Scaling limits for the transient phase of local Metropolis–Hastings algorithms

By Ole F. Christensen, Gareth O. Roberts, Jeffrey S. Rosenthal. 2005

110 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/0717ecc20a5a0956693202abd98ffd8c6224103f

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Citations in the corpus

Optimal Scaling and Diffusion Limits for the Langevin Algorithm in High Dimensions (2011, background): “product case, it is known that if the Markov chain is started “far” from stationarity, a fluid limit (ODE) is observed [11].”
Bayesian computation: a summary of the current state, and samples backwards and forwards (2015, background): “Further extensions include studying the transient phase before reaching stationarity (Christensen et al. 2005; Jour-dain et al. 2012, 2014), the scaling of multiple-try MCMC (Bédard et al. 2012) and delayed rejection MCMC (Bédard et al. 2014), and the temperature scale of parallel tempering type…”
Optimal tuning of the hybrid Monte Carlo algorithm (2010, unknown): “It is possible that different scaling analyses will be needed to study the burn-in phase of the algorithm, as for the study of random-walk type algorithms in [13].”
General state space Markov chains and MCMC algorithms (2004, background): “if the assumption X0 ∼ π(·) is violated and the chain instead begins way out in the tails of π(·); see [16].”
Bayesian Inference and Model Assessment for Spatial Point Patterns Using Posterior Predictive Samples (2017, methodology): “(1998) and Christensen et al. (2005). Girolami and Calderhead (2011) provide some extensions, including Hamiltonian Monte Carlo methods, which require less tuning.”
Bayesian computation: a perspective on the current state, and sampling backwards and forwards (2015, background): “Further extensions include the transient phase before reaching stationarity (Christensen et al. (2005); Jourdain et al. (2012, 2014)), scaling of multiple-try MCMC (B´edard et al. (2012)), delayed rejection MCMC (B´edard et al. (2014)), and temperature scale of parallel tempering type algorithms…”
Riemannian Manifold Hamiltonian Monte Carlo (2009, methodology): “Finally, in Sections 4 and 5, this new methodology is demonstrated on a number of interesting statistical problems, i.e. Bayesian logistic regression, stochastic volatility modeling, log-Gaussian Cox point processes, and parameterinference in dynamical systems.”
Weak convergence of Metropolis algorithms for non-i.i.d. target distributions (2007, background): “Optimal scaling issues have been explored by other authors, namely [15], [7], [6], [8] and [13].”
Optimal scaling of Metropolis algorithms: Heading toward general target distributions (2008, methodology): “Christensen, Roberts, and Rosenthal (2003) studied high-dimensional Metropolis algorithms in their initial transient phase.”
MCMC for Variationally Sparse Gaussian Processes (2015, methodology): “For a fixed θ, sampling v is relatively straightforward, and this can be done efficiently using HMC [12, 26, 27] or Elliptical Slice Sampling [28].”