How Can Markov Models Be Used to Compare Transition State Matrices?

This discussion focuses on comparing transition state matrices using Markov models. The user seeks methods to assess similarity between 3x4 and 4x4 matrices, noting that averaging the diagonal elements is inadequate due to the zero value in the 4,4 position. Steve Brailsford suggests utilizing eigenvalues, emphasizing that if the processes lack absorbing states, the eigenvectors associated with eigenvalue 1 represent the stationary state, providing a more reliable comparison method.

• Understanding of Markov models and their applications
• Familiarity with matrix operations and properties
• Knowledge of eigenvalues and eigenvectors
• Concept of stationary states in Markov processes

• Research methods for comparing Markov transition matrices
• Learn about eigenvalue decomposition and its applications
• Explore the concept of stationary distributions in Markov chains
• Investigate alternative similarity measures for matrices

Researchers in applied mathematics, data scientists, and anyone working with Markov models and transition state analysis.