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Weak convergence and optimal scaling of random walk Metropolis algorithms
This paper considers the problem of scaling the proposal distribution of a multidimensional random walk Metropolis algorithm in order to maximize the efficiency of the algorithm. The main result is a…
Optimal scaling for various Metropolis-Hastings algorithms
The pseudo-marginal approach for efficient Monte Carlo computations
A powerful and flexible MCMC algorithm for stochastic simulation that builds on a pseudo-marginal method, showing how algorithms which are approximations to an idealized marginal algorithm, can share the same marginal stationary distribution as the idealized method.
Examples of Adaptive MCMC
Computer simulations indicate that the use of adaptive MCMC algorithms to automatically tune the Markov chain parameters during a run perform very well compared to nonadaptive algorithms, even in high dimension.
Exponential convergence of Langevin distributions and their discrete approximations
In this paper we consider a continuous-time method of approximating a given distribution using the Langevin diusion dLtdWt 1 2 r log (Lt)dt. We ®nd conditions under this diusion converges…
Optimal scaling of discrete approximations to Langevin diffusions
An asymptotic diffusion limit theorem is proved and it is shown that, as a function of dimension n, the complexity of the algorithm is O(n1/3), which compares favourably with the O- complexity of random walk Metropolis algorithms.
Bayesian computation via the gibbs sampler and related markov chain monte carlo methods (with discus
The use of the Gibbs sampler for Bayesian computation is reviewed and illustrated in the context of some canonical examples. Other Markov chain Monte Carlo simulation methods are also briefly…
General state space Markov chains and MCMC algorithms
This paper surveys various results about Markov chains on gen- eral (non-countable) state spaces. It begins with an introduction to Markov chain Monte Carlo (MCMC) algorithms, which provide the…
MCMC Methods for Functions: ModifyingOld Algorithms to Make Them Faster
An approach to modifying a whole range of MCMC methods, applicable whenever the target measure has density with respect to a Gaussian process or Gaussian random field reference measure, which ensures that their speed of convergence is robust under mesh refinement.
Coupling and Ergodicity of Adaptive Markov Chain Monte Carlo Algorithms
We consider basic ergodicity properties of adaptive Markov chain Monte Carlo algorithms under minimal assumptions, using coupling constructions. We prove convergence in distribution and a weak law of…