Efficient Monte Carlo sampling by parallel marginalization

Markov chain Monte Carlo sampling methods often suffer from long correlation times. Consequently, these methods must be run for many steps to generate an independent sample. In this paper a method is proposed to overcome this difficulty. The method utilizes information from rapidly equilibrating coarse Markov chains that sample marginal distributions of the full system. This is accomplished through exchanges between the full chain and the auxiliary coarse chains. Results of numerical tests on the bridge sampling and filtering/smoothing problems for a stochastic differential equation are presented.Comment: 7 figures, 2 figures, PNAS .cls and .sty files, submitted to PNA

Monte Carlo sampling and variance reduction techniques

Simulation

Neutron capture cross sections from surrogate reaction data and theory: connecting the pieces with a Markov-Chain Monte Carlo approach

The neutron capture cross section for $^{90}Zr(n, \gamma)$ has recently been determined using surrogate $^{92}Zr(p, d\gamma)$ data and nuclear reaction theory. That work employed an approximate fitting method based on Bayesian Monte Carlo sampling to determine parameters needed for calculating the $^{90}Zr(n, \gamma)$ cross section. Here, we improve the approach by introducing a more sophisticated Markov Chain Monte Carlo sampling method. We present preliminary results.Comment: Accepted into the proceedings of the 6th International Workshop on Compound-Nuclear Reactions and Related Topics, Berkeley, California, September 24-28, 2018. 4 pages, 1 figur