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Elusive present: Hidden past and future dependency and why we build models
Pooneh M Ara1, Ryan G James1, James P Crutchfield1
1Complexity Sciences Center and Physics Department, University of California, Davis, One Shields Avenue, Davis, California 95616, USA.
Physical Review. E
|March 18, 2016
Summary
Many temporal processes are not Markovian, meaning the present doesn't fully capture past-future dependencies. This study quantifies this "Markov failure" and proposes state-based models for accurate analysis.
Area of Science:
- Complex Systems
- Information Theory
- Statistical Modeling
Background:
- Markovian modeling assumes present states encapsulate all historical information.
- Recent work shows structured processes often violate this Markov assumption.
- Understanding Markov failure is crucial for accurate temporal process analysis.
Purpose of the Study:
- To investigate information shared between past and future but missed by the present.
- To quantify this "elusive information" and develop calculational methods.
- To outline consequences of Markov failure for statistical modeling.
Main Methods:
- Analysis of information flow in structured temporal processes.
- Quantification of information not encoded in the present state.
- Development of methods to calculate past-future correlations hidden from the present.
Main Results:
- Identified and quantified information shared between past and future but not reflected in the present.
- Developed explicit methods for calculating this hidden information.
- Demonstrated that Markov failure is common in structured processes.
Conclusions:
- When the present state obscures past-future correlations, sequence-based statistics are insufficient.
- State-based models are necessary to capture dependencies missed by Markovian assumptions.
- This work provides a framework for analyzing non-Markovian temporal dynamics.
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