Missing values contaminate nearly every real dataset. The standard assumption — Missing At Random (MAR), where the probability of missingness depends on observed but not unobserved values — is decades old. But a basic question remained open: can you consistently estimate the distribution of the complete, uncontaminated data from MAR-corrupted observations?
For monotone missingness patterns (where the missing variables form a nested sequence), the answer was known. For general non-monotone MAR — where any variable can be missing independently — it was not.
The authors (arXiv:2603.23449) prove it can be done. Their nonparametric Bayesian approach achieves posterior contraction at the minimax rate (up to logarithmic factors) for the density of the uncontaminated data. The algorithm takes corrupted data and returns a sample from a provably consistent estimate of what the data would have looked like without missingness.
The through-claim: the contamination structure of general MAR is not an obstacle to optimal density estimation. Despite the combinatorial complexity of non-monotone missingness (any subset of variables can be absent), the uncontaminated distribution is recoverable at the same rate as if you knew which mechanism caused the gaps.