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

Onium salts as catalysts in the liquid-phase oxidation of cyclohexene or tetraline by N2O

The liquid-phase oxidation of cyclohexene or tetraline with N2O was studied in various solvents in the presence of onium salts or without them. The onium salts exerted significant promoting effect on the reactions. The activation of the oxidant was studied by IR spectroscopy. It was found that the interactions of the ions in the onium salts and the polarised N–O bond further enhanced polarisation leading to an activation of the oxidant, thus, increasing the rate of oxidation