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Scalable Inference for Bayesian Multinomial Logistic-Normal Dynamic Linear Models.

Manan Saxena1, Tinghua Chen1, Justin D Silverman1

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Summary
This summary is machine-generated.

This study introduces Fenrir, an efficient Bayesian method for analyzing longitudinal count compositional data. Fenrir significantly improves computational speed for complex models, making advanced statistical analysis more accessible.

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Area of Science:

  • Statistics
  • Computational Biology
  • Data Science

Background:

  • Longitudinal count compositional data are prevalent across scientific disciplines.
  • Bayesian Multinomial Logistic-Normal Dynamic Linear Models (MLN-DLMs) offer a flexible framework for analyzing such data.
  • Computational challenges have hindered the widespread adoption of MLN-DLMs.

Purpose of the Study:

  • To develop an efficient and accurate method for posterior state estimation in MLN-DLMs.
  • To overcome the computational limitations of existing approaches for modeling longitudinal count compositional data.

Main Methods:

  • Developed Fenrir, a novel approach for posterior state estimation.
  • Utilized a new algorithm for Maximum A Posteriori (MAP) estimation.
  • Incorporated an accurate approximation for a key posterior marginal of the MLN-DLM.

Main Results:

  • Fenrir demonstrates computational efficiency, outperforming a Stan implementation by up to three orders of magnitude.
  • The proposed methods enable joint inference of model hyperparameters within larger sampling schemes.
  • A user-friendly C++ software library with an R interface is provided.

Conclusions:

  • Fenrir offers a computationally efficient and accurate solution for analyzing longitudinal count compositional data using MLN-DLMs.
  • The developed methods and software facilitate broader application of advanced Bayesian dynamic linear models.
  • This work addresses a critical bottleneck in the analysis of complex compositional data.