Auto-validating von Neumann rejection sampling from small phylogenetic tree spaces.

Area of Science:

• Computational Biology
• Phylogenetics
• Statistical Inference

Background:

• Phylogenetic inference requires sampling from posterior distributions over tree spaces using DNA sequence data.
• Rejection sampling is a fundamental method for such sampling.
• Existing methods lack rigorous validation for posterior sampling in phylogenetics.

Purpose of the Study:

• To introduce an auto-validating rejection sampler for rigorously drawing samples from posterior distributions over small phylogenetic tree spaces.
• To address the open problem of generating independent and identically distributed samples for phylogenetic inference.

Main Methods:

• Developed an auto-validating rejection sampler utilizing interval analysis.
• Applied the sampler to small phylogenetic tree spaces (3 or 4 taxa).
• Utilized multiply-aligned DNA sequence data for sampling.

Main Results:

• Rigorously estimated posterior probabilities for rooted topologies using primate mitochondrial DNA.
• Conducted a non-parametric test of rate variation between coding sites in primates.
• Obtained a posterior estimate for human-neanderthal divergence time.

Conclusions:

• The auto-validating sampler rigorously solves the problem of sampling from posterior distributions over small tree spaces.
• Enables accurate phylogenetic analysis for various biological datasets.
• Provides a robust method for phylogenetic inference with validated sampling.