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Related Concept Videos

Entropy01:18

Entropy

The first law of thermodynamics is quantitatively formulated via an equation relating the internal energy of a system, the heat exchanged by it, and the work done on it. A quantitative formulation of the second law of thermodynamics leads to defining a state function, the entropy.
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Cognitive bias results from limitations in thinking and information processing, leading to systematic errors in judgment. Conversely, motivational bias stems from personal desires or emotions, causing distortions in perception to align with self-interest. Motivational bias influences how individuals perceive and attribute causes to events, often shaped by personal needs, goals, and self-esteem preservation. This bias can distort judgment, leading to inaccurate assessments of success, failure,...
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Related Experiment Videos

Testing maximum entropy models with e-values.

Francesca Giuffrida1,2, Diego Garlaschelli1,2, Peter Grünwald3,4

  • 1IMT School for Advanced Studies, Lucca, Italy.

Physical Review. E
|June 19, 2026
PubMed
Summary
This summary is machine-generated.

E-values offer a robust alternative to p-values for hypothesis testing, especially with optional continuation. This study introduces optimal e-values for maximum entropy models, providing exact solutions for microcanonical tests and effective approximations for canonical tests.

Related Experiment Videos

Area of Science:

  • Statistical theory
  • Information theory
  • Complex systems modeling

Background:

  • P-values are standard for hypothesis testing but have limitations, particularly with sequential data collection.
  • E-values provide a flexible and robust alternative, especially beneficial in scenarios with optional continuation.
  • Maximum entropy models are crucial for statistical inference under constraints.

Purpose of the Study:

  • To define and derive optimal e-values for hypothesis testing between maximum entropy models.
  • To address both microcanonical (hard constraints) and canonical (soft constraints) settings.
  • To develop a statistically sound and computationally efficient testing framework.

Main Methods:

  • Derivation of optimal e-values for microcanonical maximum entropy models.
  • Development of a microcanonical approximation for canonical maximum entropy model testing.
  • Analysis of constrained binary models, specifically 2xk contingency tables.
  • Theoretical analysis and numerical simulations to validate performance.

Main Results:

  • An exact analytical expression for the growth-rate optimal e-variable in microcanonical tests.
  • Demonstration that this expression is also valid for canonical tests.
  • Validation of the microcanonical approximation for canonical tests, showing excellent performance.
  • The proposed optimal e-variable is effective even when the number of groups (k) grows with sample size.

Conclusions:

  • Optimal e-values provide a powerful tool for hypothesis testing between maximum entropy models.
  • The microcanonical approximation offers a practical solution for canonical tests where exact solutions are difficult.
  • The developed method is robust and applicable to complex systems, including those with growing features.