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Bayesian computation via empirical likelihood.

Kerrie L Mengersen1, Pierre Pudlo, Christian P Robert

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Summary
This summary is machine-generated.

Empirical likelihood offers a simulation-free alternative to Approximate Bayesian Computation for complex models. This method bypasses simulation parameters, saving time and providing performance evaluation for statistical analysis.

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Area of Science:

  • Statistics
  • Computational Statistics
  • Statistical Modeling

Background:

  • Approximate Bayesian Computation (ABC) is widely used for complex stochastic models with intractable likelihoods.
  • ABC methods require careful selection of simulation parameters, including summary statistics and distance metrics.
  • These parameters can significantly influence the accuracy and efficiency of the analysis.

Purpose of the Study:

  • To introduce a novel algorithm combining empirical likelihood with Bayesian computation.
  • To provide a simulation-free approach for analyzing complex stochastic models.
  • To develop a method that bypasses the need for selecting ABC-specific parameters.

Main Methods:

  • Developed a Bayesian computation with empirical likelihood (BCEL) algorithm.
  • BCEL bypasses direct model simulations, avoiding the need for summary statistics, distance, and tolerance choices.
  • The algorithm incorporates an effective sample size calculation for performance evaluation.

Main Results:

  • The BCEL algorithm demonstrates convergence in the number of observations.
  • Significant time savings are achieved compared to traditional ABC, especially for complex models.
  • The method was successfully illustrated on standard distributions, time series, and population genetics models.

Conclusions:

  • Empirical likelihood provides a viable and efficient alternative to ABC for models with intractable likelihoods.
  • BCEL offers a robust framework for statistical inference, reducing computational burden and parameter-choice dependencies.
  • The approach has broad applicability across various complex modeling domains.