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Related Concept Videos

Linearization and Approximation01:26

Linearization and Approximation

Linearization is a mathematical technique used to approximate complex, nonlinear functions with simpler linear models in the vicinity of a chosen reference point. The method is based on the idea that, although a function may be difficult to evaluate exactly, its behavior near a specific input value can often be closely approximated by the tangent line at that point. This approach is particularly useful when small deviations from a known value are involved.Consider the square root function, for...
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A drone flying through complex terrain often relies on more than one sensing method to estimate small changes in altitude. Along with direct measurements, air pressure provides a useful indirect indicator of vertical movement. Atmospheric pressure decreases as altitude increases, and this relationship is commonly described using an exponential model. Although accurate, converting pressure measurements into altitude values requires calculations that are too complex to perform repeatedly during...
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Related Experiment Video

Updated: Jun 2, 2026

Synchronous Triplanar Reconstruction Integrated with Color Doppler Mapping for Precise and Rapid Localization of Thyroid Lesions
05:41

Synchronous Triplanar Reconstruction Integrated with Color Doppler Mapping for Precise and Rapid Localization of Thyroid Lesions

Published on: February 9, 2024

Improved least squares topology testing and estimation.

Edward Susko1

  • 1Department of Mathematics and Statistics, Dalhousie University, Halifax, Nova Scotia, Canada B3H3J5. susko@mathstat.dal.ca

Systematic Biology
|April 14, 2011
PubMed
Summary
This summary is machine-generated.

Generalized least squares (GLS) and weighted least squares (WLS) are used for topology confidence sets. New covariance estimation improves GLS, while WLS with bootstrapping offers a robust alternative for ill-conditioned matrices.

Related Experiment Videos

Last Updated: Jun 2, 2026

Synchronous Triplanar Reconstruction Integrated with Color Doppler Mapping for Precise and Rapid Localization of Thyroid Lesions
05:41

Synchronous Triplanar Reconstruction Integrated with Color Doppler Mapping for Precise and Rapid Localization of Thyroid Lesions

Published on: February 9, 2024

Area of Science:

  • Phylogenetics
  • Statistical Modeling
  • Computational Biology

Background:

  • Generalized least squares (GLS) offers efficient topology confidence set construction.
  • Estimating covariance matrices for distances can lead to ill-conditioned or non-invertible matrices.
  • Weighted least squares (WLS) is an alternative but assumes zero covariances, leading to suboptimal performance.

Purpose of the Study:

  • To develop improved methods for estimating covariance matrices in GLS.
  • To enhance the performance of WLS for constructing topology confidence sets.
  • To provide a robust alternative to GLS when covariance matrices are ill-conditioned.

Main Methods:

  • Novel estimation techniques for distance covariance matrices.
  • Performance evaluation of GLS and WLS methods.
  • Application of a normal parametric bootstrap to WLS.

Main Results:

  • New covariance estimation methods yield positive definite matrices.
  • Standard WLS results in overly large confidence sets but good topology estimation.
  • Bootstrapped WLS performs comparably to GLS, even with ill-conditioned matrices.

Conclusions:

  • Improved covariance estimation enhances GLS performance.
  • Bootstrapped WLS provides a reliable alternative to GLS.
  • These methods improve confidence set construction in phylogenetics.