  Neuroscience has recently made much progress, expanding the complexity of
both neural-activity measurements and brain-computational models. However, we
lack robust methods for connecting theory and experiment by evaluating our new
big models with our new big data. Here, we introduce new inference methods
enabling researchers to evaluate and compare models based on the accuracy of
their predictions of representational geometries: A good model should
accurately predict the distances among the neural population representations
(e.g. of a set of stimuli). Our inference methods combine novel 2-factor
extensions of crossvalidation (to prevent overfitting to either subjects or
conditions from inflating our estimates of model accuracy) and bootstrapping
(to enable inferential model comparison with simultaneous generalization to
both new subjects and new conditions). We validate the inference methods on
data where the ground-truth model is known, by simulating data with deep neural
networks and by resampling of calcium imaging and functional MRI data. Results
demonstrate that the methods are valid and conclusions generalize correctly.
These data analysis methods are available in an open-source Python toolbox
(rsatoolbox.readthedocs.io).
