NEO: Non Equilibrium Sampling on the Orbits of a Deterministic Transform

Sampling from a complex distribution \pi and approximating its intractable normalizing constant \mathrm{Z} are challenging problems. In this paper, a novel family of importance samplers (IS) and Markov chain Monte Carlo (MCMC) samplers is derived. Given an invertible map \mathrm{T}, these schemes combine (with weights) elements from the forward and backward Orbits through points sampled from a proposal distribution \rho . The map \mathrm{T} does not leave the target \pi invariant, hence the name NEO, standing for Non-Equilibrium Orbits. NEO-IS provides unbiased estimators of the normalizing constant and self-normalized IS estimators of expectations under \pi while NEO-MCMC combines multiple NEO-IS estimates of the normalizing constant and an iterated sampling-importance resampling mechanism to sample from \pi .