Improving individual committor estimates and data efficiency in reaction coordinate tests with the empirical Bayes...

Area of Science:

• Computational Chemistry
• Statistical Mechanics
• Chemical Kinetics

Background:

• Rare event methods in computational chemistry often require estimating the committor probability.
• The committor, a Bernoulli parameter, represents the probability of reaching a product state before a reactant state.
• Estimating committors involves challenges due to configuration-specific differences and binomial sampling errors.

Purpose of the Study:

• To introduce and apply the empirical Bayes method for improving committor probability estimation.
• To enhance both the ensemble description and individual committor estimates simultaneously.
• To validate the method using a tangible analogy (thumbtacks) and a chemical reaction (polyethylene pyrolysis).

Main Methods:

• Utilized the empirical Bayes method to construct a prior from ensemble estimates.
• Applied maximum posterior estimation to refine individual committor estimates.
• Demonstrated the method with a thumbtack tossing experiment and a radical chain walking reaction.

Main Results:

• The empirical Bayes method significantly improved the accuracy of individual Bernoulli parameter (committor) estimates.
• The method effectively refined the overall ensemble description of committor probabilities.
• In polyethylene pyrolysis, the antisymmetric stretch coordinate proved more accurate than the coordination number for committor analysis.

Conclusions:

• The empirical Bayes approach offers a robust strategy for enhancing rare event simulations by improving committor estimation.
• This statistical method provides more accurate insights into reaction mechanisms and rates.
• The findings suggest improved collective variables for analyzing complex chemical processes.