Extra Chance Hybrid Monte Carlo

We study a method (Extra Chance Generalized Hybrid Monte Carlo) to avoid rejections in the Hybrid Monte Carlo (HMC) method and related algorithms. In the spirit of delayed rejection, whenever a rejection would occur, extra work is done to find a fresh proposal that, hopefu lly, may be accepted. We present experiments that clearly indicate that the additional work per sample ca rried out in the extra chance approach clearly pays in terms of the quality of the samples generated.

[1]  P. Peskun,et al.  Optimum Monte-Carlo sampling using Markov chains , 1973 .

[2]  Jean-Paul Ryckaert,et al.  Molecular dynamics of liquid alkanes , 1978 .

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

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

[5]  Charles J. Geyer,et al.  Practical Markov Chain Monte Carlo , 1992 .

[6]  J. M. Sanz-Serna,et al.  Numerical Hamiltonian Problems , 1994 .

[7]  L. Tierney.  A note on Metropolis-Hastings kernels for general state spaces , 1998 .

[8]  L Tierney,et al.  Some adaptive monte carlo methods for Bayesian inference. , 1999, Statistics in medicine.

[9]  P. Green,et al.  Delayed rejection in reversible jump Metropolis–Hastings , 2001 .

[10]  A. Mira.  On Metropolis-Hastings algorithms with delayed rejection , 2001 .

[11]  T. Schlick.  Molecular modeling and simulation , 2002 .

[12]  B. Leimkuhler,et al.  Simulating Hamiltonian Dynamics , 2005 .

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

[14]  G. Stoltz,et al.  THEORETICAL AND NUMERICAL COMPARISON OF SOME SAMPLING METHODS FOR MOLECULAR DYNAMICS , 2007 .

[15]  Sebastian Reich,et al.  GSHMC: An efficient method for molecular simulation , 2008, J. Comput. Phys..

[16]  Nawaf Bou-Rabee,et al.  A comparison of generalized hybrid Monte Carlo methods with and without momentum flip , 2009, J. Comput. Phys..

[17]  J. M. Sanz-Serna,et al.  Optimal tuning of the hybrid Monte Carlo algorithm , 2010, 1001.4460.

[18]  T. Lelièvre,et al.  Free Energy Computations: A Mathematical Perspective , 2010 .

[19]  J. M. Sanz-Serna,et al.  Hybrid Monte Carlo on Hilbert spaces , 2011 .

[20]  Radford M. Neal.  MCMC Using Hamiltonian Dynamics , 2011, 1206.1901.

[21]  M. Girolami,et al.  Riemann manifold Langevin and Hamiltonian Monte Carlo methods , 2011, Journal of the Royal Statistical Society: Series B (Statistical Methodology).

[22]  Jason A. Wagoner,et al.  Reducing the effect of Metropolization on mixing times in molecular dynamics simulations. , 2012, The Journal of chemical physics.

[23]  J. M. Sanz-Serna,et al.  Compressible generalized hybrid Monte Carlo. , 2014, The Journal of chemical physics.

[24]  Jascha Sohl-Dickstein,et al.  Hamiltonian Monte Carlo Without Detailed Balance , 2014, ICML.

[25]  Jesús María Sanz-Serna,et al.  Numerical Integrators for the Hybrid Monte Carlo Method , 2014, SIAM J. Sci. Comput..

[26]  J. M. Sanz-Serna,et al.  Markov Chain Monte Carlo and Numerical Differential Equations , 2014 .

[27]  Andrew Gelman,et al.  The No-U-turn sampler: adaptively setting path lengths in Hamiltonian Monte Carlo , 2011, J. Mach. Learn. Res..

[28]  L. Einkemmer.  Structure preserving numerical methods for the Vlasov equation , 2016, 1604.02616.