis) algorithms (Vrugt et al., 2003) and produces a Markov Chain that is ergodic with a unique stationary distribution, the pr”
High‐dimensional posterior exploration of hydrologic models using multiple‐try DREAM(ZS) and high‐performance computing (2012, methodology): “For instance, one could use the ideas of Tonkin and Doherty [2005] and significantly reduce the dimensionality of the search space by reparameterizing the original inverse problem using super and base parameters derived from principal component analysis.”