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Comparing Bayesian hierarchical models: A deep learning method with cognitive applications

Lasse Elsemüller
Heidelberg University ~ Statistical Modeling in Psychology
Dr. Martin Schnuerch
University of Mannheim ~ Statistical Modeling in Psychology
Paul-Christian Bürkner
Aalto University, Finland
Stefan Radev
Rensselaer Polytechnic Institute ~ Cognitive Science

Bayesian model comparison permits principled evidence assessment but is challenging for hierarchical models (HMs) due to their complex multi-level structure. In this talk, we present a deep learning method for comparing HMs via Bayes factors or posterior model probabilities. As a simulation-based approach, its application is not limited to HMs with explicitly tractable likelihood functions, but also includes implicit likelihoods. Further, the computational cost of our method amortizes over multiple applications, providing new opportunities for method validation, robustness checks, and simulation studies. We demonstrate the ability of our method to accurately discriminate between non-nested HMs of cognition in a benchmark against bridge sampling. In addition, we present a comparison of four partly intractable evidence accumulation models that examines the utility of the recently proposed Lévy flight model of decision-making.



Bayesian statistics
model comparison
hierarchical modeling
deep learning
cognitive modeling

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Cite this as:

Elsemüller, L., Schnuerch, M., Bürkner, P.-C., & Radev, S. T. (2023, July). Comparing Bayesian hierarchical models: A deep learning method with cognitive applications. Abstract published at MathPsych/ICCM/EMPG 2023. Via