ABC random forests for Bayesian parameter inference.

Area of Science:

• Computational Statistics
• Bayesian Inference
• Machine Learning

Background:

• Approximate Bayesian computation (ABC) is standard for Bayesian inference with intractable likelihoods.
• Existing ABC methods require pre-selection of summary statistics and tolerance calibration.
• These requirements can limit robustness and introduce user-dependent choices.

Purpose of the Study:

• To develop a likelihood-free Bayesian inference method that bypasses summary statistics selection and tolerance calibration.
• To enhance the robustness and efficiency of Bayesian inference for complex models.
• To provide a practical tool for researchers in statistics and related fields.

Main Methods:

• Utilizes random forest (RF) methodology in a non-parametric regression framework.
• Advocates for a new RF derivation for each parameter component.
• Applies the method to a Normal toy example and a population genetics dataset.

Main Results:

• The proposed method demonstrates robustness to the choice of summary statistics.
• It eliminates the need for tolerance level calibration.
• Offers a favorable trade-off between estimator precision, credible interval accuracy, and computational time compared to existing ABC methods.

Conclusions:

• The novel RF-based approach provides a powerful and flexible alternative for likelihood-free Bayesian inference.
• It simplifies the inference process by removing critical user-defined parameters.
• The associated R package 'abcrf' makes the methodology readily accessible.