Speeding up Algebraic-Based Sampling via Permutations

Algebraic sampling methods are a powerful tool to perform hypothesis tests on conditional spaces. We analyse the link of the sampling method introduced in[6] with permutation tests and we exploit this link to build a two-step sampling procedure to perform two-sample comparisons for non-negative discrete exponential families. We thus establish a link between standard permutation and algebraic-statistics-based sampling. The proposed method reduces the dimension of the space on which the MCMC sampling is performed by introducing a second step in which a standard Monte Carlo sampling is performed. The advantages of this dimension reduction are verified through a simulation study, showing that the proposed approach grants convergence in the least time and has the lowest mean squared error.