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Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
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Published on: July 3, 2020

Adaptive Bayesian multivariate spline knot inference with prior specifications on model complexity.

Junhui He1, Ying Yang2, Jian Kang3

  • 1Department of Mathematical Sciences, Tsinghua University, Beijing, 100084, China.

Biometrics
|July 10, 2026
PubMed
Summary
This summary is machine-generated.

We introduce a Bayesian framework for knot inference in multivariate spline regression, improving accuracy in complex function fitting and change point detection. This method offers superior performance over existing techniques for analyzing real-world data.

Keywords:
extended Bayesian Information CriterionfMRIknot inferencereversible jump Markov chain Monte Carlotensor product spline

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Area of Science:

  • Statistics
  • Computational Statistics
  • Machine Learning

Background:

  • Knot inference in spline regression is challenging due to parameter space dimensionality and non-differentiable likelihoods.
  • Accurate knot placement is crucial for fitting complex functions and identifying critical points.

Purpose of the Study:

  • To develop a Bayesian framework for robust knot inference in multivariate spline regression.
  • To address challenges in fitting discontinuous functions, detecting change points, and locating peaks.

Main Methods:

  • Proposed a Bayesian framework with prior specifications for model complexity.
  • Applied the method to multivariate spline regression for knot number and location estimation.

Main Results:

  • The framework accurately estimates knot numbers and locations.
  • Demonstrated superior performance compared to existing methods in simulations and real-world data analysis.

Conclusions:

  • The proposed Bayesian approach effectively handles knot inference in multivariate spline regression.
  • The method shows practical utility in diverse applications, including biological and neuroimaging data analysis.