Large deviations for Dirichlet processes and Poisson-Dirichlet distributions with two parameters

Abstract

Large deviation principles are established for the two-parameter Poisson-Dirichlet distribution and two-parameter Dirichlet process when parameter \(\theta\) approaches infinity. The motivation for these results is to understand the differences in terms of large deviations between the two-parameter models and their one-parameter counterparts. New insight is obtained about the role of the second parameter \(\alpha\) through a comparison with the corresponding results for the one-parameter Poisson-Dirichlet distribution and Dirichlet process.