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