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Generalized monotonic regression using random change points.

C C Holmes1, N A Heard

  • 1Department of Mathematics, Imperial College, 180 Queen's Gate, London SW7 2BZ, U.K.

Statistics in Medicine
|February 19, 2003
PubMed
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This study presents a novel Bayesian approach for generalized monotonic curve fitting, enhancing isotonic regression by treating step number and location as random variables. The method provides robust evidence for monotonicity and detailed change point analysis.

Area of Science:

  • Statistics
  • Computational Biology
  • Biostatistics

Background:

  • Conventional isotonic regression fits monotonically increasing step functions.
  • Existing methods may lack flexibility in handling complex data patterns.

Purpose of the Study:

  • To develop a generalized monotonic curve fitting procedure using Bayesian analysis.
  • To enhance isotonic regression by treating step number and location as random variables.

Main Methods:

  • Bayesian analysis of the isotonic regression model.
  • Utilizing conjugate priors for unconstrained data distributions.
  • Employing Markov chain Monte Carlo (MCMC) simulation to sample from the unconstrained model space.
  • Retaining samples that satisfy the monotonic constraint.

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Main Results:

  • The proportion of valid samples provides Bayes factors for monotonicity.
  • Enables probability statements on quantities like the number of change points.
  • Offers posterior distributions for change point locations.

Conclusions:

  • The proposed Bayesian method offers a flexible and robust approach to monotonic curve fitting.
  • It provides quantitative evidence for monotonicity and detailed insights into data structure.
  • Demonstrated utility through reanalysis of leukaemia data.