A flexible multivariate model for high-dimensional correlated count data

Alexander D. Knudson, Tomasz J. Kozubowski, Anna K. Panorska and A. Grant Schissler ()
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Alexander D. Knudson: University of Nevada
Tomasz J. Kozubowski: University of Nevada
Anna K. Panorska: University of Nevada
A. Grant Schissler: University of Nevada

Journal of Statistical Distributions and Applications, 2021, vol. 8, issue 1, 1-21

Abstract: Abstract We propose a flexible multivariate stochastic model for over-dispersed count data. Our methodology is built upon mixed Poisson random vectors (Y1,…,Yd), where the {Yi} are conditionally independent Poisson random variables. The stochastic rates of the {Yi} are multivariate distributions with arbitrary non-negative margins linked by a copula function. We present basic properties of these mixed Poisson multivariate distributions and provide several examples. A particular case with geometric and negative binomial marginal distributions is studied in detail. We illustrate an application of our model by conducting a high-dimensional simulation motivated by RNA-sequencing data.

Keywords: Multivariate count data; Copula; Distribution theory; Big data applications; Gamma-Poisson hierarchy; Mixed Poisson distribution; Negative binomial distribution; High-dimensional multivariate simulation; RNA-sequencing data; 62E10; 62E15; 62H05; 62H10; 62H30 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1186/s40488-021-00119-y

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