Navigating Uncertainty: The Finite Information Quantity Approach to Objective Model Selection in Physics

Boris Menin

Accurate measurements of physical processes are essential for scientific research and technological advancement. From subatomic particles to celestial bodies, precise measurements underpin our understanding of the universe and drive innovation. However, selecting the right mathematical model to interpret experimental data can be challenging due to the complexities of real-world phenomena. Traditional model selection methods often rely on researcher intuition and experience, leading to subjectivity and potential biases. In this article, we explore the Finite Information Quantity (FIQ) approach—a novel solution that addresses these limitations.

The FIQ approach recognizes the inherent limitations in information processing capacity within physical systems. By acknowledging these constraints, FIQ provides objective criteria for model selection. Researchers can use comparative uncertainty to evaluate different models, minimizing bias and promoting objectivity. Through FIQ, we gain a more comprehensive understanding of phenomena by exploring diverse explanations.

To assess the effectiveness of FIQ, we compare it with ten existing model selection techniques: List Squares Method, Maximum Likelihood Estimation, Akaike Information Criterion, Bayesian Inference, Nonlinear Regression, Monte Carlo Simulation, Optimization Techniques, Machine Learning Algorithms, Principal Component Analysis, Gaussian Processes. Current methodologies for selecting models of physical phenomena and analyzing experimental data face several key limitations.

These limitations stem from their reliance on researcher subjectivity:

a. Inherent Subjectivity: Traditional model selection methods rely heavily on researchers’ knowledge, intuition, and experience. This introduces biases and inconsistencies, hindering truly objective solutions.

b. Limited Scope: Many existing approaches prioritize identifying the “best” model based on specific criteria. However, a broader understanding of the model landscape is crucial. This involves exploring alternative explanations and potential shortcomings inherent in any chosen model.

c. Overfitting Focus: Existing methods often focus on minimizing overfitting, where complex models closely fit training data but fail to generalize accurately to new data. Techniques like regularization and cross-validation address this limitation.

d. Neglecting Model Uncertainty: While these methods consider known uncertainties in experimental data, they overlook a critical source of uncertainty: the model itself. The qualitative and quantitative variables used to construct the model introduce inherent uncertainty.

These limitations are intrinsic to current model selection methods and can influence the chosen model’s reliability and validity. Careful consideration of these limitations and implementation of appropriate mitigation strategies are crucial for robust scientific inference.

Modern scientific literature generally overlooks an additional, fundamental limitation of existing methods. These methods analyze experimental data using models designed to minimize known uncertainties. However, they neglect a critical source of uncertainty: the model itself. This uncertainty arises from the qualitative and quantitative set of variables chosen to construct the model. Existing methods fail to account for this inherent and primary uncertainty, which ultimately influences the choice of the most suitable model for a specific phenomenon.