Optimal scaling for various Metropolis-Hastings algorithms

By Gareth O. Roberts, Jeffrey S. Rosenthal. 2001

1,282 citations recorded by the source corpus.

Subfields: Condensed Matter Physics, Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/2d8294ef6bdf283e4b7f524f8f388ef744e539b3

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In Condensed Matter Physics

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Citations in the corpus

Optimal scaling of Metropolis algorithms: Heading toward general target distributions (2008, methodology): “Around the same time, Roberts and Rosenthal (2001) showed that for inhomogeneous target densities of the form π(x(d)) = Qd i=1 Ci f (Cixi), where Ci > 0 are chosen from some fixed distribution, the magic number 0.234 still holds.”
Bayesian computation: a perspective on the current state, and sampling backwards and forwards (2015, background): “It has been also combined with relative eﬃciency loss due to mismatch between the proposal and target co-variance matrices (see Roberts and Rosenthal (2001)).”
Optimal Proposal Distributions and Adaptive MCMC (2008, methodology): “Numerical studies (e.g. Gelman et al., 1996; Roberts and Rosenthal, 2001) indicate that the limiting results do seem to well approximate finite-dimensional situations for d as small as five.”
Inverse problems: A Bayesian perspective (2010, background): “…effect was first undertaken in Roberts, Gelman and Gilks (1997), where random walk proposals were studied for an i.i.d. target, and subsequently in Roberts and Rosenthal (1998, 2001), Beskos and Stuart (2009) and Beskos, Roberts and Stuart (2009) for other target distributions and proposals; see…”
Optimal Proposal Distributions and Adaptive MCMC (2011, background): “Numerical studies (e.g. Gelman et al., 1996; Roberts and Rosenthal, 2001) indicate that the limiting results do seem to well approximate finite-dimensional situations for d as small as five.”
General state space Markov chains and MCMC algorithms (2004, methodology): “Then it is proved in [70] (see also [74]) that as d → ∞, the process {Zd t }t≥0 converges weakly to a diffusion process {Zt}t≥0 which satisfies the following stochastic differential equation:”
Surrogate accelerated sampling of reservoir models with complex structures using sparse polynomial chaos expansion (2015, background): “Typically the first 1000 to 5000 samples are ignored and the convergence tests are used to examine whether the chain has converged [46].”
Differential Evolution Markov Chain with snooker updater and fewer chains (2008, methodology): “Keywords Evolutionary Monte Carlo · Metropolis algorithm · Adaptive Markov chain Monte Carlo · Theophylline kinetics · Adaptive direction sampling · Parallel computing · Differential evolution”
Coupling and Ergodicity of Adaptive Markov Chain Monte Carlo Algorithms (2007, background): “(Such a proposal is optimal in certain settings according to the results of Roberts et al. (1997); see also Roberts and Rosenthal (2001) and Bédard (2006).)”
Handbook of Item Response Theory Modeling : Applications to Typical Performance Assessment (2014, background): “Roberts and Rosenthal (2001) discussed the statistical efficiency of Metropolis-Hastings samplers, and its relationship to optimal scaling.”
On adaptive Markov chain Monte Carlo algorithms (2005, background): “Some theoretical and empirical results (Roberts et al. 1997; Roberts and Rosenthal 2001) have shown that in high-dimensional spaces, under various regularity conditions, it is optimal to choose a2 such that the asymptotic acceptance 1350-7265 ? 2005 ISI/BS”
RECONSTRUCTING PLANT ROOT AREA AND WATER UPTAKE PROFILES (2004, methodology): “…were generated from Q(·|·) in a single step, acceptance of parameters was determined individually (e.g., systematic sweep, Brooks, 1998) and their step sizes were chosen so that proposal values were accepted approximately 30 to 60% of the time (Roberts et al., 1997, Roberts & Rosenthal, 2001).”
Inversion of Surface Deformation Data for Rapid Estimates of Source Parameters and Uncertainties: A Bayesian Approach (2018, background): “The aim is to achieve, at the end of the inversion, an acceptance rate between 15% and 50% (e.g., Roberts & Rosenthal, 2001).”