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Uncertainty quantification for Markov chain models
1University of Southern California, Los Angeles, California 90089, USA. meidani@usc.edu
Chaos (Woodbury, N.Y.)
|January 3, 2013
Summary
This study introduces a probabilistic model for Markov chain transition matrices to handle parameter uncertainties. It uses maximum entropy to analyze disease spread models and inform decision-making.
Area of Science:
- Probability Theory
- Stochastic Processes
- Mathematical Modeling
Background:
- Markov chains are essential for modeling dynamic systems, but parameter uncertainties can compromise their reliability.
- Uncertainties arise from environmental fluctuations or limited data, impacting decision-making based on these models.
Purpose of the Study:
- To develop a probabilistic framework for Markov chain transition matrices to quantify parameter uncertainties.
- To apply maximum entropy principles for characterizing transition rate probabilities.
- To investigate the implications of these uncertainties on decision-making in applied scenarios, such as disease spread.
Main Methods:
- A probabilistic model for transition matrices was developed to represent parameter uncertainties.
- The principle of maximum entropy was employed to define the probability measure of transition rates.
- The formalism was demonstrated using a Markov chain model for disease transmission.
Main Results:
- The study provides a method to describe the behavior of Markov chains under parameter uncertainty.
- The maximum entropy approach offers a principled way to assign probabilities to transition rates.
- Analysis of the disease spread model revealed insights into quantities relevant for decision-making.
Conclusions:
- The proposed probabilistic model effectively addresses uncertainties in Markov chain parameters.
- Maximum entropy provides a robust method for quantifying transition rate probabilities.
- This approach enhances the reliability of Markov chain models for decision support, particularly in public health contexts.
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