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Area of Science:

  • Statistics
  • Computational Mathematics
  • Functional Data Analysis

Background:

  • Registration of real-valued functions is crucial in various scientific fields.
  • Existing Bayesian models often use fixed dimension reduction rules, limiting adaptability.
  • Infinite-dimensional function spaces pose computational challenges for practical analysis.

Purpose of the Study:

  • To develop novel Bayesian models for real-valued function registration.
  • To introduce a randomized truncation rule for dimension reduction in functional models.
  • To enable data-driven inference on functional parameter smoothness and shape alteration.

Main Methods:

  • Bayesian modeling with Gaussian process priors on time warping functions.
  • Application of Markov chain Monte Carlo (MCMC) for posterior distribution exploration.
  • Randomized dimension reduction contrasting with fixed truncation methods.

Main Results:

  • The new models allow inference on the smoothness of functional parameters.
  • The truncation rule is data-informative, adapting to local features in observed functions.
  • Demonstrated flexibility in controlling shape alteration during registration using simulated and real data.

Conclusions:

  • Randomized dimension reduction offers advantages over fixed rules in Bayesian function registration.
  • The proposed models provide a more adaptive and informative approach to analyzing functional data.
  • The methodology allows for automatic concentration of posterior distributions based on data complexity.