# Probability bound analysis: A novel approach for quantifying parameter uncertainty in decision-analytic modeling and cost-effectiveness analysis

arXiv: https://arxiv.org/abs/2011.10398 · HTML: https://mlsanity.com/paper/2011.10398/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Nov 2020.

## Built on by (most cited first, 2 of 2)

- [Risks of ignoring uncertainty propagation in AI-augmented security pipelines](https://mlsanity.com/paper/2407.14540/) (2024)
- [Value of Information under Imprecise Probabilities: Decision-Rule-Specific Values and Fixed-Measure Envelopes on a Credal Set](https://mlsanity.com/paper/2607.06570/) (2026)

## Abstract (arXiv)

Decisions about health interventions are often made using limited evidence. Mathematical models used to inform such decisions often include uncertainty analysis to account for the effect of uncertainty in the current evidence base on decision-relevant quantities. However, current uncertainty quantification methodologies, including probabilistic sensitivity analysis (PSA), require modelers to specify a precise probability distribution to represent the uncertainty of a model parameter. This study introduces a novel approach for propagating parameter uncertainty, probability bounds analysis (PBA), where the uncertainty about the unknown probability distribution of a model parameter is expressed in terms of an interval bounded by lower and upper bounds on the unknown cumulative distribution function (p-box) and without assuming a particular form of the distribution function. We give the formulas of the p-boxes for common situations (given combinations of data on minimum, maximum, median, mean, or standard deviation), describe an approach to propagate p-boxes into a black-box mathematical model, and introduce an approach for decision-making based on the results of PBA. We demonstrate the characteristics and utility of PBA versus PSA using two case studies. In sum, this study provides modelers with practical tools to conduct parameter uncertainty quantification given the constraints of available data and with the fewest assumptions.