Ben Calderhead (Imperial College London): Parallel Monte Carlo with a Single Markov Chain

A major limitation of many MCMC methods is their inherently sequential nature.  We propose a natural extension to the Metropolis Hastings algorithm that allows for parallelising a single chain using existing MCMC samplers, while maintaining convergence to the correct stationary distribution.  Our approach is generally applicable and straightforward to implement.  We demonstrate how this construction may be used to greatly increase the computational speed via parallelisation of a wide variety of existing MCMC methods, including Metropolis-Adjusted Langevin Algorithms and Adaptive MCMC.  Furthermore we show how it allows for a principled way of utilising every integration step within Hamiltonian based MCMC methods, resulting in increased accuracy of Monte Carlo estimates with minimal extra computational cost.