Amortized Bayesian Model Comparison With Evidential Deep Learning.

Area of Science:

• Computational science
• Statistical modeling
• Machine learning

Background:

• Comparing mathematical models is crucial across scientific disciplines.
• Bayesian inference provides a principled framework for model comparison.
• Intractable models lacking closed-form likelihoods pose significant challenges for standard Bayesian methods.

Purpose of the Study:

• To develop a novel, simulation-based deep learning method for Bayesian model comparison.
• To overcome limitations of traditional methods when dealing with computationally expensive or intractable models.
• To introduce a new measure for quantifying epistemic uncertainty in model comparison.

Main Methods:

• Utilized specialized deep learning architectures for a purely simulation-based approach.
• Circumvented explicit model fitting to datasets.
• Developed an amortization strategy for simulation costs across models, datasets, and sizes.
• Proposed a novel method for measuring epistemic uncertainty.

Main Results:

• Demonstrated excellent accuracy, calibration, and efficiency on toy examples and complex models from cognitive science and neuroscience.
• Showcased the method's effectiveness for large-scale dataset analysis where case-based inference is infeasible.
• Validated the proposed epistemic uncertainty measure as a proxy for absolute evidence.

Conclusions:

• The proposed deep learning framework enhances model-based analysis and inference in various scientific fields.
• The novel epistemic uncertainty measure offers a unique tool for quantifying evidence in model comparison.
• This simulation-based approach provides a powerful alternative for analyzing intractable models in computational science.