Scanning a Poisson Random Field for Local Signals

Scanning a Poisson Random Field for Local Signals

\fnmsNancy \snmR. Zhang\@textsuperscript\safe@setreft3thankst3t4,\safe@setreft3thanksm3,\@nil,\@nil\@@t3,\safe@setreft3thanks    \fnmsBenjamin \snmYakir\@textsuperscript\safe@setreft2thankst2m2,\safe@setreft2thanks\@nil,\@nil\@@t2,\safe@setreft2thanks    \fnmsCharlie \snmL. Xia\@textsuperscript\safe@setreft3thankst3m4,\safe@setreft3thanks\@nil,\@nil\@@t3,\safe@setreft3thanks    \fnmsDavid \snmSiegmund\@textsuperscript\safe@setreft2thankst2m1,\safe@setreft2thanks\@nil,\@nil\@@t2,\safe@setreft2thanks

The detection of local genomic signals using high-throughput DNA sequencing data can be cast as a problem of scanning a Poisson random field for local changes in the rate of the process. We propose a likelihood-based framework for for such scans, and derive formulas for false positive rate control and power calculations. The framework can also accommodate mixtures of Poisson processes to deal with over-dispersion. As a specific, detailed example, we consider the detection of insertions and deletions by paired-end DNA-sequencing. We propose several statistics for this problem, compare their power under current experimental designs, and illustrate their application on an Illumina Platinum Genomes data set.

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