# Analysis of Diagnostics (Part I): Prevalence, Uncertainty Quantification, and Machine Learning

arXiv: https://arxiv.org/abs/2309.00645 · HTML: https://mlsanity.com/paper/2309.00645/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 51 references that are in the map.
- First posted on arXiv 30 Aug 2023.

## Builds on (most cited first, 6 of 6)

- [A Review of Uncertainty Quantification in Deep Learning: Techniques, Applications and Challenges](https://mlsanity.com/paper/2011.06225/) (2020)
- [Classification Under Uncertainty: Data Analysis for Diagnostic Antibody Testing](https://mlsanity.com/paper/2012.10021/) (2020)
- [Optimal Decision Theory for Diagnostic Testing: Minimizing Indeterminate Classes with Applications to Saliva-Based SARS-CoV-2 Antibody Assays](https://mlsanity.com/paper/2202.00494/) (2022)
- [Minimizing Uncertainty in Prevalence Estimates](https://mlsanity.com/paper/2203.12792/) (2022)
- [Modeling in higher dimensions to improve diagnostic testing accuracy: theory and examples for multiplex saliva-based SARS-CoV-2 antibody assays](https://mlsanity.com/paper/2206.14316/) (2022)
- [Prevalence Estimation and Optimal Classification Methods to Account for Time Dependence in Antibody Levels](https://mlsanity.com/paper/2208.02127/) (2022)

## Built on by (most cited first, 3 of 3)

- [Probabilistic Consistency in Machine Learning and Its Connection to Uncertainty Quantification](https://mlsanity.com/paper/2507.21670/) (2025)
- [Analysis of Diagnostics (Part II): Prevalence, Linear Independence, and Unsupervised Learning](https://mlsanity.com/paper/2408.16035/) (2024)
- [Inequalities for Optimization of Classification Algorithms: A Perspective Motivated by Diagnostic Testing](https://mlsanity.com/paper/2508.01065/) (2025)

## Abstract (arXiv)

Diagnostic testing provides a unique setting for studying and developing tools in classification theory. In such contexts, the concept of prevalence, i.e. the number of individuals with a given condition, is fundamental, both as an inherent quantity of interest and as a parameter that controls classification accuracy. This manuscript is the first in a two-part series that studies deeper connections between classification theory and prevalence, showing how the latter establishes a more complete theory of uncertainty quantification (UQ) for certain types of machine learning (ML). We motivate this analysis via a lemma demonstrating that general classifiers minimizing a prevalence-weighted error contain the same probabilistic information as Bayes-optimal classifiers, which depend on conditional probability densities. This leads us to study relative probability level-sets B^star (q), which are reinterpreted as both classification boundaries and useful tools for quantifying uncertainty in class labels. To realize this in practice, we also propose a numerical, homotopy algorithm that estimates the B^star (q) by minimizing a prevalence-weighted empirical error. The successes and shortcomings of this method motivate us to revisit properties of the level sets, and we deduce the corresponding classifiers obey a useful monotonicity property that stabilizes the numerics and points to important extensions to UQ of ML. Throughout, we validate our methods in the context of synthetic data and a research-use-only SARS-CoV-2 enzyme-linked immunosorbent (ELISA) assay.