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Optimizing observation order in Vecchia

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Area of Science:

  • Gaussian processes
  • Statistical modeling
  • Computational statistics

Background:

  • Vecchia's approximation for Gaussian processes is sensitive to observation ordering.
  • Existing ordering methods can lead to suboptimal accuracy.

Purpose of the Study:

  • To investigate the impact of observation ordering on Vecchia's approximation accuracy.
  • To develop novel ordering and grouping strategies for improved Gaussian process approximations.

Main Methods:

  • Systematic analysis of ordering effects on Vecchia's approximation.
  • Development and numerical evaluation of new ordering schemes (random, coordinate-based, and others).
  • Introduction of an automatic grouping method for approximation components.

Main Results:

  • Random orderings significantly improve Vecchia's approximation accuracy over default methods.
  • Novel ordering and grouping strategies reduce Kullback-Leibler divergence by over 60x.
  • The proposed methods enhance both accuracy and computational efficiency.

Conclusions:

  • Observation ordering is a tunable parameter that can dramatically improve Vecchia's approximation.
  • Combined reordering and grouping offer substantial gains in Gaussian process modeling accuracy and speed.
  • The methods are validated through theory, numerical results, and an application to space-time data.