Random Probability Measures via Dependent Stick-Breaking Priors

I will present a general class of stick-breaking processes with either exchangeable or Markovian length variables. This class generalizes well-known Bayesian nonparametric priors in an unexplored direction. An appealing feature of such a new family of nonparametric priors is that we are able to modulate the stochastic ordering of the weights and recover Dirichlet and Geometric priors as extreme cases.  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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About Ramsés H. Mena

Ramsés H. Mena is an Actuary from the Universidad Nacional Autónoma de México (UNAM) and holds a MSc. degree in Mathematical Sciences from the same university. He obtained his PhD in Statistics from the University of Bath in the UK in December 2003. Soon after he joined the Research Institute for Applied Mathematics and Systems (IIMAS) at UNAM, where he is currently a Professor in Statistics and serves as its Director since 2020. His research topics are in Bayesian Statistics, applied Stochastic Processes, Simulation and other disciplines that interact with these. Prof. Mena has over 70 publications, has supervised students at all levels, and has push forward collaboration agreements and initiatives aimed at young researchers and student exchange between UNAM and other institutions. He was President of the Mexican Statistical Association and, in 2022 an Elected Fellow of the International Society for Bayesian Analysis (ISBA), where he was also co-founder of the Non-parametric Bayesian Statistics Section and has served as Scientific Program Chair, among various other roles. His scientific work has been awarded by UNAM, the Fulbright García Robles Foundation, the International Centre for Economical Research and with positions such as the Global Chair Visiting Professor awarded by the University of Bath.