756 citations · 1.5k across the 42 of their papers we have counts for
17 papers · 1 filter
Efficiency of reversible MCMC methods: elementary derivations and applications to composite methods
Radford M. Neal, Jeffrey S. Rosenthal
We review criteria for comparing the efficiency of Markov chain Monte Carlo (MCMC) methods with respect to the asymptotic variance of estimates of expectations of functions of stat…
Optimal Strategies and Rules for the Game of Horse
Daniel Rosenthal, Jeffrey S. Rosenthal
We investigate the probability of scoring a point when playing the basketball shooting game called "Horse". We show that under the Traditional Rules, it is optimal to choose very e…
Convergence Rates of Attractive-Repulsive MCMC Algorithms
Yu Hang Jiang, Tong Liu, Zhiya Lou +4
We consider MCMC algorithms for certain particle systems which include both attractive and repulsive forces, making their convergence analysis challenging. We prove that a version…
Skew Brownian Motion and Complexity of the ALPS Algorithm
Gareth O. Roberts, Jeffrey S. Rosenthal, Nicholas G. Tawn
Simulated tempering is a popular method of allowing MCMC algorithms to move between modes of a multimodal target density π. The paper [24] introduced the Annealed Leap-Point Sample…
Approximations of Geometrically Ergodic Reversible Markov Chains
Jeffrey Negrea, Jeffrey S. Rosenthal
A common tool in the practice of Markov Chain Monte Carlo is to use approximating transition kernels to speed up computation when the desired kernel is slow to evaluate or intracta…
MEXIT: Maximal un-coupling times for stochastic processes
P. A. Ernst, W. S. Kendall, G. O. Roberts +1
Classical coupling constructions arrange for copies of the \emph{same} Markov process started at two \emph{different} initial states to become equal as soon as possible. In this pa…
Hitting Time and Convergence Rate Bounds for Symmetric Langevin Diffusions
Gareth O. Roberts, Jeffrey S. Rosenthal
We provide quantitative bounds on the convergence to stationarity of real-valued Langevin diffusions with symmetric target densities.
Complexity Bounds for MCMC via Diffusion Limits
Gareth O. Roberts, Jeffrey S. Rosenthal
We connect known results about diffusion limits of Markov chain Monte Carlo (MCMC) algorithms to the Computer Science notion of algorithm complexity. Our main result states that an…
Stability of adversarial Markov chains, with an application to adaptive MCMC algorithms
Radu V. Craiu, Lawrence Gray, Krzysztof Łatuszyński +3
We consider whether ergodic Markov chains with bounded step size remain bounded in probability when their transitions are modified by an adversary on a bounded subset. We provide c…
Minimising MCMC variance via diffusion limits, with an application to simulated tempering
Gareth O. Roberts, Jeffrey S. Rosenthal
We derive new results comparing the asymptotic variance of diffusions by writing them as appropriate limits of discrete-time birth-death chains which themselves satisfy Peskun orde…
Variance bounding Markov chains
Gareth O. Roberts, Jeffrey S. Rosenthal
We introduce a new property of Markov chains, called variance bounding. We prove that, for reversible chains at least, variance bounding is weaker than, but closely related to, geo…
Harris recurrence of Metropolis-within-Gibbs and trans-dimensional Markov chains
Gareth O. Roberts, Jeffrey S. Rosenthal
A -irreducible and aperiodic Markov chain with stationary probability distribution will converge to its stationary distribution from almost all starting points. The property of…
Quantitative bounds on convergence of time-inhomogeneous Markov chains
R. Douc, E. Moulines, Jeffrey S. Rosenthal
Convergence rates of Markov chains have been widely studied in recent years. In particular, quantitative bounds on convergence rates have been studied in various forms by Meyn and…
Moment conditions for a sequence with negative drift to be uniformly bounded in L^r
Robin Pemantle, Jeffrey S. Rosenthal
Suppose a sequence of random variables {X_n} has negative drift when above a certain threshold and has increments bounded in L^p. When p>2 this implies that EX_n is bounded above b…
General state space Markov chains and MCMC algorithms
Gareth O. Roberts, Jeffrey S. Rosenthal
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…
Extension of Fill's perfect rejection sampling algorithm to general chains (Extended abstract)
James Allen Fill, Motoya Machida, Duncan J. Murdoch +1
We provide an extension of the perfect sampling algorithm of Fill (1998) to general chains, and describe how use of bounding processes can ease computational burden. Along the way,…
Extension of Fill's perfect rejection sampling algorithm to general chains
James Allen Fill, Motoya Machida, Duncan J. Murdoch +1
By developing and applying a broad framework for rejection sampling using auxiliary randomness, we provide an extension of the perfect sampling algorithm of Fill (1998) to general…