On the Assessment of Monte Carlo Error in Simulation-Based Statistical Analyses

Area of Science:

• Statistics
• Computational Statistics
• Biostatistics

Background:

• Monte Carlo (simulation) studies are crucial for evaluating statistical methods under controlled conditions.
• Advances in computing have improved simulation efficiency (variance reduction), but experiments remain subject to uncertainty due to their finite nature.
• Reporting and justifying Monte Carlo error, the uncertainty in simulation results, is often neglected in published literature.

Purpose of the Study:

• To present practical methods for estimating Monte Carlo error.
• To provide guidance on determining the required number of replications for desired accuracy in simulations.
• To highlight the importance of addressing Monte Carlo error in statistical research.

Main Methods:

• Development and demonstration of simple, practical methods for estimating Monte Carlo error.
• Application of methods to determine the necessary number of replications for achieving specific accuracy levels.
• Illustrative examples using logistic regression parameter estimation and bootstrap confidence intervals.

Main Results:

• Monte Carlo error can be substantial and is often underestimated in statistical simulations.
• The proposed methods offer practical approaches to quantify and manage simulation uncertainty.
• The number of replications significantly impacts the reliability of simulation study outcomes.

Conclusions:

• There is a critical need for increased emphasis on reporting and addressing Monte Carlo error in simulation studies.
• Implementing the presented methods can enhance the rigor and reproducibility of statistical research.
• Underestimating Monte Carlo error can lead to overconfidence in statistical findings.