A Gibbs sampler in a generalized sense

Abstract

We present, in the finite case, a generalization of the cyclic Gibbs sampler - the Gibbs sampler for short. The chain obtained we call the cyclic Gibbs sampler in a generalized sense - the Gibbs sampler in a generalized sense for short. The Gibbs sampler in a generalized sense belongs to our collection of hybrid Metropolis-Hastings chains from [U. Păun, A hybrid Metropolis-Hastings chain, "Rev. Roumaine Math. Pures Appl". 56 (2011), 207-228] and we conjecture that it is the fastest chain in this collection in a sense which will be specified in article. We then present the wavy probability distributions, a generalization of the wavy probability distribution(s) of first type from [U. Păun, $G$ method in action: from exact sampling to approximate one. Submitted]. We construct a Gibbs sampler in a generalized sense, a special one, for wavy probability distributions which is fast, attaining its stationarity in a finite number of steps, and, besides this, has other important properties $-$ the computation of certain important probabilities iteratively and, for wavy probability distributions having normalization constant, the computation of this constant.