Markov Kernels Local Aggregation for Noise Vanishing Distribution Sampling

A novel strategy that combines a given collection of -reversible Markov kernels is proposed. At each transition, one the available selected via state-dependent probability distribution. In contrast to random-scan type approaches assume constant (i.e., state-independent) selection distribution, distribution specified so as privilege moving according kernel which relevant for local geometry target This approach leverages paths or other low-dimensional manifolds are typically present in noise vanishing distributions. Some examples we show (theoretically empirically) locally weighted aggregation converges substantially faster and yields smaller asymptotic variances than an equivalent algorithm provided.