Efficient sampling on the simplex with a self-adjusting logit transform proposal

A vector of k positive coordinates lies in the k-dimensional simplex when the sum of all coordinates in the vector is constrained to equal 1. Sampling distributions efficiently on the simplex can be difficult because of this constraint. This paper introduces a transformed logit-scale proposal for Markov Chain Monte Carlo that naturally adjusts step size based on the position in the simplex. This enables efficient sampling on the simplex even when the simplex is high dimensional and/or includes coordinates of differing orders of magnitude. Implementation of this method is shown with the SALTSampler R package and comparisons are made to other simpler sampling schemes to illustrate the improvement in performance this method provides. A simulation of a typical calibration problem also demonstrates the utility of this method.