# Uncertainty Quantification Via the Posterior Predictive Variance

arXiv: https://arxiv.org/abs/2603.19804 · HTML: https://mlsanity.com/paper/2603.19804/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 17 references that are in the map.
- First posted on arXiv 20 Mar 2026.

## Builds on (most cited first, 4 of 4)

- [Conformal prediction after data-dependent model selection](https://mlsanity.com/paper/2408.07066/) (2024)
- [Valid confidence intervals for post-model-selection predictors](https://mlsanity.com/paper/1412.4605/) (2014)
- [Qualitative inequalities for squared partial correlations of a Gaussian random vector](https://mlsanity.com/paper/1503.03879/) (2015)
- [Testing for the Important Components of Posterior Predictive Variance](https://mlsanity.com/paper/2209.00636/) (2022)

## Abstract (arXiv)

We use the law of total variance to generate multiple expansions for the posterior predictive variance. These expansions are sums of terms involving conditional expectations and conditional variances and provide a quantification of the sources of predictive uncertainty. Since the posterior predictive variance is fixed given the model, it represents a constant quantity that is conserved over these expansions. The terms in the expansions can be assessed in absolute or relative sense to understand the main contributors to the length of prediction intervals. We quantify the term-wise uncertainty across expansions varying in the number of terms and the order of conditionates. In particular, given that a specific term in one expansion is small or zero, we identify the other terms in other expansions that must also be small or zero. We illustrate this approach to predictive model assessment in several well-known models.