Weak convergence and optimal scaling of random walk Metropolis algorithms

By Gareth O. Roberts, Andrew Gelman, Walter R. Gilks. 1997

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Citations in the corpus

Kernel Sequential Monte Carlo (2015, methodology): “Experimental details. We use v= 100 and b= 0:1 and compare SMC algorithms using different rejuvenation MH steps: a static Random Walk Metropolis move (RWSMC) with the asymptotically optimal scaling, (Roberts et al., 1997), = 2:38= p d, ASMC, and KASMC using a Gaussian RBF kernel. For the latter two ”
Handbook of Markov Chain Monte Carlo (2011, positive): “The same optimal 23% acceptance rate for random-walk Metropolis was previously obtained using a more formal analysis by Roberts et al. (1997).”
On the flexibility of the design of multiple try Metropolis schemes (2012, methodology): “p(y)A(xjy) is satised. 3 However, it is important to remark that high acceptance rates are not a suitable indicator of good performance since, in general, the best acceptance rate is dierent from 1 [27]. On the exibility of the design of Multiple Try Metropolis schemes 13 5.2 Independent proposal pd”
Characterization of uncertainties in atmospheric trace gas inversions using hierarchical Bayesian methods (2013, background): “(15) The sizes of the proposal distributions were adjusted so that the resulting acceptance ratio for each parameter was between 0.25 and 0.5 to achieve optimal mixing (Roberts et al., 1997).”
The BUGS project: Evolution, critique and future directions (2009, background): “These limits are fairly arbitrary but are based loosely on formal analysis [46].”
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).)”
A New Algorithm for Simulating a Correlation Matrix Based on Parameter Expansion and Reparameterization (2006, methodology): “We chose τ = 1.5 for the first three blocks and τ = 2.0 for the fourth block such that the acceptance rate (a percentage of times a move to a new point is made) was equal to 0.21 (Roberts, Gelman, and Gilks 1997; Roberts and Rosenthal 2001).”
Stacking for Non-mixing Bayesian Computations: The Curse and Blessing of Multimodal Posteriors (2020, methodology): “That ensures rapid mixing for random-walk Metropolis, scaling as O ( d ) (Roberts et al., 1997; Cotter et al., 2013; Dwivedi et al., 2019), and Hamiltonian Monte Carlo, scaling as O ( d 1 / 4 ) (Beskos et al., 2013; Bou-Rabee et al., 2020; Mangoubi and Smith, 2017, 2019).”
Modeling, Inference and Optimization With Composable Differentiable Procedures (2016, unknown): “234 [89], optimized for each algorithm separately.”
MCMC Using Hamiltonian Dynamics (2011, result): “ Numerical calculation shows that the minimum is when µ = 0.41 and a(µ) = 0.65. The same optimal 23% acceptance rate for random-walk Metropolis was previously obtained using a more formal analysis by Roberts et al. (1997). The optimal 65% acceptance rate for HMC that I derive above is consistent wit”
Spatial Modeling With Spatially Varying Coefficient Processes (2003, unknown): “An alternative to componentwise updating is to introduce blockedMetropolisupdating througha Langevindiffusion (see, e.g., Roberts, Gelman, and Gilks 1997; Christensen, Möller, and Waagepetersen 2000).”