Validation and discovery in Markov models of genetics data.

Area of Science:

• Statistics
• Computational Biology
• Genetics

Background:

• Markov models are widely used for modeling time-dependent processes at the cellular and molecular levels.
• Existing Chi-squared statistics offer a global test for the Markov assumption but lack the specificity to identify individual departures.
• Analyzing time-series data, such as HIV genetic sequences, requires methods that can detect nuanced changes in process dynamics.

Purpose of the Study:

• To develop and evaluate novel diagnostic approaches for identifying specific deviations from first-order, homogeneous Markov processes.
• To enhance the analysis of time-series biological data by pinpointing localized departures from assumed models.
• To provide more granular insights into the dynamics of systems modeled by Markov processes.

Main Methods:

• Proposed a diagnostic test focusing on the number of transitions out of a specific state at a given time point.
• Developed statistics based on the observed number of observations within each state over time.
• Utilized simulations to perform statistical testing on multiple, correlated diagnostic statistics.

Main Results:

• The developed diagnostics successfully identify specific time points and states where the Markov assumption may not hold.
• Application to HIV genetics sequences demonstrated the utility of these methods in detecting non-trivial departures.
• The simulation-based testing framework proved effective for handling correlated statistics.

Conclusions:

• The proposed diagnostic methods offer a significant improvement over global tests for Markov assumptions.
• These approaches provide valuable tools for detailed analysis of time-series data in fields like molecular evolution and disease progression.
• The study highlights the importance of specific diagnostics for a comprehensive understanding of dynamic systems.