Bayesian function registration with random truncation

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.