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We introduce a powerful and flexible MCMC algorithm for stochastic simulation. The method builds on a pseudo-marginal method originally introduced in [Genetics 164 (2003) 1139–1160], showing how algorithms which are approximations to an idealized marginal algorithm, can share the same marginal stationary distribution as the idealized method. Theoretical… (More)

We investigate the use of adaptive MCMC algorithms to automatically tune the Markov chain parameters during a run. Examples include the Adaptive Metropolis (AM) multivariate algorithm of Haario et al. (2001), Metropolis-within-Gibbs algorithms for non-conjugate hierarchical models, regionally adjusted Metropolis algorithms, and logarithmic scalings.… (More)

We consider the optimal scaling problem for proposal distributions in Hastings-Metropolis algorithms derived from Langevin diffusions. We prove an asymptotic diffusion limit theorem and show that the relative efficiency of the algorithm can be characterised by its overall acceptance rate, independently of the target distribution. The asymptotically optimal… (More)

Weconsider basic ergodicity properties of adaptiveMarkov chainMonteCarlo algorithms under minimal assumptions, using coupling constructions. We prove convergence in distribution and a weak law of large numbers. We also give counterexamples to demonstrate that the assumptions we make are not redundant.

This paper surveys various results about Markov chains on general (non-countable) state spaces. It begins with an introduction to Markov chain Monte Carlo (MCMC) algorithms, which provide the motivation and context for the theory which follows. Then, sufficient conditions for geometric and uniform ergodicity are presented, along with quantitative bounds on… (More)

- Allan Borodin, Gareth O. Roberts, Jeffrey S. Rosenthal, Panayiotis Tsaparas
- ACM Trans. Internet Techn.
- 2005

The explosive growth and the widespread accessibility of the Web has led to a surge of research activity in the area of information retrieval on the World Wide Web. The seminal papers of Kleinberg [1998, 1999] and Brin and Page [1998] introduced <i>Link Analysis Ranking</i>, where hyperlink structures are used to determine the relative <i>authority</i> of a… (More)

Inference for Dirichlet process hierarchical models is typically performed using Markov chain Monte Carlo methods, which can be roughly categorized into marginal and conditional methods. The former integrate out analytically the infinite-dimensional component of the hierarchical model and sample from the marginal distribution of the remaining variables… (More)

Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at http://www.jstor.org/about/terms.html. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in… (More)

The objective of this paper is to present a novel methodology for likelihood-based inference for discretely observed diffusions. We propose Monte Carlo methods, which build on recent advances on the exact simulation of diffusions, for performing maximum likelihood and Bayesian estimation.

The major implementational problem for reversible jump Markov chain Monte Carlo methods is that there is commonly no natural way to choose jump proposals since there is no Euclidean structure in the parameter space to guide our choice. We consider mechanisms for guiding the choice of proposal. The first group of methods is based on an analysis of acceptance… (More)