Efficient maximum likelihood parameterization of continuous-time Markov processes

TL;DR

This paper introduces an efficient maximum likelihood estimator for continuous-time Markov processes, enabling faster model construction, confidence interval calculation, and enforcement of physical constraints, with applications in molecular dynamics.

Contribution

The paper presents a novel, more efficient maximum likelihood estimator for continuous-time Markov models that incorporates physical constraints and provides confidence intervals.

Findings

Estimator is significantly more efficient than previous methods.

Allows deterministic confidence intervals for all parameters.

Enables enforcement of physical constraints like detailed balance.

Abstract

Continuous-time Markov processes over finite state-spaces are widely used to model dynamical processes in many fields of natural and social science. Here, we introduce an maximum likelihood estimator for constructing such models from data observed at a finite time interval. This estimator is dramatically more efficient than prior approaches, enables the calculation of deterministic confidence intervals in all model parameters, and can easily enforce important physical constraints on the models such as detailed balance. We demonstrate and discuss the advantages of these models over existing discrete-time Markov models for the analysis of molecular dynamics simulations.