Optimal Proposal Distributions and Adaptive MCMC

We review recent work concerning optimal proposal scalings for Metropolis-Hastings MCMC algorithms, and adaptive MCMC algorithms for trying to improve the algorithm on the y.

[1]  J. Rosenthal,et al.  On adaptive Markov chain Monte Carlo algorithms , 2005 .

[2]  R. Tweedie,et al.  Bounds on regeneration times and convergence rates for Markov chains fn1 fn1 Work supported in part , 1999 .

[3]  Galin L. Jones.  On the Markov chain central limit theorem , 2004, math/0409112.

[4]  J. Rosenthal,et al.  Coupling and Ergodicity of Adaptive Markov Chain Monte Carlo Algorithms , 2007, Journal of Applied Probability.

[5]  Jeffrey S. Rosenthal,et al.  Coupling and Ergodicity of Adaptive MCMC , 2007 .

[6]  Sokal,et al.  A general limitation on Monte Carlo algorithms of the Metropolis type. , 1994, Physical review letters.

[7]  Galin L. Jones,et al.  On the applicability of regenerative simulation in Markov chain Monte Carlo , 2002 .

[8]  Gareth O. Roberts,et al.  Examples of Adaptive MCMC , 2009 .

[9]  P. Giordani,et al.  Adaptive Independent Metropolis–Hastings by Fast Estimation of Mixtures of Normals , 2008, 0801.1864.

[10]  W. K. Yuen,et al.  Optimal scaling of random walk Metropolis algorithms with discontinuous target densities , 2012, 1210.5090.

[11]  G. Parisi,et al.  Simulated tempering: a new Monte Carlo scheme , 1992, hep-lat/9205018.

[12]  Yves F. Atchad'e.  A cautionary tale on the efficiency of some adaptive monte carlo schemes , 2009, 0901.1378.

[13]  H. Haario,et al.  An adaptive Metropolis algorithm , 2001 .

[14]  J. Sexton,et al.  Hamiltonian evolution for the hybrid Monte Carlo algorithm , 1992 .

[15]  Christophe Andrieu,et al.  A tutorial on adaptive MCMC , 2008, Stat. Comput..

[16]  C. Sherlock.  Methodology for inference on the Markov modulated Poisson process and theory for optimal scaling of the random walk Metropolis , 2006 .

[17]  J. Rosenthal,et al.  Optimal scaling for various Metropolis-Hastings algorithms , 2001 .

[18]  M. Pitt,et al.  Filtering via Simulation: Auxiliary Particle Filters , 1999 .

[19]  L. Tierney.  Markov Chains for Exploring Posterior Distributions , 1994 .

[20]  Jeffrey S. Rosenthal,et al.  AMCMC: An R interface for adaptive MCMC , 2007, Comput. Stat. Data Anal..

[21]  R. Tweedie,et al.  Exponential convergence of Langevin distributions and their discrete approximations , 1996 .

[22]  M. B'edard.  Weak convergence of Metropolis algorithms for non-i.i.d. target distributions , 2007, 0710.3684.

[23]  Galin L. Jones,et al.  Honest Exploration of Intractable Probability Distributions via Markov Chain Monte Carlo , 2001 .

[24]  Mikkel N. Schmidt.  Function factorization using warped Gaussian processes , 2009, ICML '09.

[25]  A. Horowitz.  A generalized guided Monte Carlo algorithm , 1991 .

[26]  A. Gelman,et al.  Adaptively Scaling the Metropolis Algorithm Using Expected Squared Jumped Distance , 2007 .

[27]  Chao Yang,et al.  Learn From Thy Neighbor: Parallel-Chain Adaptive MCMC , 2008 .

[28]  Sourendu Gupta,et al.  The acceptance probability in the hybrid Monte Carlo method , 1990 .

[29]  J. Rosenthal,et al.  General state space Markov chains and MCMC algorithms , 2004, math/0404033.

[30]  M. Bédard.  Optimal acceptance rates for Metropolis algorithms: Moving beyond 0.234 , 2008 .

[31]  Mylène Bédard.  Efficient Sampling Using Metropolis Algorithms: Applications of Optimal Scaling Results , 2008 .

