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Estimation and uncertainty of reversible Markov models.

Benjamin Trendelkamp-Schroer¹, Hao Wu¹, Fabian Paul¹

¹Institut für Mathematik und Informatik, FU Berlin, Arnimallee 6, 14195 Berlin, Germany.

The Journal of Chemical Physics

|November 9, 2015

Summary

This study presents new algorithms for estimating reversible transition matrices from molecular kinetics simulation data. These methods are crucial for applying existing theories in Markov and master-equation models.

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Area of Science:

Molecular kinetics
Computational chemistry
Statistical mechanics

Background:

Reversibility is fundamental in Markov and master-equation models for molecular kinetics.
Analyzing transition matrices relies heavily on the reversibility property.
Estimating reversible transition matrices from simulation data is essential for theoretical applications.

Purpose of the Study:

To develop and present methods for maximum likelihood estimation of transition matrices from finite simulation data.
To introduce a novel algorithm for estimating reversible transition matrices with respect to a specified stationary vector.
To create new Bayesian inference methods for reversible transition matrices, incorporating priors that preserve metastable features.

Main Methods:

Maximum likelihood estimation for transition matrices.
Development of a new algorithm for reversible transition matrix estimation with a given stationary vector.
Bayesian posterior inference for reversible transition matrices, with and without a given stationary vector.
Utilizing prior distributions that maintain metastable process features during inference.

Main Results:

Successful implementation of novel estimation algorithms for reversible transition matrices.
Demonstration of methods for Bayesian inference that preserve key kinetic features.
Integration of all developed algorithms into the PyEMMA software package (version 2.0 and later).

Conclusions:

The developed methods provide robust tools for estimating reversible transition matrices from simulation data.
These advancements facilitate the application of theoretical frameworks in molecular kinetics.
The PyEMMA software now includes advanced algorithms for analyzing kinetic models.