Normal Kernel Coupler: An Adaptive Markov Chain Monte Carlo Method for Efficiently Sampling From Multi-Modal Distributions

摘要

The Normal Kernel Coupler (NKC) is an adaptive Markov Chain Monte Carlo (MCMC) method which maintains a set of current state vectors. At each iteration one state vector is updated using a density estimate formed by applying a normal kernel to the full set of states. This sampler is ergodic (irreducible, Harris recurrent and aperiodic) for any continuous distribution on d-dimensioual Euclidean space. The NKC outperforms standard MCMC methods on a variety of unimodal and bimodal problems in low to moderate dimension. We illustrate the utility of the NKC by fitting a mixture model for genetic instability in cancer cells. This model which has two distinct and dissimilar modes is not well handled by standard MCMC methods. In contrast, the NKC efficiently samples from this model and yields results that are consistent with current scientific understanding.