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Bayesian model selection uses Bayesian model evidence (BME) to rank models. Information criteria (ICs) for BME calculation are often biased, making numerical methods preferable for accurate model ranking.

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Area of Science:

  • Computational statistics
  • Model selection theory

Background:

  • Bayesian model selection/averaging objectively ranks models using Bayes' theorem.
  • It balances data fitting performance with model complexity.
  • Calculating Bayesian model evidence (BME) is computationally challenging due to high-dimensional integrals.

Purpose of the Study:

  • To intercompare techniques for computing BME.
  • To assess the accuracy of different BME approximation methods.
  • To benchmark BME evaluation methods against true solutions.

Main Methods:

  • Theoretical intercomparison of BME computation techniques.
  • Accuracy assessment using synthetic data with known solutions.
  • Brute-force Monte Carlo integration as a reference.
  • Application to hydrological model selection.

Main Results:

  • Information criteria (ICs) often yield heavily biased BME values.
  • The choice of approximation method significantly impacts model ranking accuracy.
  • Exact analytical solutions are limited by strong assumptions.
  • Numerical evaluation becomes infeasible for computationally expensive models.

Conclusions:

  • Bias-free numerical methods are preferred over ICs for reliable model selection.
  • Computational feasibility remains a key consideration for method selection.