Evaluating probabilistic programming and fast variational Bayesian inference in phylogenetics.

Area of Science:

• Computational Biology
• Statistical Machine Learning
• Phylogenetics

Background:

• Probabilistic programming frameworks facilitate rapid prototyping and fitting of statistical models.
• Variational inference is a scalable approximation method used in these frameworks.
• Phylogenetic models are crucial for understanding evolutionary relationships.

Purpose of the Study:

• To explore the application of the Stan probabilistic programming language to phylogenetic models.
• To compare the accuracy and computational efficiency of variational inference in Stan against Markov chain Monte Carlo (MCMC) methods.
• To evaluate the performance of specialized variational inference implementations for phylogenetic models.

Main Methods:

• Implementation of common phylogenetic models (e.g., GTR, site-rate heterogeneity, coalescent models) in Stan.
• Comparison of posterior distributions from Stan's black box variational inference with MCMC reference implementations.
• Evaluation of a custom mean-field variational inference implementation on the Jukes-Cantor model.

Main Results:

• Common phylogenetic models can be implemented using probabilistic programming in Stan.
• Stan's black box variational inference is faster but less accurate than MCMC for phylogenetic inference.
• A specialized mean-field variational inference implementation significantly outperformed general-purpose probabilistic implementations in speed and accuracy.

Conclusions:

• Probabilistic programming offers a flexible approach for implementing phylogenetic models.
• While general variational inference in Stan is computationally efficient, MCMC remains more accurate for phylogenetic inference.
• Specialized variational inference methods hold potential for accelerating accurate phylogenetic analyses.