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Methods of Ex Situ and In Situ Investigations of Structural Transformations: The Case of Crystallization of Metallic Glasses
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Isotonic regression for metallic microstructure data: estimation and testing under order restrictions.

Martina Vittorietti1,2, Javier Hidalgo3, Jilt Sietsma3

  • 1Department of Applied Mathematics, Delft University of Technology, Delft, Netherlands.

Journal of Applied Statistics
|July 28, 2022
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Summary
This summary is machine-generated.

This study validates isotonic regression for predicting metal mechanical performance by testing order relations between microstructure and properties. Findings enhance material science models by accurately incorporating known physical relationships.

Keywords:
Isotonic regressionalternating iterative methodbootstrapgeometrically necessary dislocationslikelihood ratio testorder restrictions

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Area of Science:

  • Materials Science
  • Statistical Modeling

Background:

  • Understanding metal mechanical performance relies on microstructure-property relationships.
  • Physically inspired qualitative relations offer a starting point for investigation.
  • Isotonic regression can improve accuracy by incorporating ordering relations.

Purpose of the Study:

  • To test the efficacy of order relations within a materials science-inspired model.
  • To evaluate statistical estimation procedures for isotonic regression under varying variance knowledge.
  • To develop and apply new likelihood ratio tests for order restrictions.

Main Methods:

  • Isotonic regression was employed to model relationships between material characteristics.
  • Statistical estimation considered three scenarios: known variance ratio, unknown variances, and variances under order restrictions.
  • Parametric and non-parametric bootstrap methods were used to determine test statistic distributions.

Main Results:

  • The study demonstrates the application of isotonic regression in a materials science context.
  • New likelihood ratio tests were developed for scenarios with unknown variances and order restrictions.
  • The effectiveness of the statistical procedures was validated through an application.

Conclusions:

  • Isotonic regression provides a robust framework for analyzing microstructure-property relationships in metals.
  • The developed statistical tests enhance the reliability of predictions when ordering assumptions hold.
  • This approach offers a more accurate method for understanding material mechanical performance determinants.