[32]  Radford M. Neal.  An improved acceptance procedure for the hybrid Monte Carlo algorithm , 1992, hep-lat/9208011.

[33]  O. Cappé,et al.  Population Monte Carlo , 2004 .

[34]  A. Kennedy,et al.  Acceptances and autocorrelations in hybrid Monte Carlo , 1991 .

[35]  J. Rosenthal.  QUANTITATIVE CONVERGENCE RATES OF MARKOV CHAINS: A SIMPLE ACCOUNT , 2002 .

[36]  Anne-Mette K. Hein,et al.  BGX: a Bioconductor package for the Bayesian integrated analysis of Affymetrix GeneChips , 2007, BMC Bioinformatics.

[37]  Paul B. Mackenze.  An Improved Hybrid Monte Carlo Method , 1989 .

[38]  N. Metropolis,et al.  Equation of State Calculations by Fast Computing Machines , 1953, Resonance.

[39]  C. Andrieu,et al.  On the efficiency of adaptive MCMC algorithms , 2007 .

[40]  Y. Atchadé.  An Adaptive Version for the Metropolis Adjusted Langevin Algorithm with a Truncated Drift , 2006 .

[41]  Michael W Deem,et al.  Parallel tempering: theory, applications, and new perspectives. , 2005, Physical chemistry chemical physics : PCCP.

[42]  Scott S. Hampton,et al.  Shadow hybrid Monte Carlo: an efficient propagator in phase space of macromolecules , 2004 .

[43]  A. Kennedy,et al.  Cost of the Generalised Hybrid Monte Carlo Algorithm for Free Field Theory , 2000, hep-lat/0008020.

[44]  Heikki Haario,et al.  Componentwise adaptation for high dimensional MCMC , 2005, Comput. Stat..

[45]  Jun S. Liu,et al.  Multipoint metropolis method with application to hybrid Monte Carlo , 2001 .

[46]  Radford M. Neal.  Sampling from multimodal distributions using tempered transitions , 1996, Stat. Comput..

[47]  Antonietta Mira,et al.  Ordering and Improving the Performance of Monte Carlo Markov Chains , 2001 .

[48]  P. Moral,et al.  Sequential Monte Carlo samplers , 2002, cond-mat/0212648.

[49]  R. McLachlan,et al.  The accuracy of symplectic integrators , 1992 .

[50]  W. K. Hastings,et al.  Monte Carlo Sampling Methods Using Markov Chains and Their Applications , 1970 .

[51]  Radford M. Neal.  Annealed importance sampling , 1998, Stat. Comput..

[52]  B. Alder,et al.  Studies in Molecular Dynamics. I. General Method , 1959 .

[53]  Charles H. Bennett,et al.  Mass tensor molecular dynamics , 1975 .

[54]  Creutz.  Global Monte Carlo algorithms for many-fermion systems. , 1988, Physical review. D, Particles and fields.

[55]  A. Gelman,et al.  Weak convergence and optimal scaling of random walk Metropolis algorithms , 1997 .

[56]  J. Rosenthal.  Minorization Conditions and Convergence Rates for Markov Chain Monte Carlo , 1995 .

[57]  S. Duane,et al.  Hybrid Monte Carlo , 1987 .

[58]  Pal Rujan,et al.  Playing Billiards in Version Space , 1997, Neural Computation.

[59]  J. Rosenthal,et al.  Optimal scaling of discrete approximations to Langevin diffusions , 1998 .

[60]  Jeffrey S. Rosenthal,et al.  Optimal scaling of Metropolis algorithms: Heading toward general target distributions , 2008 .

[61]  C. Andrieu,et al.  On the ergodicity properties of some adaptive MCMC algorithms , 2006, math/0610317.

[62]  J. D. Doll,et al.  Brownian dynamics as smart Monte Carlo simulation , 1978 .

[63]  Creutz,et al.  Higher-order hybrid Monte Carlo algorithms. , 1989, Physical review letters.

[64]  Chao Yang,et al.  Learn From Thy Neighbor: Parallel-Chain and Regional Adaptive MCMC , 2009 .

[65]  J. Rosenthal,et al.  Department of , 1993 .