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A novel strategy that combines a given collection of $\pi$-reversible Markovkernels is proposed. At each Markov transition, one of the available kernels isselected via a state-dependent probability distribution. In contrast torandom-scan type approaches that assume a constant (i.e. state-independent)selection probability distribution, the state-dependent distribution isspecified so as to privilege moving according to a kernel which is relevant forthe local topology of the target distribution. This approach leverages paths orother low dimensional manifolds that are typically present in noise vanishingdistributions. Some examples for which we show (theoretically or empirically)that a locally-weighted aggregation converges substantially faster and yieldssmaller asymptotic variances than an equivalent random-scan algorithm areprovided.

Markov Kernels Local Aggregation for Noise Vanishing Distribution Sampling