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Efficiency and time-dependent cross correlations in multivariable Monte Carlo updating.
Christopher C J Potter1, Robert H Swendsen2
1Department of Mathematical Sciences, Carnegie-Mellon University, 5000 Forbes Avenue, Pittsburgh, Pennsylvania 15213, USA.
Jointly updating variables in Monte Carlo (MC) algorithms can create misleading correlations, impacting efficiency estimates. Separate variable updates are generally more efficient than global ones, suggesting a need to re-evaluate optimal acceptance ratios.
Area of Science:
- Computational Statistics
- Statistical Physics
Background:
- Monte Carlo (MC) methods are widely used for complex simulations.
- Assessing the efficiency of MC algorithms is crucial for reliable results.
- Previous work established optimal acceptance ratios for global MC updating.
Purpose of the Study:
- To investigate the impact of joint variable updates in MC algorithms.
- To analyze the emergence of spurious time-shifted correlations.
- To re-evaluate optimal acceptance ratios based on global vs. local efficiency measures.
Main Methods:
- Analysis of MC algorithms employing joint variable updates.
- Theoretical examination of time-shifted correlations in MC simulations.
- Comparison of local and global efficiency measures for MC updating.
Main Results:
- Joint updates introduce spurious time-shifted correlations, even with independent equilibrium probabilities.
- These correlations affect correlation times and optimal acceptance ratios.
- Global efficiency measures yield different optimal acceptance ratios than local measures, and global updating is less efficient.
Conclusions:
- Spurious correlations from joint updates necessitate re-evaluation of MC efficiency metrics.
- Previously established optimal acceptance ratios may not be universally applicable.
- Separate or small-group variable updating is often more efficient than global updating in MC algorithms.
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