# Kernel based Dirichlet sequences

@inproceedings{Berti2021KernelBD, title={Kernel based Dirichlet sequences}, author={Patrizia Berti and Emanuela Dreassi and Fabrizio Leisen and Luca Pratelli and Pietro Rigo}, year={2021} }

. Let X = ( X 1 ,X 2 ,... ) be a sequence of random variables with values in a standard space ( S, B ). Suppose X 1 ∼ ν and P (cid:0) X n +1 ∈ · | X 1 ,...,X n (cid:1) = θν ( · ) + P ni =1 K ( X i )( · ) n + θ a.s. where θ > 0 is a constant, ν a probability measure on B , and K a random probability measure on B . Then, X is exchangeable whenever K is a regular conditional distribution for ν given any sub- σ -ﬁeld of B . Under this assumption, X enjoys all the main properties of classical…

## One Citation

A Central Limit Theorem for Predictive Distributions

- MathematicsMathematics
- 2021

Let S be a Borel subset of a Polish space and F the set of bounded Borel functions f:S→R. Let an(·)=P(Xn+1∈·∣X1,…,Xn) be the n-th predictive distribution corresponding to a sequence (Xn) of S-valued…

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