Scalable Inference for Bayesian Multinomial Logistic-Normal Dynamic Linear Models

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.