Generator estimation of Markov jump processes based on incomplete observations nonequidistant in time

Area of Science:

• Computational Statistics
• Stochastic Processes
• Mathematical Modeling

Background:

• Markov jump processes are crucial for modeling dynamic systems across various fields, including molecular dynamics and finance.
• Inverse modeling of these processes often relies on complete or regularly sampled time series data.
• Existing methods can be computationally intensive and struggle with incomplete or irregularly sampled observations.

Purpose of the Study:

• To develop an efficient inverse modeling method for Markov jump processes.
• To enable accurate estimation of the infinitesimal generator from discretely observed, incomplete time series.
• To handle time series data with non-equidistant observations.

Main Methods:

• The study proposes a novel method for inverse modeling of Markov jump processes.
• It focuses on computing the maximum likelihood estimator of the infinitesimal generator from observed time series.
• The approach is an advancement over previous work by Bladt and Sørensen, offering improved scalability.

Main Results:

• The method efficiently computes the maximum likelihood estimator for the infinitesimal generator.
• It successfully handles time series data with non-equidistant observations.
• Performance was demonstrated on both a simplified problem and complex biochemical kinetics data.

Conclusions:

• The presented method provides an efficient and scalable approach for inverse modeling of Markov jump processes.
• It effectively addresses the challenge of incomplete and irregularly sampled time series data.
• The technique has practical applications in fields requiring the analysis of dynamic systems, such as biochemical kinetics.