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Exact and approximate sum representations for the Dirichlet process
Author(s) -
Ishwaran Hemant,
Zarepour Mahmoud
Publication year - 2002
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3315951
Subject(s) - dirichlet process , hierarchical dirichlet process , dirichlet distribution , latent dirichlet allocation , mathematics , representation (politics) , context (archaeology) , bayesian probability , metric (unit) , measure (data warehouse) , process (computing) , generalized dirichlet distribution , dirichlet's energy , computer science , statistics , topic model , mathematical analysis , artificial intelligence , data mining , geography , operations management , law , boundary value problem , archaeology , operating system , political science , politics , economics
The Dirichlet process can be regarded as a random probability measure for which the authors examine various sum representations. They consider in particular the gamma process construction of Ferguson (1973) and the “stick‐breaking” construction of Sethuraman (1994). They propose a Dirichlet finite sum representation that strongly approximates the Dirichlet process. They assess the accuracy of this approximation and characterize the posterior that this new prior leads to in the context of Bayesian nonpara‐metric hierarchical models.