
A radial version of the Central Limit Theorem
In this note, we give a probabilistic interpretation of the Central Limi...
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Projective Limit Random Probabilities on Polish Spaces
A pivotal problem in Bayesian nonparametrics is the construction of prio...
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Stickbreaking PitmanYor processes given the species sampling size
Random discrete distributions, say F, known as species sampling models, ...
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On a Rapid Simulation of the Dirichlet Process
We describe a simple and efficient procedure for approximating the Lévy ...
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Enriched PitmanYor processes
In Bayesian nonparametrics there exists a rich variety of discrete prior...
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On Limit Constants in Last Passage Percolation in Transitive Tournaments
We investigate the last passage percolation problem on transitive tourna...
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Limit theorems for invariant distributions
We consider random processes whose distribution satisfies a symmetry pro...
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Functional central limit theorems for stickbreaking priors
We obtain the empirical strong law of large numbers, empirical GlivenkoCantelli theorem, central limit theorem, functional central limit theorem for various nonparametric Bayesian priors which include the Dirichlet process with general stickbreaking weights, the PoissonDirichlet process, the normalized inverse Gaussian process, the normalized generalized gamma process, and the generalized Dirichlet process. For the Dirichlet process with general stickbreaking weights, we introduce two general conditions such that the central limit theorem and functional central limit theorem hold. Except in the case of the generalized Dirichlet process, since the finite dimensional distributions of these processes are either hard to obtain or are complicated to use even they are available, we use the method of moments to obtain the convergence results. For the generalized Dirichlet process we use its finite dimensional marginal distributions to obtain the asymptotics although the computations are highly technical.
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