  Implicit neural representations (INRs) have achieved impressive results for
scene reconstruction and computer graphics, where their performance has
primarily been assessed on reconstruction accuracy. As INRs make their way into
other domains, where model predictions inform high-stakes decision-making,
uncertainty quantification of INR inference is becoming critical. To that end,
we study a Bayesian reformulation of INRs, UncertaINR, in the context of
computed tomography, and evaluate several Bayesian deep learning
implementations in terms of accuracy and calibration. We find that they achieve
well-calibrated uncertainty, while retaining accuracy competitive with other
classical, INR-based, and CNN-based reconstruction techniques. Contrary to
common intuition in the Bayesian deep learning literature, we find that INRs
obtain the best calibration with computationally efficient Monte Carlo dropout,
outperforming Hamiltonian Monte Carlo and deep ensembles. Moreover, in contrast
to the best-performing prior approaches, UncertaINR does not require a large
training dataset, but only a handful of validation images.
