Large deviation principles for the Ewens-Pitman sampling model

2014/06/28 by Stefano Favaro, Favaro, Stefano, Shui Feng +1 · 1 citation
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #FOS: Mathematics #Probability (math.PR) #Statistical Methods and Inference #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1406.7382

openalex publication_date 2014/06/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let M_l,n be the number of blocks with frequency l in the exchangeable random partition induced by a sample of size n from the Ewens-Pitman sampling model. We show that, as n tends to infinity, n^-1M_l,n satisfies a large deviation principle and we characterize the corresponding rate function. A conditional counterpart of this large deviation principle is also presented. Specifically, given an initial sample of size n from the Ewens-Pitman sampling model, we consider an additional sample of size m. For any fixed n and as m tends to infinity, we establish a large deviation principle for the conditional number of blocks with frequency l in the enlarged sample, given the initial sample. Interestingly, the conditional and unconditional large deviation principles coincide, namely there is no long lasting impact of the given initial sample. Potential applications of our results are discussed in the context of Bayesian nonparametric inference for discovery probabilities.

Citations

• The number of small blocks in exchangeable random partitions

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• Precise Deviations for the Ewens-Pitman Model

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