2009/02/03 by C. D. Graham, Carl Graham, Graham, Carl
Computer Science · Materials Science · Mathematics · #60B10 #60G09 #60K35 #62B05 #Bayesian Methods and Mixture Models #Crystallization and Solubility Studies #FOS: Mathematics #Probability (math.PR) #Statistical Distribution Estimation and Applications #math.PR #msc:60B10 #msc:60G09 #msc:60K35 #msc:62B05
paper · pdf · doi:10.48550/arxiv.0902.0539
arxiv created 2009/02/03 · openalex publication_date 2009/02/03 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Multi-class systems having possibly both finite and infinite classes are investigated under a natural partial exchangeability assumption. It is proved that the conditional law of such a system, given the vector of the empirical measures of its finite classes and directing measures of its infinite ones (given by the de Finetti Theorem), corresponds to sampling independently from each class, without replacement from the finite classes and i.i.d. from the directing measure for the infinite ones. The equivalence between the convergence of multi-exchangeable systems with fixed class sizes and the convergence of the corresponding vectors of measures is then established.