Finding Optimal Monte-Carlo Run Numbers for Stochastic Data Under Gaussian Distribution
Ekin Can Erkuş, Alper Yıldız, Sevim Açıksöz · 2023
This study investigates the optimal number of Monte Carlo runs under Gaussian conditions to enhance the efficiency of stochastic model assessments. The research involves synthetic data generation with varying lengths and error rates. The mean optimal run numbers are computed and are found to decrease as the data length increases, indicating larger datasets require fewer runs for convergence. Conversely, as the error rate decreases, more runs are needed for reliable convergence. To understand this relationship, exponential regression models are fitted for each error rate, providing a predictive tool for estimating optimal run numbers based on specific error rates and data lengths. The models exhibit an exponential decay, emphasizing the diminishing returns of additional Monte Carlo runs. Findings offer insights into stochastic model dynamics, particularly in recommender systems, machine learning, and AI. Regression models that have been fitted enable us to easily find the ideal number of runs before starting the Monte Carlo simulations and hence reduce the computational times to reach convergence. The utility of stochastic models across dynamic domains is shaped by this study’s advancement of our understanding and mapping of future research directions in the context of evolving computational techniques and AI applications.