Diffusive Nested Sampling

We introduce a general Monte Carlo method based on Nested Sampling (NS), for sampling complex probability distributions and estimating the normalising constant. The method uses one or more particles, which explore a mixture of nested probability distributions, each successive distribution occupying ~e^-1 times the enclosed prior mass of the previous distribution. While NS technically requires independent generation of particles, Markov Chain Monte Carlo (MCMC) exploration fits naturally into this technique. We illustrate the new method on a test problem and find that it can achieve four times the accuracy of classic MCMC-based Nested Sampling, for the same computational effort; equivalent to a factor of 16 speedup. An additional benefit is that more samples and a more accurate evidence value can be obtained simply by continuing the run for longer, as in standard MCMC.Comment: Accepted for publication in Statistics and Computing. C++ code available at http://lindor.physics.ucsb.edu/DNes

Accuracy and transferability of Gaussian approximation potential models for tungsten

We introduce interatomic potentials for tungsten in the bcc crystal phase and its defects within the Gaussian approximation potential framework, fitted to a database of first-principles density functional theory calculations. We investigate the performance of a sequence of models based on databases of increasing coverage in configuration space and showcase our strategy of choosing representative small unit cells to train models that predict properties observable only using thousands of atoms. The most comprehensive model is then used to calculate properties of the screw dislocation, including its structure, the Peierls barrier and the energetics of the vacancy-dislocation interaction. All software and raw data are available at www.libatoms.org