Estimation of π From Statistical Features of Acoustic Time Series Using Optimized Monte Carlo With Grid Search Algorithm

Key Points

Pi is estimated with a mean absolute error of 0.0002 using acoustic time series data and optimized algorithms.
The methodology utilizes grid search optimization for enhancing zero-crossing rate statistics in the analysis.
The approach employs Gaussian process theory to ensure global convergence while outperforming traditional Monte Carlo methods.
Validation with music audio demonstrates accuracy, while non-Gaussian financial data underscores theoretical limits of the method.

Abstract

This paper introduces a novel methodology for estimating the mathematical constant π from acoustic time series using grid search optimization of zero-crossing rate (ZCR) statistics. By leveraging Gaussian process theory and exhaustive hyperparameter tuning, we demonstrate that π emerges naturally as a fundamental parameter in oscillatory signals. Our approach ensures global convergence and reproducibility, outperforming traditional Monte Carlo methods in accuracy. Experimental validation on music audio achieves a mean absolute error of 0.0002 while failure on non-Gaussian financial data confirms the theoretical foundations of the method.

Estimation of π From Statistical Features of Acoustic Time Series Using Optimized Monte Carlo With Grid Search Algorithm

Key Points

Abstract

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