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STATISTICAL TESTS FOR LARGE TREE-STRUCTURED DATA.

Karthik Bharath1, Prabhanjan Kambadur2, Dipak K Dey3

  • 1School of Mathematical Sciences, University of Nottingham, Nottingham, NG7 2RD, U.K.

Journal of the American Statistical Association
|April 4, 2023
PubMed
Summary
This summary is machine-generated.

We developed statistical tests for analyzing tree-structured data, including detecting tumor heterogeneity in brain cancer using magnetic resonance images. Our methods provide simple, computable statistics for robust data analysis.

Keywords:
Conditioned Galton-Watson treesConsistent statistical modelsDyck pathGoodness-of-fit tests

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Area of Science:

  • Statistics
  • Computational Biology
  • Bioinformatics

Background:

  • Analyzing large tree-structured data is challenging.
  • Existing methods lack robust goodness-of-fit tests.
  • Tree-structured data is prevalent in various scientific domains.

Purpose of the Study:

  • Develop a general statistical framework for analyzing tree-structured data.
  • Introduce asymptotic goodness-of-fit tests for tree models.
  • Apply these tests to detect tumor heterogeneity in brain cancer.

Main Methods:

  • Propose a consistent statistical model for binary trees.
  • Develop invariant tests based on the binary tree model.
  • Utilize Continuum Random Tree properties for general tree analysis.
  • Employ tree-based representations of magnetic resonance images.

Main Results:

  • Developed a class of invariant goodness-of-fit tests.
  • Test statistics are simple to compute.
  • Asymptotic distributions are chi-squared and F random variables.
  • Successfully applied tests to detect tumor heterogeneity.

Conclusions:

  • The proposed framework offers a powerful tool for analyzing tree-structured data.
  • The developed tests are effective for detecting heterogeneity in biological data.
  • This approach has significant implications for cancer research and diagnostics.