Misspecification-robust likelihood-free inference in high dimensions.

Area of Science:

• Statistical Inference
• Computational Statistics
• Machine Learning

Background:

• Likelihood-free inference is crucial for simulator-based models.
• Approximate Bayesian Computation (ABC) struggles with high-dimensional parameters.
• Existing methods face scalability challenges in complex models.

Purpose of the Study:

• To develop an advanced method for likelihood-free inference in high-dimensional parameter spaces.
• To improve the efficiency and scalability of Bayesian optimization-based approaches.
• To enable robust posterior characterization even with model misspecification.

Main Methods:

• An extension of Bayesian optimization to probabilistically approximate discrepancy functions.
• Utilizing separate acquisition functions and summary statistics for parameter subsets.
• Employing an additive acquisition structure with exponentiated loss-likelihood.

Main Results:

• Achieved computational scalability for higher-dimensional parameter spaces.
• Demonstrated efficient inference in moderately sized parameter spaces.
• Outperformed existing modularized ABC methods in comparative analyses.
• Successfully fitted a bacterial transmission model in a 30-dimensional parameter space.

Conclusions:

• The proposed method offers a computationally efficient and scalable solution for likelihood-free inference.
• It provides robust posterior characterization for complex models.
• The approach has practical applications, as shown by the bacterial transmission model analysis.