In this work, we introduce a novel class of adaptive Monte Carlo methods,called adaptive independent sticky MCMC algorithms, for efficient sampling froma generic target probability density function (pdf). The new class ofalgorithms employs adaptive non-parametric proposal densities which becomecloser and closer to the target as the number of iterations increases. Theproposal pdf is built using interpolation procedures based on a set of supportpoints which is constructed iteratively based on previously drawn samples. Thealgorithm's efficiency is ensured by a test that controls the evolution of theset of support points. This extra stage controls the computational cost and theconvergence of the proposal density to the target. Each part of the novelfamily of algorithms is discussed and several examples are provided. Althoughthe novel algorithms are presented for univariate target densities, we showthat they can be easily extended to the multivariate context within aGibbs-type sampler. The ergodicity is ensured and discussed. Exhaustivenumerical examples illustrate the efficiency of sticky schemes, both as astand-alone methods to sample from complicated one-dimensional pdfs and withinGibbs in order to draw from multi-dimensional target distributions.
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