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

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.

—The Finite Information Quantity method offers elucidating contemporary challenges in scientific inquiry. This method offers a comprehensive approach to evaluate model accuracy, address uncertainty, and enhance reliability across disciplines, fostering robust scientific exploration and understanding of natural phenomena.—

This article introduces the Finite Information Quantity (FIQ) approach, which explores the relationship between information and physical systems. It highlights that information is not infinite and proposes using finite information constraints to understand various physical phenomena. The FIQ approach has implications for topics such as black hole information storage, uncertainties in physical measurements, and model building. It suggests that models serve as channels of information between the observed phenomenon and the observer, emphasizing the active role of models in shaping our understanding of the world. Additionally, it discusses the role of variables and systems of units in model construction and introduces key axioms of the FIQ method. Overall, the FIQ approach offers a novel perspective by integrating information theory with physical laws, potentially leading to groundbreaking discoveries in physics.

The article discusses the challenges facing scientific research due to issues like replication problems and a lack of expertise in measurement theory and uncertainty analysis. It introduces the concept of model complexity and highlights the need for a criterion to assess discrepancies between models and phenomena. The comparative certainty criterion, grounded in the Frame of Finite Information Quantity (FIQ) method, aims to address this need by considering the information content within the chosen system of units during model selection. The FIQ method challenges the traditional focus solely on data processing methods for achieving model accuracy, demonstrating that the information content within the chosen units impacts model accuracy. It also provides a framework to address the inherent uncertainty associated with models by enabling the selection of optimal variables. The text concludes by highlighting the potential of the FIQ method in various scientific disciplines, for example, measuring physical constants with improved uncertainty analysis, unveiling accuracy in underwater electrical discharges, optimizing speed of sound measurements, and emphasizing the need for further research to explore its applicability and address potential limitations. Overall, the FIQ method offers a promising approach to constructing more accurate and reliable models, ultimately leading to a deeper understanding of scientific phenomena.

Understanding and addressing these limitations are crucial for robust scientific inference when selecting models for various applications. The proposed novel method seeks to account for both data and model uncertainties in the selection process.

Translation of the article: Objective Model Selection in Physics: Exploring the Finite Information Quantity Approach, in Journal of Applied Mathematics and Physics, 12(5), 1848-1889, 2024

Cite this article in APA as: Menin, B. Navigating uncertainty: The finite information quantity approach to objective model selection in physics. (2024, June 6). Information Matters, Vol. 4, Issue 6. https://informationmatters.org/2024/06/navigating-uncertainty-the-finite-information-quantity-approach-to-objective-model-selection-in-physics/

Author

  • Boris Menin

    BORIS M. MENIN (Member, IEEE) received an MSc degree in 1973 at Electro-Technical Communication Institute, department of Multichannel Electrical Communications and received a PhD in Mass and Heat Transfer at the Technological Institute of Refrigeration Industry, Russia, St-Petersburg in 1981. Dr. Menin was Director of the Laboratory of Ice Generators and Plate Freezers in St. Petersburg from 1977 to 1989, after which he emigrated from the Soviet Union to Israel. There he was the Chief Scientist at Crytec Ltd. (1999–2008) and managed the development, production, and marketing of pumpable ice generators and cold energy storage systems, while also modeling and manufacturing high-accuracy instrumentation for heat and mass processes. He is now an Independent Mechanical & Refrigeration Consultation Expert. In addition, he has managed Task 3.1 of the European FP6 project in the field of food cold chain and several of Israel’s (EUREKA, integrated project of EU and Chief Scientist Office of Israel’s Ministry of Industry) in the field of cold energy storage systems based on pumpable ice technology. He is an author of five books and 67 journal articles, and is a member of ASHRAE (USA) and SEEEI (Israel).

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Boris Menin

BORIS M. MENIN (Member, IEEE) received an MSc degree in 1973 at Electro-Technical Communication Institute, department of Multichannel Electrical Communications and received a PhD in Mass and Heat Transfer at the Technological Institute of Refrigeration Industry, Russia, St-Petersburg in 1981. Dr. Menin was Director of the Laboratory of Ice Generators and Plate Freezers in St. Petersburg from 1977 to 1989, after which he emigrated from the Soviet Union to Israel. There he was the Chief Scientist at Crytec Ltd. (1999–2008) and managed the development, production, and marketing of pumpable ice generators and cold energy storage systems, while also modeling and manufacturing high-accuracy instrumentation for heat and mass processes. He is now an Independent Mechanical & Refrigeration Consultation Expert. In addition, he has managed Task 3.1 of the European FP6 project in the field of food cold chain and several of Israel’s (EUREKA, integrated project of EU and Chief Scientist Office of Israel’s Ministry of Industry) in the field of cold energy storage systems based on pumpable ice technology. He is an author of five books and 67 journal articles, and is a member of ASHRAE (USA) and SEEEI (Israel).

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