This chapter is devoted to planning and analyzing the results of simulation experiments based on independent replications. A fundamental formula—derived from the central limit theorem—relates the number of replications required to achieve a desired precision with a given confidence level and the variance of the estimator. The chapter introduces the concepts of pilot and actual simulations, and discusses their role in effective simulation planning. Key topics include the estimation of means, probabilities, and quantiles, construction of confidence intervals, and the assessment of bias, variance, and mean square error in simulation estimators. Special attention is given to evaluating the accuracy of simulation results, including a detailed discussion of the distinction between absolute and relative error and their practical implications for interpreting outcomes. Probabilistic tools such as the Chernoff bound are introduced for quantifying errors and supporting decision-making. Throughout, practical examples, algorithms, and Python code are provided to illustrate key concepts and support reproducibility. By the end of the chapter, readers will have a solid foundation for evaluating the reliability and precision of Monte Carlo simulation outputs based on independent replications.

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Simulation Output Analysis: Independent Replications

  • Paweł Lorek,
  • Tomasz Rolski

摘要

This chapter is devoted to planning and analyzing the results of simulation experiments based on independent replications. A fundamental formula—derived from the central limit theorem—relates the number of replications required to achieve a desired precision with a given confidence level and the variance of the estimator. The chapter introduces the concepts of pilot and actual simulations, and discusses their role in effective simulation planning. Key topics include the estimation of means, probabilities, and quantiles, construction of confidence intervals, and the assessment of bias, variance, and mean square error in simulation estimators. Special attention is given to evaluating the accuracy of simulation results, including a detailed discussion of the distinction between absolute and relative error and their practical implications for interpreting outcomes. Probabilistic tools such as the Chernoff bound are introduced for quantifying errors and supporting decision-making. Throughout, practical examples, algorithms, and Python code are provided to illustrate key concepts and support reproducibility. By the end of the chapter, readers will have a solid foundation for evaluating the reliability and precision of Monte Carlo simulation outputs based on independent replications.