Informative and adaptive distances and summary statistics in sequential approximate Bayesian computation.

Area of Science:

• Computational Statistics
• Bayesian Inference
• Machine Learning

Background:

• Model parameter calibration on heterogeneous data is computationally challenging, particularly for likelihood-free methods like approximate Bayesian computation (ABC).
• Existing methods like scale normalization and summary statistics derived from regression models have limitations, including inefficiency on uninformative data and potential information loss.

Purpose of the Study:

• To develop and evaluate an adaptive approach for calibrating model parameters on heterogeneous data using likelihood-free inference.
• To improve the efficiency and accuracy of approximate Bayesian computation (ABC) by addressing challenges posed by heterogeneous parameter scales and data informativeness.

Main Methods:

• Combining adaptive scale normalization with regression-based summary statistics to handle heterogeneous parameter scales.
• Employing regression models to derive sensitivity weights that quantify data informativeness, rather than transforming the data directly.
• Addressing non-identifiability issues in regression models using target augmentation.

Main Results:

• Demonstrated improved accuracy and efficiency of the adaptive approach on various problems.
• Showcased the robustness and wide applicability of the derived sensitivity weights.
• Validated the advantages of combining adaptive scale normalization with regression-based summary statistics for heterogeneous parameter scales.

Conclusions:

• The proposed adaptive approach offers significant improvements in model calibration for likelihood-free inference.
• Sensitivity weights derived from regression models provide a robust and informative measure of data utility.
• The open-source pyABC toolbox implements these algorithms, facilitating their application in scientific research.