Collective proposal distributions for nonlinear MCMC samplers: Mean-field theory and fast implementation

Over the last decades, various “non-linear” MCMC methods have arisen. While appealing for their convergence speed and efficiency, practical implementation theoretical study remain challenging. In this paper, we introduce a non-linear generalization of Metropolis-Hastings algorithm to proposal that depends not only on current state, but also its law. We propose simulate dynamics as mean field limit system interacting particles, can in turn itself be understood generalisation population particles. Under double number iterations particles prove converges. Then, an efficient GPU illustrate performance examples. The method is particularly stable multimodal examples converges faster than classical methods.