MIRA: A Score for Conditional Distribution Accuracy and Model Comparison

arXiv stat.ML / 5/5/2026

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Key Points

The article presents MIRA, a sample-based scoring method to evaluate how accurately a candidate conditional distribution matches the true data-generating process using only joint samples from the true distribution.
It derives an analytic form of the MIRA statistic, where the MIRA score is defined as the average of the statistic, grounded in the idea that two distributions are equal if they assign the same probability mass across all regions.
The framework provides theoretical reference values and uncertainty estimates for the case when the candidate distribution is correct, enabling more interpretable comparisons.
MIRA supports Bayesian model comparison by validating posterior alignment with the true process directly, avoiding the difficult model evidence (marginal likelihood) computation.
The method is evaluated on multiple toy problems and Bayesian inference tasks to demonstrate its effectiveness for comparing conditional models.

Abstract

We introduce Mira, a sample-based score for assessing the accuracy of a candidate conditional distribution using only joint samples from the true data-generating process. Relying on the principle that distributions coincide if they assign equal probability mass to all regions, we derive an analytic expression for the Mira statistic, whose average defines the Mira score. This formulation further allows us to compute theoretical reference values and uncertainty estimates when the candidate distribution matches the true one. This framework enables model comparison by quantifying the alignment between the conditional distribution of a candidate model and the true data generating process. Consequently, Mira enables Bayesian model comparison through direct posterior validation, bypassing the challenging evidence computation. We demonstrate its effectiveness across several toy problems and Bayesian inference tasks.