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# Efficient maximum likelihood parameterization of continuous-time Markov processes.

### Author information

- 1
- Department of Chemistry, Stanford University, Stanford, California 94305, USA.

### 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 a 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.

- PMID:
- 26203016
- PMCID:
- PMC4514821
- DOI:
- 10.1063/1.4926516

- [Indexed for MEDLINE]

### Publication types, MeSH terms, Grant support

#### Publication types

#### MeSH terms

- Likelihood Functions*
- Markov Chains*
- Molecular Dynamics Simulation
- Protein Folding
- Time Factors
- Uncertainty