Superposition Enhanced Nested Sampling

Use knowledge about the minima of the energy landscape obtained using global optimization techniques to improve sampling- Global optimization: Fast and powerful methods for exploring phase space. Can easily build up a database of local minima. The reason it can be so fast is that you abandon Bolzmann sampling (e.g. no detailed balance). This can be partially recovered using the harmonic superposition approximation (HSA), but this is valid only at low temperatures.- Exact SENS: Use Hamiltonian replica exchange to attempt swaps with the database of minima during the MCMC. 1. Generate a configuration XHSA randomly (and exactly) from the HSA 2. Accept a swap if E(XHSA) < EMAX and EHSA(X) < EMAX-Approximate SENS: Always accept the swap Nested Sampling reproduces the high temperature behaviour of the system and assigns the correct statistical weight to each basin. The database of minima guarantees that the basins associated with the lowest minima are visited even if the energy constraint is below the minimum energy path connecting two basins. Results The algorith