Multivariate Poisson lognormal distribution for modeling counts from modern biological data: An overview

Area of Science:

• Biostatistics
• Computational Biology
• Statistical Modeling

Background:

• Modern biological data frequently involve multivariate discrete counts, with limited efficient statistical distributions available for direct modeling.
• Existing multivariate distributions often suffer from drawbacks like non-tractable forms, complex parameter estimation, restricted correlation structures, and slow convergence.

Purpose of the Study:

• To introduce and overview the Poisson lognormal and multivariate Poisson lognormal distributions for modeling count data.
• To present efficient parameter estimation strategies, including variational approximation and Bayesian methods, suitable for high-dimensional biological data.
• To compare the performance of Poisson lognormal distributions against traditional univariate models like Poisson and negative binomial distributions.

Main Methods:

• Hierarchical formulation of Poisson lognormal and multivariate Poisson lognormal distributions.
• Development of variational approximation and hybrid Bayesian approaches for parameter estimation.
• Simulations and real-world dataset analyses to compare mean-variance relationships of different distributions.
• Exploration of multivariate Poisson lognormal properties, including modeling zero counts, over-dispersion, and covariance structures.

Main Results:

• Poisson lognormal and multivariate Poisson lognormal distributions provide a flexible framework for count data.
• Efficient estimation strategies enable scalability to high-dimensional datasets.
• Demonstrated ability to model complex count data characteristics like over-dispersion and varied covariance.
• Successful application in model-based clustering for RNA-seq and microbiome data.

Conclusions:

• Poisson lognormal and multivariate Poisson lognormal distributions offer a significant advancement in modeling complex biological count data.
• The proposed estimation methods facilitate the analysis of large, high-dimensional datasets.
• These distributions are valuable tools for applications in genomics, transcriptomics, and microbiome research, particularly for clustering analyses.