The Sparse Poisson Means Model

2015/05/06 by Ery Arias-Castro, Meng Wang, Arias-Castro, Ery +1 · 1 citation
Decision Sciences · Mathematics · #Advanced Statistical Process Monitoring #FOS: Mathematics #Statistical Methods and Bayesian Inference #Statistical Methods and Inference #Statistics Theory (math.ST) #math.ST #stat.TH

paper · pdf · doi:10.48550/arxiv.1505.01247

arxiv created 2015/05/06 · openalex publication_date 2015/05/06 · arxiv updated 2015/05/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the problem of detecting a sparse Poisson mixture. Our results parallel those for the detection of a sparse normal mixture, pioneered by Ingster (1997) and Donoho and Jin (2004), when the Poisson means are larger than logarithmic in the sample size. In particular, a form of higher criticism achieves the detection boundary in the whole sparse regime. When the Poisson means are smaller than logarithmic in the sample size, a different regime arises in which simple multiple testing with Bonferroni correction is enough in the sparse regime. We present some numerical experiments that confirm our theoretical findings.

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