  Simulation-based Bayesian inference (SBI) can be used to estimate the
parameters of complex mechanistic models given observed model outputs without
requiring access to explicit likelihood evaluations. A prime example for the
application of SBI in neuroscience involves estimating the parameters governing
the response dynamics of Hodgkin-Huxley (HH) models from electrophysiological
measurements, by inferring a posterior over the parameters that is consistent
with a set of observations. To this end, many SBI methods employ a set of
summary statistics or scientifically interpretable features to estimate a
surrogate likelihood or posterior. However, currently, there is no way to
identify how much each summary statistic or feature contributes to reducing
posterior uncertainty. To address this challenge, one could simply compare the
posteriors with and without a given feature included in the inference process.
However, for large or nested feature sets, this would necessitate repeatedly
estimating the posterior, which is computationally expensive or even
prohibitive. Here, we provide a more efficient approach based on the SBI method
neural likelihood estimation (NLE): We show that one can marginalize the
trained surrogate likelihood post-hoc before inferring the posterior to assess
the contribution of a feature. We demonstrate the usefulness of our method by
identifying the most important features for inferring parameters of an example
HH neuron model. Beyond neuroscience, our method is generally applicable to SBI
workflows that rely on data features for inference used in other scientific
fields.
