Stick-breaking processes with exchangeable length variables

2020/08/11 by Gil-Leyva, María F., Mena, Ramsés H. · 1 citation
#FOS: Computer and information sciences #FOS: Mathematics #Methodology (stat.ME) #Other Statistics (stat.OT) #Probability (math.PR) #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.2008.04475

Abstract

Our object of study is the general class of stick-breaking processes with exchangeable length variables. These generalize well-known Bayesian non-parametric priors in an unexplored direction. We give conditions to assure the respective species sampling process is proper and the corresponding prior has full support. For a rich sub-class we explain how, by tuning a single [0,1]-valued parameter, the stochastic ordering of the weights can be modulated, and Dirichlet and Geometric priors can be recovered. A general formula for the distribution of the latent allocation variables is derived and an MCMC algorithm is proposed for density estimation purposes.

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• Speeding up the ordered allocation sampler

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