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A Review of Multivariate Distributions for Count Data Derived from the Poisson Distribution.

David Inouye1, Eunho Yang2, Genevera Allen3

  • 1University of Texas at Austin.

Wiley Interdisciplinary Reviews. Computational Statistics
|October 7, 2017
PubMed
Summary
This summary is machine-generated.

This study reviews and compares multivariate Poisson distributions for modeling complex count data. It categorizes models and evaluates their performance on real-world datasets, offering insights for future research.

Keywords:
CopulasGraphical ModelsHigh DimensionalMultivariatePoisson

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Area of Science:

  • Statistics
  • Probability Theory
  • Data Science

Background:

  • Univariate Poisson distribution is standard for count data.
  • Multivariate Poisson distributions are less common despite real-world data dependencies.
  • High-dimensional count data (e.g., genomics, text) requires models capturing dependencies.

Purpose of the Study:

  • To review and categorize multivariate Poisson distributions.
  • To compare different classes of these distributions based on theory and interpretability.
  • To empirically evaluate model performance on diverse real-world datasets.

Main Methods:

  • Categorization into three classes: marginal, mixture, and node-conditional.
  • Theoretical comparison of model interpretability and properties.
  • Empirical evaluation on traffic accidents, next-generation sequencing, and text data.

Main Results:

  • Demonstrated varying advantages and disadvantages of each class.
  • Provided empirical insights into model performance across different data types.
  • Highlighted the need for appropriate multivariate models for dependent count data.

Conclusions:

  • Multivariate Poisson distributions are crucial for analyzing complex count data.
  • Empirical comparisons offer practical guidance for model selection.
  • Identified avenues for future research in multivariate count data modeling.