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Objective Bayesian trend filtering via adaptive piecewise polynomial regression.

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Summary
This summary is machine-generated.

This study introduces an objective Bayesian trend filtering method using model selection for nonparametric regression. The novel approach accurately detects variance change points, even with smooth mean changes, outperforming existing methods.

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Bayes factorintrinsic priormodel selectionnonparameteric regressionpiecewise polynomial regressiontrend filtering

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Area of Science:

  • Statistics
  • Machine Learning
  • Data Analysis

Background:

  • Nonparametric regression encompasses various methods like kernels, splines, and trend filtering.
  • Existing trend filtering methods may struggle with smoothly varying means.

Purpose of the Study:

  • To propose an objective Bayesian trend filtering method based on model selection.
  • To accurately detect variance change points under smoothly varying mean changes.

Main Methods:

  • Adaptive piecewise polynomial regression with two components.
  • Bayesian binary segmentation to identify trend intervals.
  • Bayesian model selection with intrinsic priors for trend evaluation.

Main Results:

  • The proposed method demonstrates consistency for large sample sizes.
  • Accurate detection of variance change points when means vary smoothly.
  • Outperforms existing methods that assume sudden changes.

Conclusions:

  • The objective Bayesian trend filtering method provides a robust approach for nonparametric regression.
  • The method effectively handles complex scenarios with smoothly varying means.
  • Offers improved accuracy in detecting variance change points compared to traditional methods.