  Comparing competing mathematical models of complex natural processes is a
shared goal among many branches of science. The Bayesian probabilistic
framework offers a principled way to perform model comparison and extract
useful metrics for guiding decisions. However, many interesting models are
intractable with standard Bayesian methods, as they lack a closed-form
likelihood function or the likelihood is computationally too expensive to
evaluate. With this work, we propose a novel method for performing Bayesian
model comparison using specialized deep learning architectures. Our method is
purely simulation-based and circumvents the step of explicitly fitting all
alternative models under consideration to each observed dataset. Moreover, it
requires no hand-crafted summary statistics of the data and is designed to
amortize the cost of simulation over multiple models and observable datasets.
This makes the method particularly effective in scenarios where model fit needs
to be assessed for a large number of datasets, so that per-dataset inference is
practically infeasible.Finally, we propose a novel way to measure epistemic
uncertainty in model comparison problems. We demonstrate the utility of our
method on toy examples and simulated data from non-trivial models from
cognitive science and single-cell neuroscience. We show that our method
achieves excellent results in terms of accuracy, calibration, and efficiency
across the examples considered in this work. We argue that our framework can
enhance and enrich model-based analysis and inference in many fields dealing
with computational models of natural processes. We further argue that the
proposed measure of epistemic uncertainty provides a unique proxy to quantify
absolute evidence even in a framework which assumes that the true
data-generating model is within a finite set of candidate models.
